Emergence

Landmark I version 2 characterizes destructive Enter and does not derive spacetime

The primitive is fixed. Only the outcome law and the conditional update vary inside a stated class. Later decoder, cutoff, and horizon interfaces are not premises of that uniqueness.

• thm:main identifies Born probabilities and destructive projective residual rays. No residual is specified on a zero-probability branch. The result is not record-free uniqueness and not an independence theorem for the five requirements.
• lem:path allows higher-order internal syntax and requires a first-order quantum and classical interface. thm:adequacy says that interface denotes a finite instrument. Quantum spectators are consumed or returned. That instrument is not a field instrument and not a bulk–boundary map.
• Destructive Enter, coherent recording, and represented nondestructive measurement stay distinct. prop:pullback is record compatibility. ex:equal-records shows equal records with different residuals. prop:process says complete-process equality implies equal adaptive record laws and does not claim the converse.
• thm:stability counts a total global live-qubit budget. That budget is not a scheduled laboratory peak. prop:classical-recovery shows that decoding a finite classical record is entanglement breaking and is not the identity on a code of dimension at least two. The static positive non-Born family fails operational nullity. Static marginal compatibility is not this characterization.
• En03-A, En02-B, Psy02-B, Hawk01-A, Hawk01-B, Hawk02-A, Em03-C, Em03-E, and XIV-I are source records and are not premises. The finite Frauchiger–Renner calculation is not a physical no-go. This is not metric reconstruction, not Einstein dynamics, not holographic identification, not a Page curve, and not spacetime emergence. H2, I3, and J2 stay unresolved. O.1 stays NOT_CLOSED. The series Route B is not discharged. XVI-N is not discharged. XV-B is not opened. XVI-P is registered and is not a premise. No quantum coefficient is admitted. No compilation is asserted. The source has not been compiled.

Open I · Emergence problem · Separations

Landmark II version 2 certifies a finite contact fit and does not derive spacetime

The principal certificate is unchanged. On one three-label family the contact image has rank 2, the original minor is 64, and the coefficients 2/3 and 2/3 fit the target. Global membership stays open. Companion manuscripts are comparisons, not premises.

• thm:certificate is SEP-finite. The target is (0, 16/3, 16/3). The original raw columns are (0, 8, 0) and (0, 0, 8). Their minor is 64. The complete left kernel is the span of (1, 0, 0), so no separator exists on this family. A finite fit is not a global contact identity.
• Complete response coverage is three clauses. Action equivalence is not response-space equivalence. The certificate uses an actual minor of original columns, not an arbitrary left factor. cor:affine-fits identifies the whole affine family. That family is not a unique coefficient vector.
• thm:injective makes injective evaluation a sufficient route to a global identity, not a necessary one. prop:rebase separates contact rebasing from a change of response prescription. prop:weighting shows that weighting does not preserve the unweighted integration-by-parts quotient. prop:enlargement states class enlargement as a separate successor question.
• The unweighted certificate is not transferred to a weighted source class, a changed gauge prescription, or an unidentified counterterm space. V’s cubic form is not the Einstein cubic that produces 16/3. X-F is not a contact correction inside an unchanged theory. Formal compensation is not classical descent. The catalogue size has no direct role in the XIV or XV characteristic chain and does not discharge J2.
• I, III, IV, V, VI, VIII-A, X-E, X-G, XI-G, XII-B, XII-F, XIII-E, XIV-H, XIV-I, XIV-J, and Em01-A are source records where cited and are not premises. The embedded checker is not executed. This is not metric reconstruction, not Einstein dynamics, not holographic identification, not a Page curve, and not spacetime emergence. H2, I3, and J2 stay unresolved. O.1 stays NOT_CLOSED. The series Route B is not discharged. XVI-N is not discharged. XV-B is not opened. XVI-P is registered and is not a premise. No quantum coefficient is admitted. No compilation is asserted.

Open II · Emergence problem · Separations

En01-B does not emerge a metric

The calibrated-decoherence note is now a registered sheet. A shared quadratic force shift inside an independent calibration width gives an exact overlap of attempted-run records, not containment of the alternative family. A homogeneous-sphere contrast has coefficient −5041/81920 and stays strictly negative for every finite Gaussian width. Matched centre-of-mass heating does not identify the environmental source.

• III’s quotient and VI’s second-order jet already include the gravitational equations. They are not derived from the contrast.
• IV’s represented instruments and I’s record equation are not this visibility law. VII-E’s observation boundary is not this detector event.
• V’s transfer singularity, VII-D’s finite part, X-D’s ramp limit, XIII-E’s regulator, and Em01-B’s smoothing growth are not this Gaussian width. No exclusion contour is produced.
• The overlap does not open XV-B. The spectral enclosure is not the aligned-null locus. The bounded statistic is not gravity-generated entanglement.

Open En01-B · Emergence problem · Separations

En01-C does not identify the source

The preparation-aware note is now a registered sheet. A three-separation contrast that cancels quadratic attenuation also cancels the normalized pair coherence of a centred Gaussian state. Four free-expansion times and one finite squared-position sensor retain cubic diffusion during a flat interval. The clipped statistic measures total flat-stage momentum diffusion. Corrected intermediate moments 11/32 and 239/512 leave En01-B’s sphere contrast −5041/81920 unchanged.

• III’s quotient and VI’s second-order jet already include the gravitational equations. They are not derived from the diffusion certificate.
• I’s record equation, IV’s represented instruments, and VII-E’s observation boundary are not this squared-position sensor.
• The four-time identity is total flat-stage diffusion, not source identification. White-noise localization that vanishes on a flat stage is not detector identifiability.
• The Gaussian cancellation is not containment of the alternative family and not an experimental exclusion. The certificate does not open XV-B and is not gravity-generated entanglement.

Open En01-C · Emergence problem · Separations

Em02-A does not evaluate the physical sector

The sector-reduction sheet is now registered. On displayed mathematical data, the seeds supported by R(b−a)R(a−z) and R(b−z)R(z−a) have order-two coincidence-localization coefficients, and the seed supported by R(b−a)R(b−z) has an order-three coefficient, with uniform remainders. Those powers are an internal localization parameter, not the physical smoothing scale. The executable inherited package is not supplied, so no physical singular-data sector is evaluated.

• Target I isolation is not Target II coincidence. Em01-G’s isolated failure is not imported.
• Em01-C’s plateau equality is not a smoothing gain. The smooth-data expansion is a consistency benchmark, not a singular physical coefficient.
• The stops at H2, I3, and J2 remain unresolved. XV-B is not opened. No physical limit, authorized correction, or quantum admission is asserted.
• The localization powers are not a derivation of a metric or of Einstein dynamics, and not a cosmological curvature singularity.

Open Em02-A · Aligned-null problem · Separations

XVI-N does not complete the interface

The prepared classical insertion is now a registered sheet. The unprepared complex and the prepared deformation are constructed through order kappa, with the corrected root current. One massless special family has a nonzero variation, and Theorem 11 obstructs one regular antifield-linear completion of that instance. The certified interval is only 0 ≤ m < 1.3715×10⁻⁴.

• The obstruction is not a universal completion. N-Ins.4 stays unresolved. Route B is not discharged, and arbitrary prescribed mass stays unresolved.
• The prepared theory is not a BV complex. Sampling and the numerical enclosure are corroboration, not certificates.
• Em01-G’s isolated failure is not this obstruction. Em02-A’s localization powers are not this coefficient and not the physical smoothing scale. Em02-B’s simulated numbers are not this coefficient. Em02-D’s fixed-model inverse-cubic is not this obstruction.
• The cone support is not a cosmological curvature singularity. The sheet does not derive a metric or Einstein dynamics, and it does not open XV-B.

Open XVI-N · Aligned-null problem · Separations

Em02-B does not release a physical row

The simulated audit is now registered. It evaluates declared crossed families only. For one cutoff, the localization constants and a weighted atomic cone integral are recorded by two quadratures that do not share nodes. One scalar non-tip adjoint is a simulated integral. The specialized vertex constructions agree termwise on a shared algebraic check. The seven-dimensional seed integral changes sign under refinement, so no row value is released.

• Gauss–Sobol agreement is an independent quadrature of a closed-form atomic integrand. It is not the sign-changing seed integral and not a physical coefficient.
• Target I isolation is not this quadrature. Em01-G’s isolated failure is not imported. Em02-A’s localization powers are not these numbers and not the physical smoothing scale.
• The outer cone rules do not agree. The identification ledger, the seven-row pairing, S2, and authorization stay unresolved.
• The stops at H2, I3, and J2 remain unresolved. XV-B is not opened. The archived scripts are package evidence, not a theorem and not a certificate.

Open Em02-B · Aligned-null problem · Separations

Em02-D does not evaluate the physical limit

The leading-order sheet is now registered for one fixed mathematical model. An exact signed internal convolution of the negative placement and a derivative-controlled first correction give an inverse-cubic leading distribution, including on tests that cross N inside that model. The nominal inverse-quartic term vanishes. A cone identity cancels the inner tip of the positive placement against the response coefficient, and the collected inverse-cubic still survives on a separated detecting test. The raw family does not converge, and no correction supported on z=a restores convergence.

• The model is not the designated physical package. Em01-C’s question about the retained contraction is not answered.
• Em02-A’s epsilon localization powers are not this coefficient. Em02-B’s simulated numbers are not this coefficient. Em01-G’s isolated failure is not imported.
• The compact-uniform O(delta to the minus two) remainder is not a finite part and not convergence after subtraction. An upper bound of that order does not prove that the remainder diverges.
• The stops at H2, I3, and J2 remain unresolved. XV-B is not opened. No quantum coefficient is admitted. No compilation is asserted.

Open Em02-D · Aligned-null problem · Separations

Em02-E does not remove the quantum regulator

The classical identification is now a registered sheet. On an explicit power-law Einstein–scalar background, the scalar is the clock and the original inflaton-slice harmonic rods are the spatial labels. The lapse is expanded through second order without discarding metric components. The quadratic functional is a local part plus an instantaneous spatial Green operator. Compact external smearing does not compactify the Hessian.

• The background is an input of the Einstein–scalar equations. It is not derived from an entanglement wedge, and it is not spacetime emergence.
• Em02-A’s localization powers are not this contraction. Em02-D’s inverse-cubic coefficient is not this kernel. Em02-B’s simulated numbers are not this kernel. There is no limit toward t=0.
• The quantum covariance, state, counterterm class, remainder, and gauge identity are not constructed. The outcome is an incomplete audit, not existence and not a universal obstruction.
• The stops at H2, I3, and J2 remain unresolved. XV-B is not opened. O.1 is not closed and Route B is not discharged. No quantum coefficient is admitted. No compilation is asserted.

Open Em02-E · Emergence problem · Expanding-universe problem · Separations

XVI-O does not restore the bulk theory

The kernel audit is now a registered sheet. On the invariant baseline, not on the prepared action, four prerequisites construct a massless scalar matter-loop kernel under one stated prescription: the finite-part extension, the tensor identity on the open set, the active jet pullback, and the contact moments. The kernel two-point identity is not a functional anomaly cancellation and not bulk BV restoration.

• The classical kappa-squared master stays partial. Gate 3 spanning stays partial. O.1 stays NOT_CLOSED, and bulk symmetry is not restored.
• The inherited insertion stays frozen. Route B is not discharged. A renormalized product of the seed is not closure, and success on the kernel does not complete it.
• XVI-M’s selected-graph image is comparison data. Sharing the cubic density does not identify that graph with this kernel. XVI-J’s extension freedom is not the contact term.
• Em01-G’s isolated failure, Em02-A’s localization powers, Em02-B’s simulated numbers, and Em02-D’s fixed-model coefficient are not this kernel. The archived scripts are package evidence, not a theorem and not a certificate. XV-B is not opened.

Open XVI-O · Emergence problem · Separations

XVI-P does not close O.1

The one-loop calculation is now a registered sheet. Power counting reproduces the frozen kappa-squared inventory, nine graphs out of nine, and shows no one-loop three-point sector at kappa squared, so the enlarge rule is not triggered. P.5 is renormalized at one loop and at kappa squared for the two-point functions with QdS external legs. QdS is an external-leg scheme, not a de Sitter state and not the relational lapse.

• O.1 stays NOT_CLOSED. It is not closable inside XVI-P, because the classical kappa-squared master and the bulk identity stay outside this sheet. Bulk symmetry is not restored, and XVI-O is not updated.
• The P.6 entry inventories fifteen one-loop kappa-cubed three-point graphs. That inventory is not an evaluation, not a counterterm, and not sigma-zero closure.
• The corrected projected counterterm is closed only in the named ghost plus-one sectors. That closure is not bulk symmetry. The inherited insertion stays frozen. Route B is not discharged. XV-B is not opened.
• Certificates, listings, and the archive are package evidence, not a series certificate. No quantum coefficient of the inherited characteristic graph is admitted. No compilation is asserted.

Open XVI-P · Emergence problem · Low-energy completion · Expanding-universe problem · Separations

O.1 is closed only in a narrow scope

In the one-loop, order-kappa-squared two-point sector of the bulk invariant action, the rows are cancelled by local counterterms under XVI-P's prescription. The mass is zero, the gauge is held fixed, the external legs are QdS, and the p22 evanescent counterterms are included. All 23 rows of the bulk identity are cancelled, and that cancellation is fully consistent under sigma-zero on the bulk 11 directions. An independent rebuild confirmed the closure in Q02, and Q03 recorded it as O1_closure_confirmed. Both reviews ran on the same computer. The counterterm domain is enlarged beyond XVI-O's: 11 four-dimensional directions plus 10 evanescent operators. XVI-O's prescription is not the one used.

• This scoped closure is the base for P.6. Treat O.1 as one secured foothold for a quantum-gravity theory, not proof of one. It says nothing about ultraviolet completeness. It does not restore bulk symmetry, and it does not discharge Route B or XVI-N. It says nothing about three-point functions or higher loops.
• Both reviews ran on the same computer. D01 and D03 were never rederived from fully independent Feynman rules. Q05's own rules later match XVI-P's poles for those two graphs. The record does not update XVI-O. On XVI-O, and outside this scope, O.1 stays NOT_CLOSED.
• P.6 stays an honest partial at Q11. The four identity rows close in four dimensions. The open part is the evanescent counterterm X: 43 of 104 directions stay unclassified, no direction is certified physical, and the invariant basis and the p22 consistency of that three-point counterterm stay open. This partial does not rewrite XVI-P.
• The insertion stays frozen. XV-B is not opened. XIV-J is not opened. QdS is an external-leg scheme, not a de Sitter state and not Em02-E's relational lapse. This is not a Page curve, not holographic, and not spacetime emergence. H2, I3, and J2 stay unresolved.
• The full Q11 zip has sha256 e2e5980e46ce…. The author rebuild matched 68 of 68 reference values, and the packaged XVI-Q.pdf is 221 pages. That author rebuild is not an independent rebuild of Q11. The OpenAI catalogue and the En05 through En07 sheets are not premises. Certificates and the gates are package evidence, not a series certificate. No quantum coefficient is admitted. No compilation is asserted.

Open XVI-Q · Emergence problem · Low-energy completion · Expanding-universe problem · Separations

The clock-separation programme does not identify a clock

XIX-A through XIX-E are by N. Cheung. They separate four time-related prescriptions and stop. They do not identify a clock, and they do not construct quantum evolution without an external time. Each link to an earlier sheet is a documentary separation, not a premise. The OpenAI catalogue is the exception: its authors are OpenAI. No compilation is asserted.

• XIX-A labels the harmonic relational scalar, Em02-E's original-rod lapse, the prescribed incidence register, and the density ramp. A scalar value does not determine the lapse. Original rods are not modified rods. The ramp is a named non-clock. A foliation scalar recovers the branch-normal speed only after that scalar is added. Family 271 names 271-04 only. VI is not 271-04. The direct VI–XVI-D comparison is not decided there.
• XIX-B excludes one direct first-coordinate route. After the declared metric-sign transport, the residual forcing is nonzero on a compact test. A positive formal order in Planck's constant does not cancel that frozen classical residual. The scalar-switch defect is a separate classical identity, not a coordinate obstruction. The witness also fails VI's vacuum first-metric equation and is not in the solution-jet space. XVI-D's conditional compatibility is not discharged.
• XIX-C shows that a finite incidence register does not select a continuum evolution. Matching uniqueness is not expectation acquisition. Equal records need not determine residual sources. Two refinements of one finite channel can converge to different semigroups. Scheduled support is not a physical causal relation. The XIX-B mismatch is not used. No invariant speed and no dynamical cone are derived.
• XIX-D inventories five unsupplied quantum slots for the original-rod lapse: gauge-fixed covariance, a state or parametrix, products and the counterterm image, a controlled remainder, and a retained-order gauge identity. VI's certificate stays RG-open. XVI-Q Q11 remains one scoped foothold. It is not a clock certificate and not a de Sitter state. Outside that scope O.1 stays NOT_CLOSED.
• XIX-E records what stays outside. Density multiplication is not convolution. A transition defect does not erase a plateau identity. A partial contraction is not XVI-H's full kernel. XIV-H's H2 stop is sheet-specific. XIV-I's narrower I2 advance is not withdrawn. I3 and J2 stay unresolved. XV-B is not opened. XVI-N and Route B are not discharged. Families 260, 271, 362, and 376 are not a lapse, not Einstein dynamics, and not spacetime emergence.
• A successor must choose one target. Completing one renormalized relational observable, or one native continuum limit of the incidence register, is not claimed here. Relational quantum evolution without an external time is not opened. This is not metric reconstruction, not a Page curve, and not spacetime emergence. No quantum coefficient is admitted.

Open XIX-AOpen XIX-BOpen XIX-COpen XIX-DOpen XIX-ETime problemEmergence problemSeparations

One original-rod lapse is frozen. Its quantum admission is not

XIX-A through XIX-E and XX-A through XX-F are by N. Cheung. XIX-A through XIX-E keep four time-related prescriptions apart. XX-A through XX-F then choose one of them: an independently frozen original-rod lapse on a power-law Einstein–scalar background with external cosmic time. The classical coefficients and a scoped free-field input are constructed. The native quantum lapse is not. Each link to an earlier sheet is a documentary separation, not a premise and not a proof transfer. The OpenAI catalogue is not by N. Cheung, and Family 271 is not a mathematical input. No compilation is asserted.

• XX-A fixes the background, the matter-scalar clock, the positive lapse branch, the original rod equation, and the label density. The second coefficient keeps the first-rod term. The second spatial rod is constructed and stays out of the quadratic lapse because the background lapse has no spatial derivative. This is not a wholesale identification with Em02-E. The quantum milestone stays unresolved at Q1.
• XX-B converts the Euler linearization to the action Hessian and, after fiber normalization, presents a normally hyperbolic operator, causal inverses, and an algebraic Hadamard class. Q1 is closed only for that compact-test free multiplet. Rods are not propagating fields. A Hadamard class on an indefinite bundle is not a positive physical state. VI's quantum certificate stays open.
• XX-C shows why the class is not a state. One same-class representative is negative on a nonzero invariant observable, and that example does not exclude every other representative. Local subtraction is not global decay. Compact-source dipole tails are not covariance tails. The native two-rod commutator has an inverse-distance term, so an inverse-square bound cannot be demanded of both ordered two-rod covariances. The subsidiary defect stays unsolved. Q2 is not closed.
• XX-D constructs the unsmoothed classical polynomial on a spatial Schwartz domain and compact-source-cutoff Wick symbols. The native cutoff-free one-contraction theorem stays conditional on separate internal and external infrared estimates. Those estimates are not verified for a selected representative. A compact approximation is not the native insertion. One contraction is not a complete interacting loop. Native Q3 stays open.
• XX-E and XX-F correct the proposed Ward calculation without entering it. Ordinary compact gauge translations do not preserve the gauge-fixed free-equation quotient. The unfiltered central-second-jet defect begins at total order three on the stated weighted algebra, so it does not itself obstruct a common second-order truncation. The free-equation obstruction remains at order one. Weighted Newton bounds are criteria, not a selected covariance. Conditional breaking formulas, including a change of the Ward operation, are not an evaluation. Native Q4 and Q5 stay unentered and unclosed.
• The series does not supply relational quantum evolution on a constrained state space, a clock-conditioned evolution law, or an identification of VI, VIII, XVI-D, and Em02-E as one theory. The XIV characteristic graph is not this cosmological lapse. XV-B is not opened. XVI-N and Route B are not discharged. O.1 stays NOT_CLOSED outside the narrow XVI-Q scope. This is not a Page curve, not Einstein dynamics, and not spacetime emergence. No quantum coefficient is admitted.
• The useful next milestone is a verified native insertion on one specified quantum domain, then a quantum gauge operation on that same domain. Another general audit does not close the gate. External time has not disappeared.

Open XX-AOpen XX-BOpen XX-COpen XX-DOpen XX-EOpen XX-FTime problemEmergence problemLow-energy completionSeparations

Scheduler consistency does not select a Lorentz cone

En08-A is by N. Cheung. It separates operational consistency from Lorentz-cone selection. Acyclic dependency, schedule-independent records, operational sensitivity, finite reachability, and confluence do not determine a Lorentz cone. The Euclidean ball and the orthant are countermodels. A Lorentz cone appears only after extra geometric hypotheses: a faithful generated affine representation, and, by the cited Ito–Lourenço classification, homogeneity together with strict convexity in dimension at least three. That classification is not re-proved here. A finite set of ordered events does not determine the metric, and chronology alone does not. Each link to an earlier sheet is a documentary separation, not a premise. No compilation is asserted.

• thm:main is the obstruction. Terminating finite experiments, commuting independent operations, and schedule-independent joint records can coexist with a non-Lorentzian generated cone. Finite models do not force a continuum identification. This does not prohibit emergence from a more restrictive operational theory. It says those premises alone are not enough.
• thm:mainpositive and thm:weaker are the conditional route. Homogeneity and strict convexity select a Lorentz cone up to linear isomorphism, by the cited classification, not a new proof. The orthant is homogeneous and self-dual, and it fails strict convexity. The diamond is irreducible, and it fails both homogeneity and strict convexity. A generated null boundary need not contain an attained null event pair. Cone closure is not an admissible signal.
• Two refinements can share the identity channel at the sampled times and still have different continuous-time limits. Locality of the refinements does not choose the generator. XIX-C's finite incidence register is a different sheet and is not a premise. Origin availability, in thm:typing, is a typing condition. It is not a transport certificate and not a relational clock.
• A small diamond allowance bounds influence. It is not exact causal containment. Correlation is not intervention-based influence. Those distinctions are safeguards for a later measurement ledger. They are not gravity-generated entanglement, not a gravitational mediator, and not an experimental exclusion.
• thm:malament reconstructs a conformal factor only after a distinguishing Lorentzian realization is already supplied. A chronological automorphism of a smooth order topology need not be differentiable. Uniqueness of a Lorentzian realization is not existence of one. VII-J's scheduled ancestry, operational influence, and supplied causal relation stay distinct. En05-B's prescribed speed and En06-B's paced lattice are not the limit of this cone.
• The remaining emergence obligation is to derive the representation, the homogeneity, and the strict convexity from a specified operational theory, and then to connect one gauge-invariant gravitational observable. En08-A does not do that. It does not derive Einstein dynamics, an invariant speed, a Page curve, an interior, or quantum evolution without an external time. It has no vacuum-energy calculation. O.1 stays NOT_CLOSED. XV-B is not opened. XVI-N and Route B are not discharged. No quantum coefficient is admitted.

Open En08-AOpen VII-JOpen XIX-COpen En05-BEmergence problemTime problemSeparations

A prescribed null boundary can be approximated. It is not derived.

En08-B is by N. Cheung. In one frozen Euclidean model it builds finite local SWAP protocols that approximate a prescribed future-null boundary. The spatial metric, the calibration, and the speed are inputs. The ideal logical channel is exactly the identity on a fixed finite-dimensional payload, including every untouched reference. The spatial error is of order one over j squared, and the nonnegative arrival delay is of order one over j, uniformly on bounded-distance targets. Ticks and initialized registers grow linearly with refinement, with a matching static-site lower bound. That approximation is not a derived Lorentz cone, not Einstein dynamics, and not spacetime emergence. En08-A, En05-B, and En06-B are documentary comparisons, not premises. No compilation is asserted.

• thm:main combines a locality lower bound, an explicit route, exact identity transport, and a resource ledger. cor:speed uses Heisenberg support of payload-independent controls and the supplied cone. It does not derive the speed. lem:identity is exact SWAP transport of the unknown register. prop:memory-lower counts initialized, retained, and discarded sites in the static-site model.
• cor:operational-limit is the modest continuum claim: geometric endpoints and arrival times converge, and the payload channels are identified in the half-diamond norm. It is not a field algebra, not a regional observable net, and not an unrestricted interpolation theorem. XIX-C's two-limit and interpolation statements still block reading a finite certificate as a unique continuum evolution. XIX-C is not a premise.
• cor:gate-noise is conditional. A per-gate half-diamond error that is little-o of one over j is enough when preparations, spectators, waits, and output identifications are exact. prop:accumulation shows that a merely vanishing per-gate error can accumulate. prop:near-local shows that a small channel error is not exact causal containment. Exact locality still requires the implemented maps to stay on the permitted blocks.
• prop:record obstructs record-only transmission: a finite classical record followed by a prepared output stays a positive half-diamond distance from the identity. A destructive record is not the residual quantum register. prop:fixed-stencil shows that one fixed finite velocity set cannot approximate every Euclidean null direction. prop:exact-null characterizes the exceptional finite-scale null pairs of this permission family. Approximation does not require their absence, and their presence is not the aligned-null contraction through N.
• En05-B's direction-uniform relays and En06-B's reference-preserving finite-network transport are predecessors in the documentary sense. Their networks are not identified with this route family, and neither is the continuum limit of the VIII cone or of En08-A. En08-A selects a Lorentz cone only under extra geometric hypotheses and does not supply this protocol. VII-J keeps scheduled ancestry, operational influence, and a supplied causal relation apart.
• The remaining emergence obligation is to derive the cone or the speed from a specified operational theory, or to identify these protocols with a generated null pair, and then to connect one gauge-invariant gravitational observable. En08-B does not do that. It has no vacuum-stress calculation, no de Sitter state, no cosmological singularity, and no Page curve, island, or interior. O.1 stays NOT_CLOSED. XV-B is not opened. XVI-N and Route B are not discharged. No quantum coefficient is admitted.

Open En08-BOpen En08-AOpen En05-BOpen En06-BEmergence problemTime problemSeparations

A destructive clock record is relational time. It is not a geometry.

En09-A is by N. Cheung. On one finite clock and one system it implements Page–Wootters conditioning by destructive Enter. The complete output is a classical clock code and the surviving system. The measured clock names are consumed. thm:main equates that instrument with the subnormalized conditioning channel, including every untouched reference. Stationarity plus sampled clock covariance gives the conditional unitary at the calibrated readings. An exact finite spectrum inhabits those hypotheses. The readout does not remove the external time used to prepare, calibrate, and schedule the experiment. A classical record is not a surviving clock, not a decoder, and not a metric. En08-A, En08-B, XIX-C, and Em02-E are documentary comparisons, not premises. No compilation is asserted.

• thm:main is the instrument identity. Destructive computational-basis Enter, after a declared basis change, returns the Born record and the unnormalized conditional system block. Discarding the record traces out the clock. No quantum clock factor remains in the output.
• The dynamical clause is separate. Stationarity of the joint state is not enough for an arbitrary clock basis. Sampled covariance of the reading projectors is an extra hypothesis. prop:spectral-realization supplies one commensurate finite example. An energy eigenbasis need not be a time-reading basis.
• lem:density-semantics attributes the Born law and the residual ray to Landmark I only when the full predecessor class applies. Writing a Born-form instrument does not rederive that characterization. A classical record is not a quantum return of the clock. prop:record-not-residual keeps those interfaces apart.
• thm:refinement is stability inside a declared class that already shares one frozen target. A one-step error of order the mesh alone need not vanish when accumulated. Two families converge to the same channel only inside that class. XIX-C still blocks reading a finite sample as a unique continuum evolution. XIX-C is not a premise.
• prop:causal places dependency edges inside a supplied relation. Scheduled ancestry, operational influence, and that relation stay distinct. The embedding does not derive a Lorentz cone. En08-A shows that scheduler consistency alone does not select one. En08-B approximates a prescribed null boundary and is not this clock.
• The remaining time obligation is a gravitational clock observable, gauge descent, and a continuum limit that is not frozen in advance. En09-A does not do that. It has no vacuum-stress calculation, no de Sitter state, no cosmological singularity, and no Page curve, island, or interior. The scoped XVI-Q record is not altered. Outside that scope O.1 stays NOT_CLOSED. XV-B is not opened. XVI-N and Route B are not discharged. No quantum coefficient is admitted.

Open En09-AOpen Landmark IOpen XIX-COpen Em02-ETime problemEmergence problemSeparations

A source-weight record is not a geometry.

En10-A is by N. Cheung. On one declared qubit–antiqubit toy model it returns a classical occupation word by destructive Enter and estimates a normalized source weight. The antiqubit factor is a declared inverse unitary, not antimatter and not backward time. thm:main is the complete instrument and the calibrated estimator, including every untouched reference. The measured names are consumed. A classical record is not a residual, not a decoder, and not a metric. The zone labels are not the Milky Way. En09-A’s clock, XIX-C’s token, and En08-B’s prescribed transport are documentary comparisons, not premises. No compilation is asserted.

• lem:identity equates destructive computational-basis Enter with the projective recorded channel on all operators, including an arbitrary untouched reference. lem:consumption removes both measured names. No quantum data output remains.
• The estimator is a separate classical map. It needs the declared family, the sensitivity denominator, the shot count, and the calibration constants. prop:no-return shows that those same records cannot restore the input. Parameter information can survive while arbitrary quantum recovery fails.
• prop:nuisance gives omitted parameters zero Fisher information. prop:inversion shows that replacing the antiqubit inverse by the forward unitary leaves the occupation law unchanged. The records do not certify the sign of the response.
• prop:thermal shows that equality of the visible channel does not fix bath heat, work, or a cyclic reset cost. A relaxation surrogate is not a thermal machine and not annihilation.
• The remaining emergence obligation is a derived metric and Einstein dynamics. En10-A does not do that. It has no vacuum-stress calculation, no de Sitter state, no cosmological singularity, and no Page curve, island, or interior. O.1 stays NOT_CLOSED. XV-B is not opened. XVI-N and Route B are not discharged. No quantum coefficient is admitted.

Open En10-AOpen En09-AOpen Landmark IOpen XIX-CEmergence problemDecisive testSeparations

A conditional acquisition bridge is not positron identification.

En10-B is by N. Cheung. It derives a finite synthetic source channel from frozen generators, including an opposite-sign kick, a random-kick nuisance, and a collision surrogate. thm:derived is that instrument, with arbitrary untouched references. thm:calibrated and thm:competition are finite-shot certificates. thm:main transfers them to a named physical observable only when a source encoding, a microscopically derived instrument, and certified comparison allowances are supplied. Those data are not in the manuscript. The unconditional positron acquisition-and-identification theorem remains unconstructed. En10-A is the finite analog, not this derived channel. No compilation is asserted.

• lem:law is the exact four-outcome record. At fixed nuisance the source weight is sensitive. prop:overlap shows that distinct weights can share one complete law when the nuisance is allowed to vary. More shots do not separate identical record laws.
• thm:competition discriminates only predeclared families, and only when the complete-law gap exceeds the calibration, implementation, and sampling allowances. That margin is not an experimental exclusion of classical gravity. The installed CZ gate is not gravitational mediation.
• The durations of the kick, the collision, and the exchange are externally scheduled controller inputs. They are not acquired relational time. prop:schedule does not derive a causal cone. VII-J is not a premise.
• prop:charge shows that an opposite-charge label does not generally invert the graph evolution. prop:residual leaves Galactic rate, continuum turbulence, and spacetime embedding off the ledger. prop:thermal does not fix a heat or reset cost. Hawk02-B’s emission recovery and Em03-D’s local effect are comparisons, not this channel.
• The remaining test obligation is a gravitationally derived interaction, a declared classical alternative, and a proved record-law separation after nuisance and apparatus error. En10-B does not do that. It has no vacuum-stress calculation, no de Sitter state, no cosmological singularity, and no Page curve, island, or interior. O.1 stays NOT_CLOSED. XV-B is not opened. XVI-N and Route B are not discharged. No quantum coefficient is admitted.

Open En10-BOpen En10-AOpen XIX-COpen En01-CDecisive testEmergence problemTime problemSeparations

A conditional Lorentz cone is not emergence.

XXII-A through XXII-F are by N. Cheung. They freeze a narrower question than spacetime emergence: whether named quantum operational data can yield a faithful generated affine Lorentz cone, and what would still be missing for transport and dynamics. The implication is conditional. The nonempty package, the single-valued rule, and the compatible transport are not constructed. No metric field and no Einstein equation is derived. No compilation is asserted.

• XXII-A thm:separation keeps scheduled ancestry, operational influence, and a supplied causal relation distinct. thm:obstruction records that scheduler consistency does not force a Lorentz cone. The ball and the orthant remain countermodels. thm:classification applies only after homogeneity and strict convexity are supplied. target:selection is not a theorem. En08-A is the obstruction source, not a premise of a positive selection.
• XXII-B does not select a data class. prop:signalling-cycle, prop:static, prop:finite-generation, prop:tolerance, and prop:two-limits are failure witnesses. A static record is not causal order. A finite marginal is not a null boundary. A tolerance channel is not exact containment. Two finite limits need not agree. Oai265-A and XIX-C are documentary, not premises.
• XXII-C freezes a countably indexed tripartite qubit process family. thm:order proves that the signalling-component quotient is a partial order. Each future has at most three components. That order is not Minkowski space and not a metric. spec:access yields data only for tested directions. The single-valued rule remains open. An experiment identifier is not time.
• XXII-D thm:anchored-obstruction says one unchanged component cannot approximate the whole future-null boundary. prop:calibration does not fix units or an invariant speed. thm:geometry-not-transport shows a Lorentz representation whose designated channel is classical. En08-B’s prescribed boundary and SWAP route are not this extraction. En05-B and En06-B are not this theorem.
• XXII-E thm:flat says a constant affine quadratic form is flat. prop:conformal says a pointwise cone field does not determine the Einstein tensor. prop:energy and prop:improvement say process data do not identify stress-energy, and conservation is not that identification. thm:surjective says unrestricted matching at one point does not select the source. A declared comparison coupling is not an admitted quantum coefficient.
• XXII-F thm:assembly is an implication: if a nonempty additional package and a single-valued faithful rule are supplied, the cited classification gives a Lorentz cone. cor:approximation needs a separately justified transport realization. Neither hypothesis is constructed. prop:symmetry blocks an injective finite-dimensional embedding of infinitely repeated indistinguishable blocks. target:existence stays open. The identifier En10-A@1 has no passage in this note. Registered En10-A is not a premise.
• The remaining emergence obligation is a nonempty operational package, a matched single-valued rule, a compatible transport realization, and independently extracted geometry and stress-energy. XXII-A through XXII-F do not do that. They have no Page curve, no island, no de Sitter state, no cosmological bounce, and no radiative vacuum stability. A transmission certificate does not exclude classical gravity. O.1 stays NOT_CLOSED. XV-B is not opened. XVI-N and Route B are not discharged. No quantum coefficient is admitted.

Open XXII-AOpen XXII-COpen XXII-EOpen XXII-FOpen En08-AEmergence problemDecisive testTime problemSeparations

An engineered passage front is not emergence.

Oai212-A is the supplied sheet. The title page names Ngo Cheung. A declaration in the same source also withholds an authorship assertion. The companion does not resolve that conflict. The sheet gives explicit interfaces from named quantum models to first-passage percolation. It does not verify OpenAI manuscript 212-02. A passage front is not a metric, not an invariant speed, and not Einstein dynamics. No compilation is asserted.

• thm:exact-otoc identifies a normalized squared commutator on one flag-controlled CNOT circuit with undirected first-passage arrival. cor:cnotchannel is the declared complete-channel lift. A maximal commutator is not unknown-qubit transmission. The timers are externally calibrated. VII-J and Hawk04-B are not premises.
• thm:clifford-coupling bounds support-history disagreement by a term that vanishes only under the stated growing local dimension. Fixed dimension is not shape-regularity transfer. XIX-C's finite register is not this continuum limit and is not a premise.
• thm:quench and thm:membrane give exact exponential local Rényi-2 costs and a declared dual optimization that is first-passage percolation. prop:truncation states the finite-dimensional allowances. That cost geometry is not logical recovery and not a gravitational area law. Oai265-A is not a premise.
• thm:measured puts an atom at zero into the cost law. For a positive measurement probability the exact exponential and Gamma interfaces fail. That obstruction is not a measurement threshold and not a critical exponent. Family 213 is not a premise.
• thm:serial is additive advertised serial teleportation, with an identity channel on the message. prop:parallel shows that concurrent generation is not additive even on a two-link chain. The route cost and the quantum channel are separate certificates. En06-B and En08-B are not premises.
• thm:transfer moves an asymptotically identical front onto the classical shape body. cor:regularity transfers strict convexity and a C1 boundary only if 212-02 is independently verified. prop:cone promotes the planar norm to a three-dimensional epigraph and does not supply the homogeneity required by the cited Lorentz classification. prop:nonstable says a small comparison error does not transfer regularity to the approximants. prop:no-gravity supplies no metric field and no Einstein tensor. En08-A is not a premise. Family 212 is not a premise.
• prop:descent and prop:relative are elementary factorization and relative-lifting criteria. They are not the full characteristic map and do not open XV-B. The six analytic gates stay unsupplied. O.1 stays NOT_CLOSED. XVI-N and Route B are not discharged. No quantum coefficient is admitted. This is not a Page curve and not spacetime emergence.

Open Oai212-AOpen En08-AEmergence problemPage curveTime problemDecisive testSeparations

A restricted boundary dictionary is not emergence.

Oai365-A is the supplied sheet. The title page names Ngo Cheung. A declaration in the same source also withholds an endorsement assertion. The companion does not resolve that conflict. The sheet gives an explicit enriched-process Lorentz pilot and a restricted scaled-ball dictionary. It does not verify OpenAI Family 365. A comparison metric is not spacetime emergence. No compilation is asserted.

• thm:pilot-cone represents one rich tagged family of tripartite qubit processes by the four-dimensional Lorentz cone. prop:order is the component partial order. prop:finite and prop:symmetry obstruct a finite carrier and a matched permutation representation. A Bloch ball is not an event cone until faithfulness and generation are proved. XXII-C and En08-A are not premises.
• thm:scaled identifies one operational tag with the scaled-ball metric on a predeclared class, with vanishing connection. That dictionary installs a comparison class. It is not a physical Dirichlet-to-Neumann apparatus and not a Lorentzian metric. Family 365 is not a premise.
• thm:boundary is conditional on a calibrated same-patch energy form and an independently established uniqueness theorem. prop:signature and prop:lapse keep Riemannian data, a lapse, and a Lorentzian reading distinct. 365-01 and 365-02 are not verified. The Lean note names 365-03 only.
• thm:future keeps one unchanged component future finite. thm:transport and thm:bus certify complete-channel endpoint approximation only after additional transport resources are declared. Geometry does not supply the wires. En08-B and En09-A are not premises.
• prop:flat and prop:conformal separate a cone from the Einstein tensor. A conserved improvement is not a physical source. XXII-E is not a premise. This is not Einstein dynamics.
• thm:pilot-stat is a finite-shot bound for a declared tag. Estimating that tag is not acquiring an unknown physical boundary form. En10-A and En10-B are not premises.
• thm:assembly assembles these conditional certificates. It does not instantiate the general physical inverse bridge. The six analytic gates stay unsupplied. O.1 stays NOT_CLOSED. XVI-N and Route B are not discharged. XV-B is not opened. No quantum coefficient is admitted. This is not a Page curve and not spacetime emergence.

Open Oai365-AOpen XXII-FEmergence problemTime problemDecisive testSeparations

A constant-error synthesis certificate is not emergence.

Oai283-A is the supplied sheet. The title page names Ngo Cheung. A declaration in the same source also withholds an authorship assertion. The companion does not resolve that conflict. The sheet certifies a finite coherent-oracle circuit and prices its resources. It does not verify OpenAI manuscript 283-01. A channel budget is not a metric and not spacetime emergence. No compilation is asserted.

• lem:normalization converts a full-diamond tolerance of 1/2 into a half-diamond tolerance of 1/4. That bound is an additive discrepancy. It is not arbitrary precision and not a vanishing-error limit. 283-01 is documentary and is not a premise.
• thm:phasepilot constructs an exact uniform phase-family pilot. prop:comb inserts that pilot in one tripartite qubit process. A larger message space is a carrier change, not a silent substitution. XXII-C is not a premise. This is not universal unitary synthesis.
• thm:tomography and cor:inhabited-test give a finite-confidence certificate for a declared channel. prop:scalar-insufficient says a source-weight family does not certify every coherence. prop:Bell says an unadjusted Bell overlap is not a dimension-free worst-case bound. En10-A and Em03-E are not premises.
• thm:transport requires endpoint, arrival, locality, and resource certificates. prop:workspace says reduced logical accuracy does not specify a clean returned workspace. prop:accumulation says local errors can accumulate. A constant allowance is not a null-boundary limit. En08-B, En07-B, and En09-A are not premises.
• thm:teleport is a finite serial comparison with its resources declared. It does not import a quench membrane or an infinite-volume shape theorem. prop:l4 keeps a smooth strictly convex cone from being automatically quadratic or operationally causal. Oai212-A and Oai365-A are not premises. Family 212 and Family 365 are not premises.
• prop:finitecone, prop:schedule, and prop:generator keep finite generation, scheduled support, and one-time unitary data from selecting a Lorentz cone, a physical speed, or a Hamiltonian. En08-A, XXII-A, XXII-E, and VII-J are not premises. XXII-F's nonempty extraction package is not supplied.
• The ledger is scoped. It is not an exhaustive audit of every catalogue manuscript and not a solution of a standing problem. Local constructions: circuit semantics, two resource ledgers, the phase pilot, tomography, and the serial comparison. Documentary pointers, not premises: 283-01, Family 212, and Family 365. Registered comparisons, not premises: En08-A, En08-B, En09-A, En10-A, En10-B, VII-J, XXII-A through XXII-F, Em03-E, En02-B, En07-B, VIII-A, XIV-I, XIV-J, Oai212-A, and Oai365-A. Those sheets are in the corpus. Their full texts do not become premises. A general n-qubit message is not one laboratory qubit. A classical table is not a coherent oracle. A Bell overlap is not a diamond certificate. A constant allowance is not a vanishing limit.
• Against the standing problems the certificate is a boundary, not an answer. It does not quantize a relational observable. It does not renormalize the inherited singular product. It is not ultraviolet completeness and not a completion beyond the low-energy sheet. It is not a Page curve. It does not derive spacetime. It is not a de Sitter state. It is not autonomous time. It is not a cosmological bounce. It is not radiative vacuum stability. It does not exclude classical gravity. XIV-I thm:I2 does not become I3, and the appendix does not admit the characteristic coefficient. No standing problem is solved.
• thm:assembly assembles these conditional certificates for a supplied finite instance. The six analytic gates stay unsupplied. O.1 stays NOT_CLOSED. XVI-N and Route B are not discharged. XV-B is not opened. No quantum coefficient is admitted. This is not a Page curve and not spacetime emergence.

Open Oai283-AOpen En08-BOpen XXII-FEmergence problemDecisive testTime problemAligned-null problemSeparations

A finite secret-bit certificate is not emergence.

Oai272-A is the supplied 14 October 2026 development. The identifier is Oai272-A. The source withholds a Cheung endorsement, and the companion does not resolve that conflict. It proves a local 1/5 transcript gap, a rational certificate, a conditional trace-preserving completion, and a promise-dependent witness procedure. It does not verify OpenAI manuscript 272-01. A finite Choi corner is not a metric and not spacetime emergence. No compilation is asserted.

• thm:bit-gap gives an unhalved trace-norm distance of at least 1/5 from every ideal secret bit, for every admitted completed bit protocol on a represented state. thm:rational-gap is the exact rational form. The conventional trace distance is 1/10. The gap is not a statement about every entangled state.
• thm:transcript factors Eve's complete public transcript. A selected bit, a finite prefix, or a thermal occupation is not that transcript. En07-C, Hawk04-B, and Oai265-A are not premises.
• lem:choiEB and lem:range convert a product-free Choi range into entanglement and into a non-entanglement-breaking composition. Product-free range is sufficient for entanglement, not necessary for the key gap. Em03-F is an entanglement-breaking specimen and is the opposite interface. Em03-G's error can vanish with resources. Neither is a premise.
• thm:completion builds a trace-preserving PPT channel in dimension 2d+1 from a supplied pair. The full channel Choi matrix can contain product vectors from its absorbing flag. The entangled corner, not the entire range, is the witness. Dimensions 10 and 21 are not claimed minimal. Failure at the second iterate is not failure of eventual entanglement breaking.
• thm:witness-algorithm terminates only under an exact rational support promise. thm:statistics is a finite-sample contract for one specified witness. En01-B and En01-C are comparison certificates, not this arithmetic. No finite sample enumerates every copy number and protocol.
• prop:generator separates a static entangled record from a gravitational generator and from an exclusion of classical gravity. prop:selected separates that record from a Page curve, an island, and a radiation-entropy history. A finite Choi corner is not an all-orders completion. De Sitter, autonomous time, cosmological singularities, vacuum energy, and the aligned-null contraction are not reached.
• The ledger is scoped. It is not an exhaustive audit of every catalogue manuscript and not a solution of a standing problem. Local constructions: the represented class, the four-effect inequality, the transcript factorization, the 1/5 gap, Choi transfer, the flag completion, and the witness procedure. Documentary pointers, not premises: 272-01, Family 265, Family 280, Family 282, Family 290, Family 211, and Family 069. Registered comparisons, not premises: I, VIII-B, En01-B, En01-C, En02-A, En02-B, En02-C, En07-A, En07-C, En10-B, Hawk04-B, Em03-F, Em03-G, Oai265-A, Oai265-B, Oai283-A, Oai290-A, Oai280-C, Oai211-A, Oai069-A, and Oai282-A. The inspected Lean targets contain sorry and do not formalize the secret-key theorem.
• thm:assembly assembles these conditional certificates for a supplied finite instance. The single active successor is that missing instance: the dimension-ten state, the two PPT maps, the 21-dimensional channel, and the numerical corner. O.1 stays NOT_CLOSED. XVI-N and Route B are not discharged. XV-B is not opened. No quantum coefficient is admitted. This is not a Page curve and not spacetime emergence.

Open Oai272-AFamily 272Emergence problemDecisive testPage curveSeparations

A finite one-use Holevo certificate is not emergence.

Oai276-A is the supplied 14 October 2026 development. The title page names Ngo Cheung. A declaration in the same source withholds an authorship assertion, and the companion does not resolve that conflict. It proves a one-use Holevo formula and one finite certificate for the frozen generalized amplitude-damping channel at gamma 1/2 and nu 1/4. It does not verify OpenAI manuscript 276-01. A finite Holevo interval is not a metric and not spacetime emergence. No compilation is asserted.

• thm:oneuse identifies the one-use Holevo information with a one-variable maximum and an equiprobable phase pair. The product ensemble is a lower bound on block Holevo information, not an upper bound on entangled signals. 276-01 is not a premise.
• thm:finite-certificate isolates the maximizer in (469/1000, 47/100) and encloses the one-use value strictly between 412377/10^6 and 412378/10^6 bits. The algebraic pair with populations 1061/2000 and 939/2000 loses less than one millionth of a bit and is not asserted to be optimal. The rational appendix is supplied and not executed. It is not an independent rerun.
• prop:conditional keeps the repeated-use reduction under an unverified population bound. Partner additivity is not proved. The inspected AmplitudeDamping target ends in sorry and does not formalize this certificate. A Lean scope note is not a premise.
• prop:ledger prices one coherent realization and is not En02-A's capacity ledger and not En02-B's decoder. prop:readout uses readout-and-drop as partial trace and is not a horizon. En07-A, En07-C, Hawk04-B, and I are not premises. A stationary population is not a Hawking occupation and not a Page curve.
• prop:statistics is finite coverage for a predeclared score and is not an asymptotic rate. En01-B and En01-C are not premises.
• prop:notEB shows that the frozen channel is not entanglement breaking. Em03-F is the opposite specimen. Em03-G's error can vanish under growing resources. Em04-A, Em05-A, Em05-B, and VII-G are channel comparisons, not gravitational tests. None is a premise. The witness is not gravity-generated entanglement and does not exclude classical gravity.
• Oai265-A thm:separation is a static record, not this Holevo formula. Oai272-A thm:bit-gap is not classical capacity. Oai290-A thm:exact is not this channel. Oai283-A is not reconstructed as a decoder. Catalogue families that are not registered companion sheets are not premises.
• The ledger is scoped. It is not an exhaustive audit and not a solution of a standing problem. Relational observables, ultraviolet completion, de Sitter, autonomous time, cosmological singularities, vacuum energy, and the aligned-null contraction are not reached. A finite Holevo interval is not an all-orders completion. O.1 stays NOT_CLOSED. XVI-N and Route B are not discharged. XV-B is not opened. No quantum coefficient is admitted. This is not a Page curve and not spacetime emergence. The single active successor is checking the unexecuted arithmetic appendix, not a new theorem.

Open Oai276-AFamily 276Emergence problemDecisive testPage curveSeparations

A finite prime list is not emergence.

Oai279-A is the supplied 14 October 2026 development. The title page names Ngo Cheung. A declaration in the same source withholds an authorship assertion, and the companion does not resolve that conflict. It proves one explicit reversible circuit: 175 gates, 16391 qubits, and the complete prime list for every integer from 2 through 15. On the frozen input 12 the only output is (2,2,3). It does not verify OpenAI manuscript 279-01. A finite prime list is not a metric and not spacetime emergence. No compilation is asserted.

• thm:finite is exact computational-basis support. The input is preserved, the three scratch qubits return to zero, and every other output word has probability zero. The same circuit handles the whole four-bit domain. It is a reversible lookup, not a quantum speedup.
• The named polynomial bounds only the stated partial family. Scaling the lookup to every bit length is exponential. The partial family is not an all-input factoring family and is not an extracted Family 279 generator.
• lem:records-local retains coherent history for a hybrid controller. That is not the external order trial. lem:pstar records the source padding n at least 128 and an intermediate probability. That probability is not the success probability of this circuit. ExactQuantumFactoring.lean ends in sorry and does not formalize thm:finite or 279-01.
• prop:statistics says finitely many successes do not prove probability one. prop:noise says a positive channel error is not exact support. En01-B, En01-C, and Em03-G are not premises.
• I, VIII-B, En01-A, En02-A, En02-B, En07-A, and Hawk04-B compare records, ledgers, and readout. None is a factoring subroutine and none is a premise. A classical prime list is not quantum recovery, not a horizon, and not a Page curve.
• Oai265-A thm:separation is a static record, not this circuit. Oai272-A thm:bit-gap is not a factoring theorem. Oai276-A's Holevo interval is not this gate list. Oai283-A is not an oracle for this lookup. Catalogue families 274 and 276 are not premises.
• The ledger is scoped. De Sitter, relational observables, cosmological singularities, vacuum energy, ultraviolet completion, and the aligned-null contraction are not reached. A finite gate list is not an all-orders completion. O.1 stays NOT_CLOSED. XVI-N and Route B are not discharged. XV-B is not opened. No quantum coefficient is admitted. This is not a Page curve, not gravity-generated entanglement, and not spacetime emergence. The finite certificate is complete for the stated domain. The optional checker is unexecuted and is not an independent rerun. The all-input extraction remains unverified.

Open Oai279-AFamily 279Emergence problemDecisive testPage curveSeparations

A finite SK autocorrelation is not emergence.

Oai227-A is the supplied 14 October 2026 development. The title page names Ngo Cheung. A declaration in the same source withholds an authorship assertion, and the companion does not resolve that conflict. It proves one explicit two-spin certificate at beta=1: on the compact [4,5] times [1,2], for every real coupling, the rescaled stationary autocorrelation exceeds the rescaled uniform-quench autocorrelation by less than 1/98304, hence by less than 1/65536. It does not verify OpenAI manuscript 227-01. A classical autocorrelation is not a metric and not spacetime emergence. No compilation is asserted.

• thm:finite-certificate is a uniform comparison for one classical heat-bath chain. The same bound holds with probability one under Gaussian disorder and under Rademacher disorder. It does not identify those finite-size laws. prop:finite-laws shows that at two spins the laws of the stationary function have total-variation distance one.
• lem:two-functions writes the exact difference. lem:two-generator is the four-state generator. That generator is not a quantum Hamiltonian. QAOA and Family 281 are not this dynamics.
• prop:gap shows that the spectral gap can be arbitrarily small as the coupling grows, while the certificate stays uniform in J. A fast comparison from the uniform start is not a disorder-uniform mixing gap.
• The external functional scaling limit is audited and not imported. SKRatio.lean and CriticalSKMixing.lean end in sorry and do not formalize thm:finite-certificate or 227-01. A Lean scope note is not a premise. The displayed inequalities are finite rational comparisons. No further next theorem is opened.
• Em04-A is an XY generator, not this heat bath. Hawk02-D and Hawk02-E are fermionic and regulated SYK comparisons, not this chain. En07-C's thermal input is not this inverse temperature. I and VIII-B and Hawk04-B compare readout and records. None is a premise. A classical autocorrelation is not quantum recovery, not a horizon, and not a Page curve.
• Oai265-A thm:separation is a static record, not this clock. XXII-A thm:separation keeps a causal relation apart from a time rescaling. n to the 2/3 is bookkeeping, not a derived metric and not quantum evolution without an external time. En01-B, En01-C, and Em03-G are finite-statistical comparisons and are not premises. Oai272-A and Oai283-A are dossier nominations and are not premises.
• The ledger is scoped. Relational observables, renormalization, ultraviolet completion, de Sitter, cosmological singularities, vacuum energy, and the aligned-null contraction are not reached. A finite two-spin comparison is not an all-orders completion. O.1 stays NOT_CLOSED. XVI-N and Route B are not discharged. XV-B is not opened. No quantum coefficient is admitted. This is not a Page curve, not gravity-generated entanglement, and not spacetime emergence. The finite certificate is complete for the stated compact. The functional limit of Family 227 remains unverified.

Open Oai227-AFamily 227Emergence problemDecisive testPage curveSeparations

A finite Hellinger certificate is not emergence.

Oai119-A is the supplied 14 October 2026 development. The title page names Ngo Cheung. A declaration in the same source withholds an authorship assertion, and the companion does not resolve that conflict. It proves one explicit Hellinger comparison for every Boolean function on the two-dimensional cube at correlation 1/2. Equality holds exactly for the four signed coordinates. Every other function has gap greater than 27/1000. It does not verify OpenAI manuscripts 119-01 or 119-02. A classical Hellinger gap is not a metric and not spacetime emergence. No compilation is asserted.

• thm:finite is an exact comparison of all sixteen functions. The loss is at most 1 minus the square root of 3 over 2. Parity lies strictly between 102/1000 and 103/1000. The exceptional-vertex orbit lies strictly between 27/1000 and 28/1000. lem:orbits and lem:roots are the classification and the integer-square enclosure.
• cor:finiteCK is the finite Courtade--Kumar corollary. Mutual information is at most 1 minus the binary entropy of 1/4, with the same equality cases. Every other function loses more than 1/50 bit. prop:HtoI is that classical conversion and is not an all-dimensional theorem. 119-02 is not a premise.
• prop:conditionalflow says a scalar production inequality would imply soft contraction on one cube. The external production inequality is not proved. lem:capacities is an algebraic allocation and is not a physical channel. The joining optimizer is not evaluated.
• prop:sampler uses six fair bits. prop:coverage is a finite-sample allowance for a declared score and is not the sharp constant. The optional checker is unexecuted and is not an independent rerun. CourtadeKumar.lean and SoftChannel204.lean end in sorry and do not formalize thm:finite, 119-01, or 119-02. A Lean scope note is not a premise.
• I, VIII-A, VIII-B, En02-A, En02-B, and En07-A compare readout, records, and ledgers. None is a contraction subroutine and none is a premise. A classical kernel is not quantum recovery, not a horizon, and not a Page curve.
• En01-B and En01-C are finite-sample templates and are not premises. Em03-F is an entanglement-breaking packet channel and is not this kernel. Em03-G's positive bound is not this gap. Oai265-A thm:separation is a static record, not this contraction. Catalogue families 272, 274, 276, and 279 are not premises. Family 274 is not this Walsh identity.
• The ledger is scoped. De Sitter, relational observables, cosmological singularities, vacuum energy, ultraviolet completion, and the aligned-null contraction are not reached. A finite cube certificate is not an all-orders completion. A Markov-semigroup parameter is not physical time and is not evolution without an external time. O.1 stays NOT_CLOSED. XVI-N and Route B are not discharged. XV-B is not opened. No quantum coefficient is admitted. This is not a Page curve, not gravity-generated entanglement, and not spacetime emergence. The finite certificate is complete for the stated cube. The all-dimensional claims remain unverified.

Open Oai119-AFamily 119Emergence problemDecisive testPage curveSeparations

Every one of the 749 manuscripts, and every excerpt of those manuscripts, is read against the nine standing problems and the sheets by Ngo Cheung that carry them. A match is a separation, not a premise and not a verification. The authors are OpenAI. The manuscripts are not listed in Browse. The companion does not verify those proofs and does not adopt them as theorems of this series.

• Thirty-seven manuscripts name a standing-problem phrase in the title, the abstract, or the family claim. The other 712 are still linked to XVI-P and XVI-N. They do not close any of the nine problems.
• Ten manuscripts use emergence language: 362-01 and 376-01 through 376-09. Families 362 and 376 are relativistic Vlasov–Maxwell smoothness and forced Navier–Stokes computation. That language is not spacetime emergence and not a derivation of a metric.
• O.1 stays NOT_CLOSED. The catalogue is not a premise of XVI-P or of XVI-Q, does not restore bulk symmetry, and does not update XVI-O. Route B is not discharged. XV-B is not opened.
• Family 260 records spacetime Penrose inequalities, and the linked texts are anti-de Sitter or asymptotically flat. That is not a de Sitter state, not Em02-E's relational lapse, and not XVI-P's QdS external-leg scheme.
• Family 264's strong cosmic censorship statement near two-ended Kerr is not a cosmological bounce. Family 282's scale-to-conformal statement is not an ultraviolet completion. XVI-Q's sigma-image record is not Family 282 and not spacetime emergence. Oai282-A records that claim and does not verify it. Oai282-B constructs the free local action and does not verify it. Coverage in one homogeneous class is not a metric. Family 069's quantum Langlands equivalence is not a gravitational dictionary. Oai069-A records that claim and does not verify it. The torus benchmark is not a specialization of the connected-simple theorem. A DG equivalence is not an AdS dual. XVIII-A's witness contract is not an evaluated coefficient. XVIII-B's massive stress kernel is not a relational observable. XIX-A's four labels are not one clock. XIX-B's residual is not an identification. XIX-C's finite register is not a continuum evolution. XIX-D's inventory is not a certificate. XIX-E's boundary is not a prohibition. XX-A through XX-F attempt one original-rod lapse and do not close its quantum admission. En08-A separates scheduler consistency from a Lorentz cone and does not derive one. En08-B approximates a prescribed null boundary and does not derive one. En09-A realizes a finite relational clock by destructive Enter and does not derive a geometry. En10-A estimates a declared source weight from destructive records and does not derive a geometry. En10-B states a conditional acquisition bridge and does not derive a geometry. XXII-A through XXII-F state a conditional Lorentz-cone programme and do not derive a geometry. Oai212-A states engineered first-passage interfaces and does not derive a geometry. Oai365-A states a restricted boundary dictionary and does not derive a geometry. Oai283-A states a constant-error synthesis certificate and does not derive a geometry. Oai272-A states a conditional secret-bit certificate and does not derive a geometry. Oai276-A states a finite one-use Holevo certificate and does not derive a geometry. Oai279-A states a finite factoring certificate and does not derive a geometry. Oai227-A states a finite SK certificate and does not derive a geometry. Oai119-A states a finite Hellinger certificate and does not derive a geometry. None of these is spacetime emergence.
• Full preprint sources are stored, not only the catalogue abstracts. Lean scope notes for 242 families name 341 preprints. A note names only the linked preprints, not every paper in the family. A scope note is not a verification and not spacetime emergence. Family 265 has the full area-law preprint and no Lean scope note. That area law is not a Page curve.
• Three manuscripts were withdrawn on 7 October 2026 and are not current results. No quantum coefficient of the inherited graph is admitted. No compilation is asserted.

Open the OpenAI sectionFamily 260Family 362Family 376Family 265Emergence problemLow-energy completionExpanding-universe problemSeparations

From Landmark I, the OpenAI notes stay separations

Each sheet from Landmark I through En08-A, En08-B, En09-A, En10-A, En10-B, XXII-A, XXII-B, XXII-C, XXII-D, XXII-E, and XXII-F, and Oai212-A, and Oai365-A, and Oai283-A, and Oai272-A, and Oai276-A, and Oai279-A, and Oai227-A, and Oai119-A, already has a separation from the OpenAI catalogue. The full preprint sources and the Lean scope notes do not change that role. They are not premises of any sheet in the walk, and they are not a solution of a standing problem.

• I’s Born characterization is not an OpenAI formalization and not a metric. II’s SEP-finite contact fit is not family 265’s area law.
• III and VI record classical jet descent. That descent is not family 362’s Vlasov–Maxwell smoothness and not Einstein dynamics. The Lean note names 362-01. Family 376’s forced Navier–Stokes computation is not spacetime emergence. The note names 376-04, 376-06, 376-07, and the earlier edition e-011, not 376-01, 376-02, 376-03, 376-05, 376-08, or 376-09.
• V’s singularity reading is not family 264’s Kerr censorship. Family 264 has no Lean scope note. Em02-E’s relational lapse and XVI-P’s QdS scheme are not family 260. The Lean note names 260-13 only, not 260-01 through 260-12. VI’s clock is not family 271. The note names 271-04 only.
• En02-A’s finite capacity is not family 272’s secret-key statement. The Lean note names 272-01 only. Oai272-A records a conditional local audit and does not verify 272-01. Oai276-A records a conditional one-use audit and does not verify 276-01. Oai279-A records a finite factoring certificate and does not verify 279-01. Oai227-A records a finite stationary--quench certificate and does not verify 227-01. Oai119-A records a finite Hellinger certificate and does not verify 119-01. En07-C’s thermal input is not family 265’s gapped area law. Oai265-A states a conditional area-law audit and does not verify Family 265. Oai265-B’s memory certificate is not a laboratory calibration of that law. Oai290-A’s typed certificate is not a verification of Family 290 and not bulk reconstruction. Oai211-A’s path-sum certificate is not a verification of Family 211 and not spacetime. Oai280-A’s sector-label certificate is not a verification of Family 280 and not spacetime. Oai280-B’s five-qubit certificate is not a gravitational surface. Oai280-C’s logical-algebra certificate is not a gravitational dictionary and not spacetime. Oai282-A’s local Ward certificate is not a verification of Family 282 and not spacetime. Oai282-B’s free Ward action is not a verification of Family 282 and not spacetime. Oai069-A’s finite-monodromy certificate is not a verification of Family 069 and not spacetime. XVIII-A’s witness contract is not an evaluated coefficient and not spacetime. XVIII-B’s massive stress kernel is not a relational observable and not spacetime. XIX-A through XIX-E separate four clock prescriptions, one coordinate residual, a finite register, an unclosed quantum inventory, and a release boundary. XX-A through XX-F freeze one original-rod lapse and leave its native quantum admission open. En08-A does not select a Lorentz cone from scheduler consistency. Oai283-A certifies a finite coherent-oracle circuit and does not derive a geometry. 283-01 is not verified. None of those is spacetime. Family 265 has no Lean scope note. Family 003’s zero-free half-plane is not vacuum energy. The note names 003-01 and 003-03, not 003-02.
• This is not metric reconstruction, not Einstein dynamics, not holographic identification, not a Page curve, and not spacetime emergence. H2, I3, and J2 stay unresolved. O.1 stays NOT_CLOSED. The series Route B is not discharged. XVI-N is not discharged. XV-B is not opened. No quantum coefficient is admitted. No compilation is asserted.

Open IOpen En07-COpen Oai265-AOpen Oai265-BOpen Oai290-AOpen Oai211-A · Open Oai280-A · Open Oai280-BOpen Oai282-A · Open Oai282-BOpen Oai069-AFamily 265Emergence problemPage curveSeparations

The walk from I, against the standing problems

Each sheet from I, I-B, II-B, III-B, IV-B, V-B, VI-B, VII-A-ST, VII-E-ST, VII-F-ST, and VII-J-ST, and VIII-ST, and IX-A-ST, and IX-B-ST, and IX-C-ST, and IX-D-ST through En08-A, En08-B, En09-A, En10-A, En10-B, XXII-A, XXII-B, XXII-C, XXII-D, XXII-E, and XXII-F, and Oai212-A, and Oai365-A, and Oai283-A, and Oai272-A, and Oai276-A, and Oai279-A, and Oai227-A, and Oai119-A, is already a separation from the OpenAI catalogue and from the standing problems it names. The new parse does not add a premise. It says which preprint a Lean note actually names.

• I’s Born characterization is not a Lean formalization and not a metric. Emergence stays not reached.
• II’s SEP-finite contact fit is not family 265. Both 265-01 and 265-02 are full sources and have no Lean note. The Page curve stays not reached.
• III and VI are classical jets, not 362-01 and not Einstein dynamics. V is not family 264, and 264 has no Lean note. Singularities stay named, not solved.
• Em02-E and XVI-P are not 260-13. The other twelve Penrose preprints in family 260 are not named by that note. None is a de Sitter state.
• VI is not 271-04. En02-A is not 272-01. Oai272-A records a conditional local audit and does not verify 272-01. Oai276-A records a conditional one-use audit and does not verify 276-01. Oai279-A records a finite factoring certificate and does not verify 279-01. Oai227-A records a finite stationary--quench certificate and does not verify 227-01. Oai119-A records a finite Hellinger certificate and does not verify 119-01. Family 003’s named papers, 003-01 and 003-03, are not vacuum energy. 003-02 is not named and is not vacuum energy either.
• En07-A, En07-B, and En07-C stay separations from family 265. Oai265-A states a conditional area-law audit and does not verify Family 265. Oai265-B certifies one implemented decoder and is not a laboratory calibration. Forty shots per setting cannot accept the 0.1 threshold. Oai290-A separates full-code recovery from a named observable and from a modular-band witness. Family 290-02 is not verified. The Lean note names 290-02 only, not 290-01. Oai211-A separates a path-sum certificate from the Family 211 continuum-random-tree claim and does not verify that preprint. Oai280-A separates a sector-label certificate from the Family 280 VOA-net claim. Oai280-B separates a five-qubit certificate from that claim and from a gravitational dictionary. Oai280-C separates a logical-algebra certificate from that claim and from a gravitational dictionary. Oai282-A separates a finite local-Ward certificate from the Family 282 scale-to-conformal claim. Oai282-B separates a free local Ward action from that claim and from a metric. Oai069-A separates a finite-monodromy decoder from Family 069 and from a gravitational dictionary. XVIII-A separates a witness contraction from the compact kernel and from spacetime. XVIII-B separates a massive stress response from the companion coefficient and from spacetime. XIX-A separates four clock prescriptions. XIX-B separates one coordinate residual from a universal obstruction. XIX-C separates a finite register from a continuum evolution. XIX-D separates an unclosed quantum inventory from a certificate. XIX-E separates a release boundary from a prohibition. XX-A separates a classical lapse from a quantum certificate. XX-B separates a compact-test free input from lapse admission. XX-C separates a Hadamard class from a selected state. XX-D separates a conditional symbol from native admission. XX-E separates a classical Ward identity from a quantum one. XX-F separates conditional formulas from Q4 closure. A named Lean note is not an area law, not a Page curve, and not a recovery certificate.
• Family 342’s note names e-015, the 23 September preprint, not 342-01. Neither is spacetime emergence.
• This is not metric reconstruction, not Einstein dynamics, not holographic identification, not a Page curve, and not spacetime emergence. H2, I3, and J2 stay unresolved. O.1 stays NOT_CLOSED. The series Route B is not discharged. XVI-N is not discharged. XV-B is not opened. No quantum coefficient is admitted. No compilation is asserted.

Open IOpen VIOpen En07-COpen Oai265-AOpen Oai265-BOpen Oai290-AOpen Oai211-A · Open Oai280-A · Open Oai280-BOpen Oai282-A · Open Oai282-BOpen Oai069-AFamily 260Family 265Family 376Emergence problemPage curveExpanding universe

En02-A does not make finite capacity into spacetime emergence

The finite-resource geometry is now a registered sheet. An update grammar gives cut conservation and scalar monotonicity. The decohered fine-graining cost is a closed form. Under a faithful computational diagonal, Born readout holds on every sub-capacity input once capacity is at least three. Residual freedom is the full-capacity boundary and diagonal-unfaithful slack. The hierarchy probe does not close that open problem.

• I’s unrestricted uniqueness is not this capacity restriction. I’s static marginal slack is not this update slack, and the budgeted record theorem is not the register cost.
• X-Enter’s four-live-qubit program class is not this register cost and not the mesh bound. IV’s three models are not the one-shot instrument ledger.
• A cut potential is not a gravitational Noether current, not an antibracket, and not XVI-N’s frozen insertion. XVI-O’s kernel counterterm is not this geometry.
• En01-A, En01-B, and En01-C are not premises. The embedded listing is package evidence, not a certificate. XV-B is not opened. This is not spacetime emergence and not gravity-generated entanglement.

Open En02-A · Emergence problem · Separations

En02-B does not reconstruct an entanglement wedge

The finite decoder is now a registered sheet. For one five-qubit perfect-code triple, batch access uses peak three and streaming access uses peak two. One live laboratory qubit cannot implement subsystem recovery, even with unrestricted classical memory. A rooted tree has batch peak three to the height, and streaming peak height plus one only inside a declared serial module class.

• The model is one perfect-code triple and a declared serial module class, not a bulk–boundary map.
• En02-A’s global capacity is not this laboratory peak. The conditional transfer does not solve En02-A’s uniqueness problem.
• X-Enter’s four-live-qubit restriction is not this streaming optimum. IV’s three models are not instantiated.
• Observable readout at peak one is not subsystem recovery. Environment dimension four does not bound adaptive memory.
• The module-class tree bound is not unrestricted decoder optimality. Em02-B is a different manuscript and is not a premise.
• The checks are package evidence, not a certificate. H2, I3, and J2 stay unresolved. XV-B is not opened. No quantum coefficient is admitted. No compilation is asserted.

Open En02-B · Emergence problem · Page-curve problem · Separations

En02-C does not compute a Page curve

The finite radiation benchmark is now a registered sheet. The first two prefixes are independent of the message. The third prefix permits exact information-theoretic recovery. An ordered single-pass observer with one live qubit still has optimal error one half. A seven-gate programme attains exact recovery only with two live qubits.

• The model is one three-step unitary channel with a two-qubit remnant, not Hawking evaporation and not an old black hole.
• En02-A’s global capacity is not this laboratory peak. En02-B’s perfect-code optimum is not this one-live-qubit error.
• Information-theoretic availability is not executable recovery. Laboratory peak is not total radiation storage.
• The priced conjugate-evolution ledger is not an island and not an entanglement wedge.
• Thresholds and completion times hold only for the declared interface. They are not a Page time.
• The appendix checks are package evidence, not a certificate. H2, I3, and J2 stay unresolved. XV-B is not opened. O.1 stays NOT_CLOSED. No quantum coefficient is admitted. No compilation is asserted.

Open En02-C · Emergence problem · Page-curve problem · Separations

En02-D does not derive Hawking radiation

The energy-labelled channel is now a registered sheet. Unrestricted recovery error is three times one minus the full-transmission probability, over four. At atomic packet width q the even-family error is larger. One extra qubit attains the unrestricted optimum. Five ordinary emissions give the prepared sequence 0, 1, 2, 2, 1, 0 without a terminal drain.

• The model is one finite energy-conserving channel, not a derivation of Hawking radiation and not generic scrambling.
• En02-C’s one-live-qubit error of one half is not this transmission-dependent gap. En02-A’s global capacity is not the packet width q.
• The Smolin identification is an inherited unlocking mechanism, not a new joint measurement.
• The prepared entropy sequence is not a Page curve, not an island, and not an entanglement wedge.
• Em02-D’s inverse-cubic coefficient is not this channel. Em02-E’s relational lapse is not a Hawking flux. The identifier En02-D is not Em02-D.
• The supplement is not reported as executed. It is package evidence, not a certificate. H2, I3, and J2 stay unresolved. XV-B is not opened. O.1 stays NOT_CLOSED. No quantum coefficient is admitted. No compilation is asserted.

Open En02-D · Emergence problem · Page-curve problem · Separations

Em03-A does not derive quantum-gravitational evaporation

One fixed-background emission law is now a registered sheet. Surface gravity is computed from the Schwarzschild metric. The affine horizon vacuum produces the Bose factor. The radial equation constructs the greybody. Compact-band number expectations equal the greybody-weighted integral.

• The model is a free scalar on a fixed exterior, not backreaction, not a collapse packet, and not an evaporation law.
• Bulk Unruh existence and the Hadamard property are a declared external theorem, not a result of an earlier sheet.
• En02-D’s energy-sector isometry does not select this spectrum. Its rate was an input. Here the rate is an output.
• Em02-E’s relational lapse is not this state. Em02-D’s inverse-cubic coefficient is not this covariance.
• The conditional peeling estimate is not a collapse theorem. The law is not a Page curve and not an island.
• O.1 stays NOT_CLOSED. XVI-N is not discharged. XV-B is not opened. XVI-P is registered and is not a premise. H2, I3, and J2 stay unresolved. No quantum coefficient is admitted. No compilation is asserted.

Open Em03-A · Emergence problem · Page-curve problem · Separations

En02-E does not release the Hawking information

One finite selected-packet channel is now a registered sheet. The state is a zero-mean gauge-invariant Gaussian determined by the full packet covariance. The flagged cutoff is completely positive and trace preserving, and for this state the trace-distance error is the discarded probability. One declared recovery benchmark is calibrated by the nonvacuum probability alone.

• Quasifreeness is an input. Number covariance alone does not determine a non-Gaussian state. Em03-A's packet mean is not this density operator.
• Bulk Unruh existence and the Hadamard property remain an external theorem. This is not a collapse theorem and not backreaction.
• The nonvacuum probability is not En02-D's transmission probability. The decoder does not access the full covariance.
• Em02-E's relational lapse is not this state. Em02-D's inverse-cubic coefficient is not this covariance. Landmark I does not supply the state.
• The channel is not a Page curve, not an island, and not a microscopic Hawking information-release mechanism.
• The implementation appendix is not reported as executed. It is package evidence, not a certificate. O.1 stays NOT_CLOSED. The series Route B is not discharged. XVI-N is not discharged. XV-B is not opened. XVI-P is registered and is not a premise. H2, I3, and J2 stay unresolved. No quantum coefficient is admitted. No compilation is asserted.

Open En02-E · Emergence problem · Page-curve problem · Separations

Em03-B does not construct a local Schwarzschild detector

One apparatus-model readout is now a registered sheet. Under an inherited centered quasifree prescription, one selected packet has a normal geometric density. A finite-switching passive port has an explicit transfer kernel. Number-selective pulses extract into a finite register, and a complete instrument prices the readout, including visible failures.

• The mean alone does not determine the density. Quasifreeness is an inherited input. Em03-A's packet mean does not construct this apparatus.
• Unselected positive-frequency radiation is not replaced by vacuum. The Markov port is not a local scalar-field coupling.
• q_h is not En02-D's transmission probability and not En02-E's nonvacuum probability. A packet occupation is not an emission rate.
• Landmark I characterizes a finite readout after the carrier is qubits. It does not supply the capture or the Unruh occupation.
• The model is not a Page curve, not an island, not a collapse theorem, and not quantum-gravitational evaporation.
• Numerical execution is not reported as executed. O.1 stays NOT_CLOSED. The series Route B is not discharged. XVI-N is not discharged. XV-B is not opened. XVI-P is registered and is not a premise. H2, I3, and J2 stay unresolved. No quantum coefficient is admitted. No compilation is asserted.

Open Em03-B · Emergence problem · Page-curve problem · Separations

Em03-C does not recover the microscopic label

One joint-packet interface is now a registered sheet. Under the inherited quasifree prescription, two orthonormal packets have a normal Gaussian state and an interpacket number covariance. A shared temporal port captures both tests in one window. An informationally complete Pauli family and a bounded-effect comparison say which departures the model can certify.

• Orthogonal packets are independent only when the off-diagonal covariance vanishes. Number counts do not determine its phase.
• Em03-A's packet mean does not construct this apparatus. Em03-B's one-packet budget is not this joint budget. The destructive count tail is not the coherent approximation tail.
• En02-E's finite-mode theorem is not imported as an unseen premise and does not supply the shared port. En02-D's transmission probability does not select the occupation matrix.
• Landmark I is optional semantic input after the carrier is qubits. It does not supply the field state or the Unruh occupation.
• An input-independent radiation channel cannot recover an unknown label. A certified departure is not quantum gravity, not information recovery, and not a firewall resolution.
• The model is not a local Schwarzschild detector, not a collapse theorem, not a Page curve, and not quantum-gravitational evaporation. Local coupling and microscopic dynamics remain open. Numerical execution is not reported as executed. O.1 stays NOT_CLOSED. The series Route B is not discharged. XVI-N is not discharged. XV-B is not opened. XVI-P is registered and is not a premise. H2, I3, and J2 stay unresolved. No quantum coefficient is admitted. No compilation is asserted.

Open Em03-C · Emergence problem · Page-curve problem · Separations

Em03-D does not supply a pointlike detector

One local system-probe comparison is now a registered sheet. A compact scalar coupling on a full angular shell induces a bounded Weyl effect for one outgoing massless s-wave packet. The coupling region may grow with the approximation. The state-class error is quantitative.

• Stationary scattering, local Green operators, and the bulk Unruh state are external theorems. The bulk-to-packet approximation is constructed in Em03-D.
• Em03-A's packet mean does not construct the probe. Em03-B's apparatus and Em03-C's joint port are not premises. This effect is not channel equivalence with Em03-C.
• The result is one quadrature effect. It is not packet-number detection, not coherent state transfer, and not a pointlike detector.
• A binary departure from the inherited baseline is not mechanism identification. It does not name quantum gravity, microscopic recovery, or evaporation as the cause.
• The comparison is not a Page curve, not an island, not a collapse theorem, and not quantum-gravitational evaporation. Numerical execution is not reported as executed. O.1 stays NOT_CLOSED. The series Route B is not discharged. XVI-N is not discharged. XV-B is not opened. XVI-P is registered and is not a premise. H2, I3, and J2 stay unresolved. No quantum coefficient is admitted. No compilation is asserted.

Open Em03-D · Emergence problem · Page-curve problem · Separations

Em03-E does not recover black-hole information

One finite dynamical model is now a registered sheet. Explicit bounded Hamiltonians randomize a qubit message, emit the key, and transfer the ciphertext. Each cell is message-independent. The collective output can transmit the message. The optimal worst-case recovery error is (3 − p − 2pη)/4.

• p is the sine squared of the ciphertext pulse. It is not En02-D's full-transmission probability, not Em03-B's q_h, and not Em03-C's occupation matrix.
• Em03-A does not supply the Hamiltonians. Occupation calibration is not a derivation of the greybody law and not identification of the full cell with Em03-C's two-packet state.
• No Em03-D source is assumed. The local Weyl effect is not this finite circuit.
• Em03-C's identical-input obstruction does not contradict this channel: C's accessible inputs are not message-dependent, and E's Hamiltonians are.
• Entropy is not a decoder certificate and not a Page curve. The model is not unitarity restoration, not a firewall resolution, not an evaporation endpoint, and not a local Schwarzschild evaporation process.
• Numerical execution is not reported as executed. O.1 stays NOT_CLOSED. The series Route B is not discharged. XVI-N is not discharged. XV-B is not opened. XVI-P is registered and is not a premise. H2, I3, and J2 stay unresolved. No quantum coefficient is admitted. No compilation is asserted.

Open Em03-E · Emergence problem · Page-curve problem · Separations

Em03-F does not recover the unknown qubit

One exterior source is now a registered sheet. A degenerate qubit drives a compact full-shell interaction with the massless scalar field. Tracing the source leaves a measure-and-prepare channel on the outgoing packets.

• The optimal diamond error is (3-d)/4, where d is the trace distance of the two conditional packet states. That error is strictly greater than one half at every finite coupling.
• A sine-Weyl effect distinguishes the source signs. Selected joint number probabilities do not. The phase gap is linear at weak coupling; the occupation-mean departure is quadratic.
• There is no additional radiation payload. Em03-E does not supply the Hamiltonian. Em03-D's cosine readout does not distinguish opposite displacements.
• Classical source dependence is not quantum recovery. The channel is entanglement breaking. Switching work is not black-hole mass loss.
• The model is not a pointlike detector, not a coherent field-to-memory channel, not interior information escape, not a Page curve, and not quantum-gravitational evaporation. Numerical execution is not reported as executed. O.1 stays NOT_CLOSED. The series Route B is not discharged. XVI-N is not discharged. XV-B is not opened. XVI-P is registered and is not a premise. H2, I3, and J2 stay unresolved. No quantum coefficient is admitted. No compilation is asserted.

Open Em03-F · Emergence problem · Page-curve problem · Separations

Em03-G does not supply a local receiver

One ordered two-pulse source is now a registered sheet. A degenerate qubit couples first through Z and then through X to the massless scalar field. Outgoing packet restrictions are normal channels with interference, not independently assigned displaced Gaussians.

• A phase-matched comparison has an explicit mathematical decoder. Its worst-case referenced recovery error tends to zero only in a growing-resource family. That limit is not exact recovery at finite first-pulse coupling.
• Finite compact parameters exist for which the identified packet channel is not entanglement breaking. The decoder assumes information-theoretic quantum access. It is not a coherent local receiver.
• Local access is a bounded Weyl probability certificate only. Postprocessing Em03-F's measure-and-prepare channel stays entanglement breaking. Em03-F does not supply the second pulse.
• Em03-D's sine probe is not a coherent-receiver premise. Em03-E's payload model does not supply this scalar channel. Em03-A's packet mean does not supply the source. Switching work is not black-hole mass loss.
• The model is not a pointlike detector, not interior information escape, not a Page curve, and not quantum-gravitational evaporation. Numerical execution is not reported as executed. O.1 stays NOT_CLOSED. The series Route B is not discharged. XVI-N is not discharged. XV-B is not opened. XVI-P is registered and is not a premise. H2, I3, and J2 stay unresolved. No quantum coefficient is admitted. No compilation is asserted.

Open Em03-G · Emergence problem · Page-curve problem · Separations

Em03-H does not supply the gravitational dictionary

Version 8 of the fixed quartic bath is the registered sheet. An even spectral code carries the logical qubit. The controlled extractor replaces the quartic Hamiltonian by the number operator and transfers by resonant hopping. A retained-interaction reading is a different target. The continuum excitation code is declared, not derived.

• The finite channel interface, signed branches, and uniform microscopic decoder are proved. Ideal full transfer is exact. For frozen instance P8 the reached-space dimension is at most forty. That extractor is not passive Hawking evaporation.
• Odd operators vanish on the initial even code, but hopping still changes parity. A nonzero boundary subspace invariant under the full CAR family is the entire boundary Fock space.
• The specified continuum decoder has exact error one minus eta. Reported candidate values suggest an error near 0.38687, above one quarter. The reported transmission enclosure is the unit interval. That suggestion is not a validated exclusion. The new v8 programs are unexecuted.
• No P8 gravitational dictionary is constructed. Target B does not discharge Target A. The declared reduction is not a controlled full-gravity remainder.
• Quench work is not black-hole mass loss. Em03-G's two-pulse source does not supply this Hamiltonian. The model is not a Page curve, not an island, not a smooth interior, and not quantum-gravitational evaporation. O.1 stays NOT_CLOSED. The series Route B is not discharged. XVI-N is not discharged. XV-B is not opened. XVI-P is registered and is not a premise. H2, I3, and J2 stay unresolved. No quantum coefficient is admitted. No compilation is asserted.

Open Em03-H · Emergence problem · Page-curve problem · Separations

Em04-A proves the chain and does not execute it

Version 2 of one finite open XY chain is now a registered sheet. Uniform zero-temperature relaxation and local dephasing are part of the model. A single excitation reduces exactly to an N by N matrix and a scalar survival probability. Concurrence, the complete partial-transpose spectrum, and logarithmic negativity are explicit. Two dissipative coordinates are required.

• thm:reduction is exact inside the vacuum-plus-single-excitation class. Higher excitations, bath raising, and nonuniform relaxation are not covered. The N-level matrix is a computational reduction, not a new factorization for entanglement.
• thm:concurrence gives C equal to 2 q times the absolute coherence. thm:negativity gives the full partial-transpose spectrum, including the zero multiplicities. thm:scaling shows that one chi coordinate is not enough.
• thm:instruments and thm:deferral are finite local instruments for this chain. They are not IV’s three models and not a theorem of I. Lindblad dynamics and Born probabilities are assumptions here, not conclusions inherited from a measurement-strategy characterization.
• The oscillator is a separate model. thm:bosonerror and thm:completion bound a compressed-position POVM, including trapezoidal, tail, and arithmetic errors. V and Em03-D do not supply that measurement. The residual theorem is an interface for a certificate. It is not evidence that a run has been enclosed.
• Source alignment remains unresolved. Reported simulator correspondences are not validated. Independent execution is not asserted. The verification appendix is unexecuted. Em03-H’s fermionic decoder is not this reduction and not a gravitational dictionary. The chain is not a Page curve, not an island, and not passive Hawking evaporation. O.1 stays NOT_CLOSED. The series Route B is not discharged. XVI-N is not discharged. XV-B is not opened. XVI-P is registered and is not a premise. H2, I3, and J2 stay unresolved. No quantum coefficient is admitted. No compilation is asserted.

Open Em04-A · Tests problem · Emergence problem · Separations

Em05-A proves the diagnostics and does not execute them

Version 1 of one signed fermionic extraction channel is now a registered sheet. Occupation, coherence, purity, Bell-input mutual information, and reference negativity are exact. A specified decoder has error one minus eta. That decoder is not presumed optimal. At the endpoints the optimal errors are three quarters and zero.

• thm:channels is an isometry with an explicit Kraus family and a complete complement. Channels and Born probabilities are assumptions here, not theorems of I. Em03-H and Em04-A are not premises.
• thm:marginals gives occupation 2 p eta and 2 p t. thm:information gives the Bell spectra and the mutual-information balance of two. prop:rawneg gives the reference-accessible negativity. These are not Em04-A's XY formulas.
• thm:specified has half-diamond error one minus eta, Bell fidelity (1+3 eta)/4, worst-case overlap eta, and decoded concurrence eta. prop:optimal shows that this decoder is not optimal at zero transfer: the optimal error there is 3/4.
• thm:fullNoise keeps an extra dephasing environment. At full transfer the optimal error is (1-lambda)/2, while the Bell-input accessible marginal, occupation, and purity do not depend on lambda. Identical marginals do not certify recovery.
• prop:noexact is an independent continuum obstruction. It is not a numerical error floor and not a quarter-error exclusion. No numerical execution is asserted. The proposed checks are unexecuted. Independent execution is not asserted. The channel is not a Page curve, not an island, and not passive Hawking evaporation. O.1 stays NOT_CLOSED. The series Route B is not discharged. XVI-N is not discharged. XV-B is not opened. XVI-P is registered and is not a premise. H2, I3, and J2 stay unresolved. No quantum coefficient is admitted. No compilation is asserted.

Open Em05-A · Page-curve problem · Emergence problem · Separations

Em05-B proves the improved bounds and does not execute them

Version 1 of the same signed extractor is now a second registered sheet. It restates the channel and proves complementary leakage, a flagged instrument, and an improved recovery sandwich. Em05-A is not a premise. The specified decoder still has error one minus eta, and that error is not the improved bound.

• thm:channels is an isometry with an explicit Kraus family and a complete complement. Channels and Born probabilities are assumptions here, not theorems of I. Em05-A, Em03-H, and Em04-A are not premises.
• thm:marginals gives occupation 2 p eta and 2 p t, plus coherence and purity. thm:information gives the Bell spectra and the mutual-information balance of two. prop:negativity gives the reference-accessible negativity. These are not Em04-A's XY formulas.
• thm:constantComplement is proved locally: exact recovery if and only if the complement is constant, hence only at full transfer. prop:pairDistances proves pair-distance leakage one minus eta squared and a recovery lower bound locally. En02-C does not supply that criterion.
• thm:specified still has half-diamond error one minus eta. prop:instrument flags off-code events without postselection. thm:optimalBell gives maximal decoded Bell fidelity (1+4 eta minus eta squared)/4. thm:balanced gives the improved sandwich and endpoint errors 3/4 and 0. An exact intermediate half-diamond optimum is not asserted.
• thm:fullNoise keeps an extra dephasing environment. At full transfer the optimal error is (1-lambda)/2, while the Bell-input accessible marginal does not depend on lambda. Identical marginals do not certify recovery. The Pauli diamond formula and the entanglement-breaking floor of one half are proved locally, not imported from En02-D. The Choi conversion is proved locally, not imported from Em03-H.
• prop:continuumEndpoint is an independent continuum obstruction. It is not a numerical error floor and not a quarter-error exclusion. No numerical execution is asserted. The proposed checks are unexecuted. Independent execution is not asserted. The channel is not a Page curve, not an island, and not passive Hawking evaporation. O.1 stays NOT_CLOSED. The series Route B is not discharged. XVI-N is not discharged. XV-B is not opened. XVI-P is registered and is not a premise. H2, I3, and J2 stay unresolved. No quantum coefficient is admitted. No compilation is asserted.

Open Em05-B · Page-curve problem · Emergence problem · Separations

VII-G specifies a finite instrument and does not supply gravitational dynamics

Version 1 replaces an unrestricted deterministic coupling by a finite classical-quantum instrument. The unconditional map is completely positive and trace preserving. The example selects ordered slices of one fixed cone. That selection is matter-controlled slicing, not matter-driven gravitational dynamics.

• thm:structure is a state-independent hybrid channel. thm:observation is a direct-sum specialization of an adjoint inclusion, not a new general channel theorem. VII-E is not a premise.
• thm:histories requires branchwise closure. thm:spectators keeps every unnormalized history block when the controller is spectator blind. VII-F, VIII-B, and VIII-C are comparisons, not premises.
• thm:decouple and cor:informative show that an informative classical record is incompatible with exact recovery of every input. En02-C is not a premise. This is not a Page curve.
• prop:affine shows that a nonconstant deterministic packet selection is not the classical output of an affine channel. Option N is not this instrument. prop:energy is an operator identity, not physical energy conservation.
• thm:finite-model keeps the ambient cone, the particle worldline, the deficit, and the peripheral holonomy fixed. The pilot bound is unexecuted as a numerical certificate. Independent execution is not asserted. No quantum-field source, changing deficit, moving particle, or gravitational field equation is constructed.
• Gravitational dynamics and the field-theoretic source remain unresolved. VII-A through VII-D do not supply a quantum source instrument. O.1 stays NOT_CLOSED. The series Route B is not discharged. XVI-N is not discharged. XV-B is not opened. XVI-P is registered and is not a premise. H2, I3, and J2 stay unresolved. No quantum coefficient is admitted. No compilation is asserted.

Open VII-G · Page-curve problem · Emergence problem · Separations

VII-H constructs a free-field response and does not close the gravitational coefficient

Version 1 completes one declared sequence for a free massless scalar: a connected vacuum susceptibility, its complete contact ambiguity, and one nonzero pairing that survives every admissible normalization. The background is Minkowski space. The source and the readout are the vacuum-centred Wick square. That construction is not spacetime emergence.

• lem:kernel gives the punctured retarded kernel. thm:ambiguity shows that reality, translation covariance, agreement off coincidence, and scaling degree at most four leave only a real multiple of hbar delta_0.
• thm:main evaluates one annular test at exactly minus hbar t_0 over 2 pi squared for every prescription. thm:experiment realizes the same value with one delayed source and one smeared readout.
• thm:descent-observation is the general separation criterion, proved locally. VII-E's dictionary does not construct the response. Em01-A's reconstruction criterion is not a premise. VI's classical descent is not a premise.
• VII-D's reflected triangle is not this kernel. A numerical finite part is not an embedding in an interacting response. IX-A's sharp nonconvergence and IX-B's missing second multiplication are not removed.
• VII-G's finite instrument is not this distribution and is not a substitute for the missing gravitational response. A response distribution is not an instrument that measures it. Matter-controlled slicing is not matter-driven gravitational dynamics.
• XII-F's auxiliary remainder is a classical off-shell pairing. It is not this susceptibility and not a quantum Ward identity. A local counterterm is not its propagated image. Late source agreement does not erase preparation memory.
• H2, I3, and J2 stay unresolved. The inherited gravitational characteristic coefficient is not constructed. This is not a Page curve, not an island, and not passive Hawking evaporation. O.1 stays NOT_CLOSED. The series Route B is not discharged. XVI-N is not discharged. XV-B is not opened. XVI-P is registered and is not a premise. No quantum coefficient is admitted for the inherited response. No compilation is asserted.

Open VII-H · Emergence problem · Low-energy problem · Separations

VII-I constructs a finite-width free algebra and does not close the sharp interacting observable

Version 1 keeps the coordinate-time Cauchy prescription and the restricted plateau gauge domain. It proves an off-shell non-admission, two finite-width comparisons, and a density-prepared free polynomial algebra through second coordinate order. The original sharp nonlinear interacting quantum observable is not constructed.

• prop:normal keeps coordinate-time derivatives. A metric-dependent unit normal would change the observable. thm:sharp excludes the original nonzero-smearing first dressing from the off-shell microcausal polynomial domain.
• thm:convdefect gives an explicit positive covariance defect for field-argument convolution. thm:rampadmission and thm:freealgebra construct the density-prepared free algebra, with adjoints and ordering transport. thm:transmission shows that the sharp limit has changed transmission data.
• thm:bdcarrier is a minimal boundary-sensitive classical carrier. Unchanged regular approximants do not converge in its topology. thm:incompatibility shows that old-product agreement, convergent sharp admission, bounded-set hypocontinuity, and continuous triangle extraction cannot coexist through hbar cubed.
• VII-D's numerical finite part is not renamed as a binary product. VII-H's class of hbar delta_0 is a different free-field benchmark. IX-A, IX-B, IX-E, XII-D, and XII-F are not premises. A local counterterm is not its propagated image.
• thm:auxequivalence is classical auxiliary equivalence. Quantum elimination needs inherited cross-contractions. thm:linear-quantum gives free-shell representatives of linear sharp coordinates. That linear repair is not nonlinear interacting gauge closure.
• I3 and J2 stay open. XIV-I supplies I2 and does not finish I3. This is not spacetime emergence, not a Page curve, and not a constructed gravitational dictionary. O.1 stays NOT_CLOSED. The series Route B is not discharged. XVI-N is not discharged. XV-B is not opened. XVI-P is registered and is not a premise. No quantum coefficient is admitted for the inherited response. No compilation is asserted.

Open VII-I · Emergence problem · Low-energy problem · Separations

VII-J certifies a causal network and does not derive the cone

Version 1 separates scheduled reachability, intervention-based influence, and an independently supplied physical causal relation. Target A is the decoded simulation channel. Target B embeds elementary communication. The cone application is a finite carrier on a prescribed metric cone.

• thm:schedule bounds the Heisenberg support of every jointly observed output by the complete timed ancestor set. Absence of a scheduled path implies absence of signalling, including with an untouched reference. A scheduled path need not carry a signal.
• thm:physical gives exact containment once dependency edges are causally embedded. thm:signal-stability gives the diamond-norm signalling bound. Simulation accuracy and causal safety are separate.
• VII-F thm:certificate is the three-to-six particle-link event on a fixed spinless cone. thm:implementation is a finite reversible event-code circuit. VII-J adds localization, timing, and one buffered two-qubit transport. Abstract cell transport is not a physical trajectory. prop:instant excludes a zero-duration remote SWAP on one slice.
• VII-E's schedule bound is cited and is not a premise. VII-G's finite instrument is not the physical event theorem. VII-H is neither a schedule nor an instrument. VIII-C's backwards support is not this physical cone.
• Certified matter communication on a fixed cone is not matter-driven evolution of the cone. The metric, deficit, and worldline are inputs. This does not advance the characteristic quantum-product programme. This is not spacetime emergence, not a Page curve, not an island, and not a holographic connecting map. O.1 is not changed. The series Route B is not discharged. XVI-N is not discharged. XV-B is not opened. XVI-P is registered and is not a premise. No quantum coefficient is admitted. No compilation is asserted.

Open VII-J · Emergence problem · Separations

Em06-A proves a scalar-only limit and does not derive spacetime

Version 1 keeps the metric classical and quantizes only the free scalar. The observable is the first plateau coefficient, not the joint metric-scalar insertion and not a second-order completion.

• prop:plateau is exact first-order invariance on the declared plateau. prop:support keeps the dependence inside a compact Minkowski past. prop:test writes an exact compact scalar test after the metric is fixed.
• thm:main equates the mean with the named classical value for every positive classicality parameter. The variance is exactly that parameter times a finite one-particle norm. Spectral convergence holds in the quadratic Wasserstein metric.
• prop:fixedCCR shows that coherent displacement at fixed commutation relations does not make the absolute variance vanish. prop:noadmission transfers nothing to XI-G's frozen cubic class.
• VII-A's first-order identity is reproduced and is not a premise of the quantum limit. VII-B's sharp joint insertion, VII-H's free-field pairing, and V's represented response are not this coefficient.
• This is not metric reconstruction, not Einstein dynamics, not a holographic map, and not spacetime emergence. H2, I3, and J2 stay unresolved. O.1 stays NOT_CLOSED. The series Route B is not discharged. XVI-N is not discharged. XV-B is not opened. XVI-P is registered and is not a premise. No quantum coefficient is admitted. No compilation is asserted.

Open Em06-A · Emergence problem · Separations

XVII-A reconstructs one bulk effect and does not supply holographic emergence

Version 1 is a newly declared finite-matrix scalar benchmark on a fixed global AdS2 background. The boundary region is a time interval on the right conformal boundary. The named bulk observable is a bounded sine effect at the central point.

• lem:smearing identifies the boundary integral with the central field under the declared occupation correspondence. thm:main puts the sine effect in the boundary algebra and reproduces the bulk measurement channel, including reference systems.
• lem:timeband says every nonempty open time interval is algebraically complete in this finite cutoff. That fact is not an entanglement wedge and not a spatial subregion theorem.
• prop:record-obstruction shows that the binary record does not recover a noncommuting population effect. prop:radius shows that the declared dimensionless data do not identify the background radius. The diagnostic probability is one half plus the square root of three over eight.
• This is not an identification with VII-A, V, or Em03. Em06-A's classical limit is not this reconstruction. En02-B's decoder is not the correspondence U. Em03-A's emission law is not the connecting map.
• This is not metric reconstruction, not Einstein dynamics, not holographic emergence, not a Page curve, not an island, and not an interior partner. H2, I3, and J2 stay unresolved. O.1 stays NOT_CLOSED. The series Route B is not discharged. XVI-N is not discharged. XV-B is not opened. XVI-P is registered and is not a premise. No quantum coefficient is admitted. No compilation is asserted.

Open XVII-A · Emergence problem · Separations

Em06-B concentrates finite families and does not enter the metric gate

Version 1 keeps the metric coefficient classical and quantizes only the free scalar. The release is the scalar-only package B1 through B5. The optional finite-mode metric gate B6 is not entered.

• prop:test and prop:gauge rederive the compact scalar test and the restricted plateau identity. thm:estimate bounds the one-particle map by six derivatives of the test and metric coefficient and three derivatives of the switch. The orders are sufficient and are not claimed optimal.
• thm:commuting gives a joint spectral law for a finite commuting family. thm:ordered treats a general family by ordered Weyl expectations and does not assume a joint probability distribution.
• thm:states makes epsilon times the observable-specific second moment the exact concentration criterion. A finite residual number expectation with epsilon n_epsilon tending to zero is sufficient and not necessary. cor:uniform gives mean, variance, mean-square, and spectral Wasserstein concentration on bounded input families.
• thm:input-stability controls changes of the metric coefficient, switch, observation test, and preparation. thm:fluctuations keeps the declared, possibly degenerate CCR. The fluctuation law is the law of the undisplaced fields in the residual state. Concentration alone does not determine a fluctuation limit. prop:noise separates one additive-noise measurement from the intrinsic variance.
• Em06-A is not a premise. VII-A's first-order identity is reproduced and is not an imported second-order theorem. IX-A's boundary-sensitive obstruction is not this estimate. XI-G is not repaired. XVII-A is a different project and is not an input.
• This is not metric reconstruction, not Einstein dynamics, not holographic identification, and not spacetime emergence. H2, I3, and J2 stay unresolved. O.1 stays NOT_CLOSED. The series Route B is not discharged. XVI-N is not discharged. XV-B is not opened. XVI-P is registered and is not a premise. No quantum coefficient is admitted. No compilation is asserted.

Open Em06-B · Emergence problem · Separations

Psy02-A separates a carrier ledger and does not derive Orch-OR

Version 1 keeps the carrier, concentration, coherence, response, causal support, a regularized reduction, and a consciousness assignment in different modules. None of those modules is spacetime emergence.

• thm:concentration gives finite-family mean, variance, and Wasserstein bounds for displaced Fock-normal states. The exact criterion is the observable-specific second moment. A residual number bound is sufficient and not necessary.
• thm:ordered uses ordered Weyl expectations and does not assume a joint probability distribution. thm:fluctuations keeps the residual-state law. Concentration alone does not certify coherence survival. thm:witness requires an independent trace-distance certificate.
• thm:contact and thm:response-invariant construct a separate massless Wick-square benchmark. That benchmark is not VII-H's pairing and not residual-state variance.
• thm:support bounds scheduled ancestors. thm:nonidentifiable requires separated complete-record laws before a mechanism is identified. A microtubule effect is not thereby an Orch-OR mechanism.
• thm:collapse-channel is one regularized finite reduction whose rate is an input. Mass assignments remain additional inputs. thm:nonentailment does not derive subjective experience from the stated physical premises.
• Em06-A, Em06-B, VII-H, VII-J, VIII-C, En01-A, En01-C, Em05-A, and En02-E are source records and are not premises. This is not a derivation of Orch-OR, not neuronal quantum viability, not metric reconstruction, not Einstein dynamics, not holographic identification, not a Page curve, and not spacetime emergence. H2, I3, and J2 stay unresolved. O.1 stays NOT_CLOSED. The series Route B is not discharged. XVI-N is not discharged. XV-B is not opened. XVI-P is registered and is not a premise. No quantum coefficient is admitted. No compilation is asserted.

Open Psy02-A · Emergence problem · Separations

Psy01-A bounds pruning and does not supply a density law of emergence

Version 1 is an analytic framework for one task-gated ReLU class. A connection count is not cue use, not stress tolerance, and not spacetime emergence.

• thm:cueobstruction bounds conflicting tasks and the midpoint cue. thm:cuecertificate controls accuracy changes by the margin. Successful endpoint switching is a certificate of cue influence, not a density theorem.
• thm:nothreshold constructs a sparse member with perfect endpoint switching at a ten-percent target. A universal cue-loss threshold near twenty percent density is false for the architecture class.
• thm:nesting shows that fixed-weight nested magnitude pruning agrees with one-shot pruning at the same integer retention counts. Learning between prunes can change rankings. prop:harddiscontinuity shows that hard pruning is not a Lipschitz density surface.
• prop:equaldensity shows that identical masks and identical clean outputs need not determine identical stress tolerance. The affine-Gaussian diagram is a comparison model, not a saved-network certificate.
• Em06-A, Em06-B, VII-H, VII-I, and VII-J are not premises. Psy02-A is a different project and is not an input. No empirical density threshold, biological pruning mechanism, or treatment recommendation is asserted.
• This is not metric reconstruction, not Einstein dynamics, not holographic identification, and not spacetime emergence. H2, I3, and J2 stay unresolved. O.1 stays NOT_CLOSED. The series Route B is not discharged. XVI-N is not discharged. XV-B is not opened. XVI-P is registered and is not a premise. No quantum coefficient is admitted. No compilation is asserted.

Open Psy01-A · Emergence problem · Separations

Psy02-B version 2 fixes a branch-matched pilot and does not derive Orch-OR

Version 2 completes one finite mathematical pilot and an independent analytic interface. The witness and the mass difference use the same two branches. Excerpts are not a reconstruction of the unavailable full map. That pilot is not biological viability and not spacetime emergence.

• thm:colored gives exact colored dephasing for one finite thermal oscillator bath. Recurrences are not removed. thm:pilot is a separately specified memoryless loss-dephasing semigroup. The extra rate R is E_G over hbar only as a phenomenological hypothesis.
• prop:effect and thm:matrixunits separate a named effect from a channel. thm:energy is an energy-constrained finite-code bound. The biological estimates are not supplied.
• thm:concentration and thm:filters keep temporal covariance separate from equal-time concentration. thm:patterns and thm:massstability calculate aligned, alternating, localized, and correlated-domain Gaussian energies. Collective language does not imply n squared scaling. The Wick-square contact class is not this Coulomb energy.
• thm:process and thm:overlap show that equal complete accessible records do not select which conditional unraveling is real. thm:gap and thm:pilotexample give one dimensionless robust gap. Those parameters are not biological measurements.
• thm:Euler, thm:tree, thm:descent, thm:lifting, thm:jets, and thm:admission are independent interface theorems. prop:nontransfer does not identify the pilot with the grouped map. They do not construct the missing full map at I3, J2, or the XV-B interface. Unavailable tensor components are not invented.
• Psy02-A, Em06-B, VII-H, VII-J, Em04-A, XII-A, XII-C, XIII-C, XIV-H, XIV-I, and XIV-J are source records and are not premises. Psy01-A is a different project and is not an input. This is not a derivation of Orch-OR, not neuronal quantum viability, not metric reconstruction, not Einstein dynamics, not holographic identification, not a Page curve, and not spacetime emergence. H2, I3, and J2 stay unresolved. O.1 stays NOT_CLOSED. The series Route B is not discharged. XVI-N is not discharged. XV-B is not opened. XVI-P is registered and is not a premise. No quantum coefficient is admitted. No compilation is asserted.

Open Psy02-B · Emergence problem · Separations

Psy03-A fixes intervention budgets and does not derive a treatment

Version 1 formalizes the supplied pruned-network computation and a separately defined finite quantum extension. Weight displacement is not a universal dose. The quantum network is not the classical simulation and not spacetime emergence.

• thm:zerodose shows that changing damping or the activation can change the logits while every weight stays fixed. prop:rescaling shows that a clean ReLU rescaling need not preserve the weight budget. prop:samemask separates equal masks and equal clean logits from equal stressed accuracy.
• cor:stress and thm:stressaccuracy give a damped path bound and a margin certificate. Damping changes both the clean signal and the injected noise. prop:tanh records that noise added after tanh is not a bounded stressed activation.
• thm:descent is a signed sparse-gradient local guarantee. The source's magnitude-ranked random initialization does not inherit it. thm:ranking rejects a nearest candidate that lies outside the declared tolerance.
• thm:classicalboundary is an exact classical Markov reduction when the Hamiltonian vanishes and the record is diagonal. thm:phase and thm:gap are finite coherence-sensitive contrasts. thm:equalop shows that equal operational distance need not fix performance.
• prop:nontransfer does not identify the classical simulation with the quantum extension. Psy01-A, Psy02-A, Psy02-B, Em06-B, Em04-A, and VII-J are source records and are not premises. This is not an antidepressant mechanism, not a clinical ranking, not metric reconstruction, not Einstein dynamics, not holographic identification, not a Page curve, and not spacetime emergence. H2, I3, and J2 stay unresolved. O.1 stays NOT_CLOSED. The series Route B is not discharged. XVI-N is not discharged. XV-B is not opened. XVI-P is registered and is not a premise. No quantum coefficient is admitted. No compilation is asserted.

Open Psy03-A · Emergence problem · Separations

Psy03-B fixes irreversible structural memory and does not derive kindling

Version 1 formalizes repeated threshold-triggered damage-and-repair in the supplied pruned network and a separately defined finite quantum extension with a classical scar register. Permanent scars constrain repair capacity. They do not establish progressive vulnerability or a kindling mechanism.

• prop:reset shows that the post-discontinuation gain reset forces effective gain one for every protection level. prop:duration separates a duration-grid threshold fraction from a continuous survival law. prop:severitysource identifies the implemented severity rule and its assigned-gain contribution.
• cor:capacity and thm:depletion give scar-mask invariants and finite-count depletion. thm:optimalrisk orders optimal achievable risks under nested coordinate constraints. prop:counterexamples exclude a universal ordering of current checkpoint performance by scar count.
• thm:conditional and thm:paired give feedback-aware threshold certificates on fresh challenge blocks and paired-intervention contrasts. The source controller uses the test accuracy to drive future scars, so ordinary held-out independence is not available.
• thm:hybrid and thm:classical specify the enlarged evolution with a classical persistent scar register. thm:operationalmemory is a carrier-only causal-break witness. thm:pilot gives a finite coherence-sensitive contrast. The scar register is classical memory, not a quantum-memory resource.
• Psy01-A, Psy02-A, Psy02-B, Psy03-A, Em06-B, Em04-A, and VII-J are source records and are not premises. This is not a kindling mechanism, not a clinical mania probability, not metric reconstruction, not Einstein dynamics, not holographic identification, not a Page curve, and not spacetime emergence. H2, I3, and J2 stay unresolved. O.1 stays NOT_CLOSED. The series Route B is not discharged. XVI-N is not discharged. XV-B is not opened. XVI-P is registered and is not a premise. No quantum coefficient is admitted. No compilation is asserted.

Open Psy03-B · Emergence problem · Separations

Psy03-C fixes recurrent stability and does not derive a cognitive construct

Version 1 formalizes the supplied scar-constrained GRU and a separately defined finite input-driven quantum model. An ordinary-ReLU cube bounds hidden states. It does not certify predictions, a cognitive construct, or spacetime emergence.

• lem:convex and thm:reluinvariance give an ordinary-ReLU invariant cube despite unbounded input noise. thm:tanh bounds externally tanh-activated paths. Biased ReLU has a finite-horizon envelope and no deterministic unit-cube bound when hidden noise is present.
• thm:celllip and thm:recurrence give gate-aware Lipschitz constants and a temporal perturbation certificate. Boundedness is not contraction. prop:repetition records that twenty repeated steps are one latent point, not twenty independent samples.
• thm:bayes and thm:blend give exact Gaussian-task and noiseless-blend references. Invertible rotation and scaling preserve ideal label information. Distractor weight does not destroy information monotonically. cor:battery separates probe accuracy, clean-to-probe gaps, and checkpoint changes.
• thm:qforget and prop:register separate fixed-sector forgetting from a persistent classical register. thm:qpilot is an exactly solved delayed phase-label pilot. Phase sensitivity is not quantum computational advantage. The ordinary and biased evaluators are not the earlier feed-forward stress model.
• Psy01-A, Psy02-A, Psy02-B, Psy03-A, Psy03-B, Em06-B, Em04-A, and VII-J are source records and are not premises. This is not a cognitive construct, not a biological treatment mechanism, not metric reconstruction, not Einstein dynamics, not holographic identification, not a Page curve, and not spacetime emergence. H2, I3, and J2 stay unresolved. O.1 stays NOT_CLOSED. The series Route B is not discharged. XVI-N is not discharged. XV-B is not opened. XVI-P is registered and is not a premise. No quantum coefficient is admitted. No compilation is asserted.

Open Psy03-C · Emergence problem · Separations

Psy03-D fixes hidden-rule observability and does not derive adaptation

Version 1 formalizes an uncued modular recurrent rule-switching task and a separately defined finite quantum cue pilot. Point history does not reveal a stationary uncued rule. Optimal accuracy is not rule adaptation.

• lem:uniform and thm:observability prove that the point sequence is independent of a stationary four-ID rule process. prop:duplicates records that two rule IDs implement the same label function. thm:ceiling gives the exact population optimum three quarters, attained by a memoryless classifier. Oracle rule access gives accuracy one.
• thm:switchfrequencies separates rule-ID changes, label-function changes, and informative disagreements. One sixth of stationary ID switches change no label function. prop:cues, thm:noisycues, and thm:feedback declare cued, delayed-cue, erased-cue, and causally ordered feedback protocols. These are new protocols, not silent corrections of the uncued task.
• def:oldfraction and prop:metriccounterexamples separate old-function responses from repeated responses. thm:sequencehoeffding, thm:ratio, and thm:recovery give sequence-level certificates. A zero denominator leaves a ratio unresolved. The five-trial success pattern is a declared statistic, not a recovery time.
• thm:maskedgradient explains zero stored derivatives at inactive linear weights. prop:reference separates mask reopening from recovery of a pre-pruning parameter. thm:cancel and prop:division give recurrent-protection counterexamples. def:statuses, thm:interpolation, and thm:isoacute distinguish executed matches, bracketed surrogates, and unsupported targets.
• cor:qobstruction and thm:qpilot keep the quantum cue pilot subordinate to the observation obstruction. Changing the carrier does not supply a missing observation channel. Psy01-A, Psy02-A, Psy02-B, Psy03-A, Psy03-B, Psy03-C, Em06-B, Em04-A, and VII-J are source records and are not premises. This is not a cognitive construct, not a biological treatment mechanism, not metric reconstruction, not Einstein dynamics, not holographic identification, not a Page curve, and not spacetime emergence. H2, I3, and J2 stay unresolved. O.1 stays NOT_CLOSED. The series Route B is not discharged. XVI-N is not discharged. XV-B is not opened. XVI-P is registered and is not a premise. No quantum coefficient is admitted. No compilation is asserted.

Open Psy03-D · Emergence problem · Separations

Psy04-A bounds a declared classical memory and does not certify quantum memory

Version 1 formulates a delayed random-access experiment. Two fresh bits are encoded before an independent query. The complete input-dependent classical state at decoding has two values. The random-access inequalities are established benchmarks, not new discoveries.

• ass:boundary states the complete storage and access boundary. lem:deterministic reduces randomized strategies to deterministic tables. thm:classical proves the sharp two-state success bound of three quarters, attained by storing one bit and guessing the other.
• thm:quantumattainment and thm:quantumoptimal give the standard one-qubit value, one half plus one over two square root of two, including a sequential encoding that uses only the current bit and the qubit. thm:delay gives the depolarizing retention threshold. A nonzero coherence witness is not by itself a task violation.
• thm:robustgap, thm:fixedtest, and thm:anytime keep failures in the attempted-run law and give fixed-sample and anytime exclusion certificates. The rejection excludes the declared capacity, access, freshness, and error assumptions. It does not establish those assumptions from the score alone.
• thm:nonentailment records the environmental-memory boundary. A Markovian qubit can violate the wholly classical bound. A persistent classical register can create causal-break history dependence. Neither observation certifies quantum environmental memory.
• Psy03-B, Psy03-C, Psy03-D, Psy02-A, Psy02-B, Em06-B, and VII-J are source records and are not premises. This is not a cognitive construct, not a biological memory identification, not metric reconstruction, not Einstein dynamics, not holographic identification, not a Page curve, and not spacetime emergence. H2, I3, and J2 stay unresolved. O.1 stays NOT_CLOSED. The series Route B is not discharged. XVI-N is not discharged. XV-B is not opened. XVI-P is registered and is not a premise. No quantum coefficient is admitted. No compilation is asserted.

Open Psy04-A · Emergence problem · Separations

Psy04-B makes the storage boundary a causal cut and does not derive a cone

Version 1 places the delayed query in a complete finite causal network. Scheduled ancestors upper-bound influence. They do not equal it, and they do not certify quantum environmental memory.

• thm:schedule proves that the adjoint of the complete channel pulls terminal observables back only onto scheduled ancestors. The inclusion of operational influence need not be equality. A constant decoder can have a scheduled memory input with no actual influence. Complete instruments, not selectively normalized branches, enter the proof.
• ass:fresh separates two hypotheses. The query is absent from the encoding causal past, and it is statistically fresh. A later query can still be correlated with an earlier shared seed. prop:late says that graph order alone does not make the query unpredictable.
• thm:factor reads the decoder-relevant cut as the complete joint accessible state, including correlated ancillas. An input-independent marginal is not enough. thm:classical independently proves the two-state benchmark. thm:qubit realizes the standard qubit code by sequential local gates and destructive Enter readout. Enter consumes the carrier.
• thm:retention gives the exact depolarizing threshold. prop:parameterstability gives a quantitative score allowance. thm:nonentailment and ex:causalbreak keep the environmental-memory refusal: a Markovian qubit already wins, and a classical register can produce a carrier-only causal break.
• Psy04-A, VII-J, Psy02-B, Psy03-B, Psy03-D, and Em06-B are source records and are not premises. No metric or physical causal cone is inferred from the score. This is not a derivation of the Born rule, not metric reconstruction, not Einstein dynamics, not holographic identification, not a Page curve, and not spacetime emergence. H2, I3, and J2 stay unresolved. O.1 stays NOT_CLOSED. The series Route B is not discharged. XVI-N is not discharged. XV-B is not opened. XVI-P is registered and is not a premise. No quantum coefficient is admitted. No compilation is asserted.

Open Psy04-B · Emergence problem · Separations

En03-A separates destructive readout from geometry and does not derive a field equation

The observation boundary includes coupling observables, control, guards, capacity tests, locations, and retained storage. Geometry is primitive metadata. A circuit dependency region is not a physical light cone.

• def:enter, def:recording, and def:nondestructive separate destructive Enter, coherent recording, and a residual instrument. thm:deferred identifies immediate destructive readout with a restricted coherent-then-readout implementation on their common record-matter output. Intermediate access to the record, the measured factor, or the carrier is excluded.
• thm:spectators says that arbitrary spectator extensions with the same accessible reduction preserve geometric traces, once control and resources are blind. Coupling-algebra blindness alone is not enough. thm:pullback and prop:recorderror make record compatibility the pullback of coarse effects. The exact unassisted error is an event operator norm. thm:obstruction and ip:process keep residual compatibility and mechanism identification separate from complete-record equality.
• ip:nosignal and ip:networkcut factor prescribed channel networks through scheduled ancestors, including an untouched reference. The inclusion need not be equality, and the channel statement is not transferred to nonlinear geometric coupling. ip:classicalmemory shows that a persistent classical register can produce carrier-only history dependence without a quantum-memory-resource claim.
• ip:stability, ip:residual, ip:scalar-sampling, and ip:record-sampling state conditional approximation and sampling certificates. They do not establish the observation boundary from a score alone. thm:exchange certifies one four-face adjacency exchange on a fixed spacetime: charts, edge laws, an exact guard, a compact collar, and a finite reversible event implementation. op:transitions, op:approximation, and op:dominance remain open.
• I, VII-E, VII-J, Psy02-A, Psy02-B, Psy04-A, Psy04-B, Em05-A, Em06-B, and En01-B are source records and are not premises. No gravitational field equation, continuum limit, or Born-rule derivation is asserted. This is not metric reconstruction, not Einstein dynamics, not holographic identification, not a Page curve, and not spacetime emergence. H2, I3, and J2 stay unresolved. O.1 stays NOT_CLOSED. The series Route B is not discharged. XVI-N is not discharged. XV-B is not opened. XVI-P is registered and is not a premise. No quantum coefficient is admitted. No compilation is asserted.

Open En03-A · Emergence problem · Separations

Hawk01-A scores delayed-query retrieval and does not derive recovery

The source is a fixed Schwarzschild scalar calculation. The recovery completion is phenomenological. An emission spectrum is not the message-to-radiation channel.

• ass:unruh and lem:current give the affine-vacuum horizon current and the Bose occupation. thm:source is the normalized greybody-modified emission law and the finite-packet covariance. prop:mass is a quasistatic mass ledger. An instantaneous Schwarzschild sequence is not an exact evaporating metric, and the adiabatic indicator is not a channel-error theorem.
• thm:score is the exact optimal retrieval formula for the trusted four-state ensemble. thm:null gives one half when the accessible radiation is message-independent, with failed capture kept in the complete attempt. thm:classical gives three quarters only for a complete trusted measure-before-query channel. These three bounds are not interchangeable.
• thm:complement and thm:completion construct a finite-energy emission isometry whose late marginal is thermal for every message, and a second conserving completion with the same late state and no retrieval advantage even with the early key. thm:completionoptima separates coherent access, destructive number records, and referenced recovery. Equal late spectra do not identify the assisted channel.
• prop:cutoff, prop:stability, prop:nullcover, and thm:sampling are regulator, model-error, and attempted-run certificates. The sample size counts complete independent attempts. A simulated source is not an astronomical observation. A three-quarter violation excludes only the trusted measure-before-query null. It does not establish quantum environmental memory, interior escape, or a solution of the information paradox.
• Em03-A, Em03-B, Em03-E, Em05-B, Em06-B, En02-E, En03-A, Psy04-A, Psy04-B, VII-J, Psy02-B, Psy03-D, XIV-I, and XIV-J are source records and are not premises. No microscopic gravitational recovery law is asserted. This is not metric reconstruction, not Einstein dynamics, not holographic identification, not a Page curve, and not spacetime emergence. H2, I3, and J2 stay unresolved. O.1 stays NOT_CLOSED. The series Route B is not discharged. XVI-N is not discharged. XV-B is not opened. XVI-P is registered and is not a premise. No quantum coefficient is admitted. No compilation is asserted.

Open Hawk01-A · Emergence problem · Separations

Hawk01-B certifies residual decoupling and does not derive evaporation

The logical task is arbitrary-code preservation, including every external reference. The couplings, degeneracies, and endpoint are model assumptions. A spectrum or entropy history is not the recovery channel.

• thm:exact makes arbitrary-input recovery equivalent to a constant complete complement on every matrix unit. thm:approximate translates the Kretschmann--Schlingemann--Werner continuity theorem into half-diamond bounds: recovery error is at most the square root of twice the leakage distance, and conversely. prop:Bell keeps Bell fidelity as a dimension-dependent diagnostic, not a worst-case substitute.
• thm:physicality and thm:prefixchannels construct an energy-conserving sequence that generates its own key, retains vacuum and pending branches, and does not reset internal memory. thm:optima gives prefix recovery error equal to the residual leakage distance. Individual emitted blocks are message-independent. The joint radiation carries the logical coherence. thm:endpoint releases every residual degree of freedom through a separately declared endpoint map.
• thm:entropyseparation exhibits a second conserving evolution with the same radiation density operators for one preparation, and the same radiation entropy histories for every pure code preparation, while retaining the code in a disclosed inaccessible memory. The counterexample does not challenge island or entanglement-wedge reconstruction. prop:thermalcomparison records truncation and compatibility obstructions. Local statistics do not reproduce Hawking pair production.
• thm:number separates destructive occupation access from coherent recovery. prop:cutoff, prop:robustness, and the sampling bounds are regulator and attempted-run certificates. A simulated source is not an astronomical observation. Passive observation does not supply the prepared code and its reference.
• Hawk01-A, Em05-A, Em05-B, Em03-A, Em03-E, En02-B, En02-C, En02-E, En03-A, Psy02-B, Psy03-D, XIV-I, and XIV-J are source records and are not premises. No microscopic gravitational recovery law is asserted. This is not metric reconstruction, not Einstein dynamics, not holographic identification, not a Page curve, and not spacetime emergence. H2, I3, and J2 stay unresolved. O.1 stays NOT_CLOSED. The series Route B is not discharged. XVI-N is not discharged. XV-B is not opened. XVI-P is registered and is not a premise. No quantum coefficient is admitted. No compilation is asserted.

Open Hawk01-B · Emergence problem · Separations

Hawk02-A certifies a conditional interface and does not derive evaporation

A fixed-background spectrum does not jointly determine the geometry, the emission process, and the code-transfer channel. The theorems below are finite certification statements. The physical model that would instantiate them is not supplied.

• def:source records the fixed-background scalar comparison. prop:adiabatic is a mass-ledger diagnostic. prop:massstability is a Lipschitz allowance on a compact mass interval. Neither is a semiclassical Einstein theorem. Em06-B thm:input-stability is classical input stability and is not a diamond-norm channel bound. Em06-B is not a premise.
• thm:sequential bounds stepwise reference-preserving comparison error. thm:constant makes exact recovery equivalent to a constant complete complement. prop:approximate and thm:stability give the half-diamond information-disturbance and stability consequences. lem:flag shows that a commuting truncation equality need not hold for a noncommuting input.
• thm:thermalnonid and cor:spectrum construct two energy-conserving models with the same late thermal state and different assisted recovery. prop:jointresidual shows that separate residual marginals need not make the joint complement constant. thm:pairentropy is a pair-entropy inequality under stated partner hypotheses. It is not a derivation of the Hawking pair state.
• ass:physical and thm:main certify recovery error only after a stated action, geometry, complete transfer interface, and leakage bound are supplied. cor:claims keeps a semiclassical-plus-backreaction baseline separate from a conditional recovery claim. A spectrum does not derive the transfer law. XIV-I constructs the named I2 amplitude; the full map stays unresolved at I3 and J2.
• Hawk01-A, Hawk01-B, Em03-A, Em03-F, Em05-B, Em06-B, En02-E, Psy02-B, En03-A, XIV-H, XIV-I, and XIV-J are source records and are not premises. Hawk01-B leakage conventions are not imported without a normalization check. No microscopic black-hole Hamiltonian is asserted. This is not metric reconstruction, not Einstein dynamics, not holographic identification, not a Page curve, and not spacetime emergence. H2, I3, and J2 stay unresolved. O.1 stays NOT_CLOSED. The series Route B is not discharged. XVI-N is not discharged. XV-B is not opened. XVI-P is registered and is not a premise. No quantum coefficient is admitted. No compilation is asserted.

Open Hawk02-A · Emergence problem · Separations

Hawk02-B derives a finite emission isometry and does not derive evaporation

The pulse Hamiltonians determine the complete emission isometry. The recovery error is calculated from that isometry. Entropy turnover is not used to certify recovery. The model is an externally scheduled evaporation analogue, not a gravitational Hawking mechanism.

• thm:B1 derives the interval propagator from the prescribed pulse and proves bare-energy conservation on the one-excitation sector. The schedule is externally prescribed. No autonomous controller is constructed. Em06-B thm:input-stability is classical input stability and is not a channel allowance. Em06-B is not a premise.
• thm:B2 derives the complete emission isometry and both channels. def:enlargement requires every added inaccessible output to enlarge the residual. thm:B3 gives the exact single-cell half-diamond recovery error q_N times one minus d to the minus two. thm:B4 gives the matching residual leakage. thm:B5 gives the many-cell bound.
• thm:B6 and cor:feasibility supply a Duhamel implementation budget and a compatible finite-time regime. thm:B7 calculates entropy turnover and states that it does not certify recovery. prop:time, prop:destructive, and prop:collection separate access controls from the ideal recovery claim.
• A supplied diagnostic record reports 32 predicates for one configuration at d equals 2, N equals 3, and theta equals pi over 4. It supports selected matrix identities and Bell witnesses. It does not replace the analytical proofs or constitute diamond-norm optimization. Hawk02-A, Hawk01-B, Em03-E, and Em05-B are source records and are not premises.
• This is not metric reconstruction, not Einstein dynamics, not holographic identification, not a Page curve, and not spacetime emergence. H2, I3, and J2 stay unresolved. O.1 stays NOT_CLOSED. The series Route B is not discharged. XVI-N is not discharged. XV-B is not opened. XVI-P is registered and is not a premise. No quantum coefficient is admitted. No compilation is asserted.

Open Hawk02-B · Emergence problem · Separations

Hawk02-C version 2 derives an autonomous source-field bridge and does not derive Hawking radiation

The Hamiltonian is time-independent and excitation-conserving. The packet channel is calculated from that dynamics. Hawk02-B remains a scheduled comparison. Neither model is gravitational Hawking radiation.

• thm:C2 constructs the autonomous Hamiltonian and reduces the prepared one-excitation sector to a Friedrichs operator. thm:C3 derives the complete source-field isometry from the survival amplitude and the emitted wavefunction. The channel is not selected by occupation-spectrum agreement. Em03-A is a source record and is not a premise.
• thm:C4 gives the exact half-diamond recovery error and residual leakage: one minus d to the minus two, times source survival plus uncollected one-particle weight. Uncollected modes stay in the complete residual, coherently with the surviving source. A discarded probability alone does not give the complete-isometry allowance. That allowance is at most the square root of twice the missed weight.
• thm:C5 gives a bound-state-free prepared spectral measure for the semicircle form factor, with survival at most four over pi squared c squared T squared. lem:packetbound gives a factorial tail for the predetermined Chebyshev packets. thm:C7 separates an identified endpoint comparison with Hawk02-B from a predictive finite-chain remainder. The first is not the second. Hawk02-B is not a premise.
• thm:C6 is a sector Duhamel allowance on the invariant prepared sector. Em06-B thm:input-stability is classical input stability and is not that allowance. Em03-F's switched propagator is not this autonomous group. VII-G thm:stability is a different instrument. cor:epsilon gives a nonempty finite-time regime in which the implemented recovery error is at most any prescribed positive tolerance.
• Version 2 incorporates a supplied execution manifest. It reports all 18 finite-proxy predicates at d=2, c=1, omega_0=3, and T=1, with eight collected packets and a 24-packet reference chain. The reported recovery and leakage formula is 0.2494586279164458. That number is a finite-proxy formula value, not a continuum result. The record supports selected finite-matrix identities and norm comparisons. It is not continuum simulation, not numerical diamond-norm optimization, and not machine proof verification. No independent rerun is claimed. The T=1 run is not the T=40 analytical small-error example and does not show recovery error below 1/100. A floating-point residual printed as zero is not exact arithmetic. A rectangular isometry is not a unitary. Hawk02-B's 32-predicate execution record is a different run and does not apply here. The word unexecuted in the archived script describes its original release status, not this reported record.
• This is not metric reconstruction, not Einstein dynamics, not holographic identification, not a Page curve, and not spacetime emergence. H2, I3, and J2 stay unresolved. O.1 stays NOT_CLOSED. The series Route B is not discharged. XVI-N is not discharged. XV-B is not opened. XVI-P is registered and is not a premise. No quantum coefficient is admitted. No compilation is asserted.

Open Hawk02-C · Emergence problem · Page curve · Separations

Hawk02-D derives a quadratic fermionic residual and does not derive evaporation

The Hamiltonian is positive, time-independent, and number-conserving. A finite fermionic code is loaded by a message-independent swap, and a finite reservoir prefix has a proved complete residual. The model is quadratic. It is not interacting SYK, not a horizon, and not gravitational backreaction.

• prop:spectral gives the exact source survival, the square of J_1(2ct) over ct. The complete inaccessible weight is source survival plus the uncollected reservoir tail. Uncollected modes stay in the residual. Hawk02-C is a source-boson comparison and is not a premise.
• thm:main constructs a complete decoder for every code of at most K particles. Recovery error and complete residual leakage are at most the minimum of one and the square root of twice one minus (1 minus s_M(t)) to the power K/2. cor:window gives a nonempty finite-time recovery regime for every prescribed accuracy.
• thm:erasure gives the exact one-particle values: both optimal recovery error and complete residual leakage equal one minus d to the minus two, times s_M(t). thm:endpoint derives an outgoing scattering channel with a constant complete complement from the same Hamiltonian. No terminal release map is added. thm:recurrence says that a fixed finite chain length prevents permanent late-time recovery.
• thm:energy is an energy-transfer ledger, not gravitational dynamics. thm:finite-chain is a reference-preserving finite-chain approximation. prop:omission, prop:area-law, prop:gram, and prop:semiclassical separate source mixing, a gap-plus-area law, a Gram certificate, and a semiclassical replacement channel from complete residual independence. The interacting SYK target remains unproved.
• OpenAI families 227, 229, 260, 262, 264, 265, 272, and 273 are a documentary catalogue. They are not premises. Hawk01-B, Hawk02-A, Hawk02-C, Hawk03-A, En02-B, En02-C, En02-E, and Em03-C are source records and are not premises. No horizon, no infalling diary, no coherent local radiation receiver, and no gravitational backreaction is constructed.
• This is not metric reconstruction, not Einstein dynamics, not holographic identification, not a Page curve, and not spacetime emergence. H2, I3, and J2 stay unresolved. O.1 stays NOT_CLOSED. The series Route B is not discharged. XVI-N is not discharged. XV-B is not opened. XVI-P is registered and is not a premise. No quantum coefficient is admitted. No compilation is asserted.

Open Hawk02-D · Emergence problem · Page curve · Separations

Hawk02-E specifies a regulated interacting diary and does not derive evaporation

The source is one frozen quartic SYK Hamiltonian coupled to a regulated free scalar reservoir. A pure source is prepared before an even-parity diary arrives. One message-independent parity-preserving swap loads the diary and keeps the displaced carrier in the complete residual. The model is interacting. It is not a horizon, not gravitational backreaction, and not an evaporation endpoint. The quadratic Hawk02-D benchmark is not a premise.

• thm:selfadjoint constructs the self-adjoint continuum Hamiltonian on one frozen coupling array. prop:preparation prepares a normalized Euclidean-filtered pure source state before the diary arrives. No finite-N thermal or gravitational correspondence is inferred from that preparation. prop:insertion loads the even-parity qubit by one message-independent swap. The carrier can stay correlated with the remaining source, so it remains in the complete residual.
• thm:regulator bounds a finite-mode, finite-occupation approximation of the complete prepared channel on every finite observation interval. The allowance keeps the infrared and ultraviolet cutoffs. It does not prove the limits of a vanishing infrared cutoff or an infinite ultraviolet cutoff. cor:regulator-selection chooses those finite parameters and is not removal of the regulator.
• thm:certificate bounds complete residual leakage and recovery error from a complementary Choi certificate, with the code-dimension factor retained. prop:decoder certifies a specified finite CPTP decoder on its normalized Choi operator. That decoder is not a coherent local radiation receiver and not a Page curve.
• thm:energy is an exact microscopic energy ledger, not gravitational dynamics. thm:QND obstructs recovery for a commuting source coupling. thm:endpoint-continuity states continuity consequences of a declared common-output limit and does not construct wave operators or asymptotic completeness. prop:zero-energy shows that vanishing source energy can coexist with perfect residual storage. prop:recurrence says that a fixed finite occupation cutoff and frequency mesh cannot establish permanent information release.
• thm:release records the constructed interface. It does not establish a small dynamical complete-residual bound, a controlled gravitational correspondence, or a gravitational evaporation endpoint. OpenAI families 227, 260, 262, 264, 265, 272, and 273 are a documentary catalogue. They are not premises. Hawk01-B, Hawk02-A, Hawk02-C, Hawk02-D, Hawk03-A, En02-B, En02-C, En02-E, Em03-C, Em03-D, Em03-F, Em03-G, and Em03-H are source records and are not premises. No horizon, no infalling diary, no coherent local radiation receiver, and no gravitational backreaction is constructed.
• This is not metric reconstruction, not Einstein dynamics, not holographic identification, not a Page curve, and not spacetime emergence. H2, I3, and J2 stay unresolved. O.1 stays NOT_CLOSED. The series Route B is not discharged. XVI-N is not discharged. XV-B is not opened. XVI-P is registered and is not a premise. No quantum coefficient is admitted. No compilation is asserted.

Open Hawk02-E · Emergence problem · Page curve · Separations

Hawk03-A encodes a partner in radiation and does not resolve the firewall

Message recovery and a declared pair test can coexist when the partner is part of the radiation algebra. That finite compatibility is not an independent interior, not a smooth horizon, and not an infalling diary.

• thm:amps is a quantitative independent-factor entropy benchmark. It needs an explicit tensor-product hypothesis and a near-pair trace-distance hypothesis. Unitarity alone does not supply negative conditional entropy of a selected late packet. thm:twopurifiers bounds two Bell tests on independent purifiers by one plus one over d. Exterior-only distillation cannot violate that bound.
• thm:exact is the constant-complement recovery criterion, and thm:approx gives the half-diamond information-disturbance bounds. Hawk01-B states a comparable criterion for a different sequential model and is not a premise. thm:partner constructs a state-independent partner algebra as a subalgebra of the radiation algebra. thm:commuting shows why two commuting representations cannot both intertwine the same noncommutative logical algebra.
• thm:compatibility puts exact message recovery and exact prepared-state pair-proxy statistics in one linear unitary model. A pair proxy is not Hadamard regularity, and a finite Gibbs marginal is not a Hawking spectrum. Hawk01-A and Em03-A remain source records. prop:distill moves the purifier and changes the original proxy-pass probability while preserving the message. The original pair test is intervention-dependent.
• thm:physical is conditional. Its bridge hypotheses are not constructed. req:horizon still requires a metric or controlled approximation, infalling couplings, short-distance regularity, stress-energy and backreaction, and a post-distillation calculation. req:diary still requires a physical diary subsystem, its crossing, and a decoder that preserves the diary-reference correlations. Em03-C, Em03-H, Em03-F, Hawk02-C, Hawk02-D, and Hawk02-E do not supply those data.
• This is not metric reconstruction, not Einstein dynamics, not holographic identification, not a Page curve, and not spacetime emergence. H2, I3, and J2 stay unresolved. O.1 stays NOT_CLOSED. The series Route B is not discharged. XVI-N is not discharged. XV-B is not opened. XVI-P is registered and is not a premise. No quantum coefficient is admitted. No compilation is asserted.

Open Hawk03-A · Emergence problem · Page curve · Separations

Hawk04-A preserves the complete code and does not recover it from radiation

Complete unitary evolution of a finite code has a CPTP left inverse on the complete output. That global preservation does not imply recovery from a chosen radiation subsystem. Exact radiation recovery holds if and only if the complete complementary channel is constant. The paper is not a horizon, not a Page curve, and not an evaporation endpoint.

• thm:global proves a CPTP left inverse for a finite code, a fixed pure preparation, and a unitary on the complete system, with every external reference retained. cor:injective says a complete replacement channel cannot describe that evolution. Subsystem entropy may still rise after a partial trace.
• thm:exact recovers the code from radiation if and only if the complete complement is constant, and supplies the decoder. cor:nohiding is that criterion with the outputs interchanged. It is not a claim that correlations are irrelevant, and it does not apply to one marginal or one selected ensemble. Hawk01-B states a comparable criterion for a sequential model and is not a premise.
• thm:certificate lifts a finite complementary Choi number e and a regulator allowance b to a complete residual at most d e plus b, and a recovery error at most the square root of 2 d e plus b. thm:regulator reconstructs a finite-time approximation of the regulated quartic SYK--scalar architecture of Hawk02-E. It does not prove the small dynamical residual. Hawk02-E is not a premise.
• thm:four-majorana evaluates one frozen four-Majorana realization with nonzero coupling. Radiation recovery error is (3 minus z_R(t)) over 4, at least one half, while global preservation stays exact. That is a dynamical negative control, not a scrambling argument. Appendix prop:erasure is the quadratic flagged-transfer identity of Hawk02-D and does not transfer to the quartic source. Hawk02-D is not a premise.
• thm:endpoint requires access-preserving output identifications. A unitary that mixes radiation and residual changes the recovery task. prop:recurrence says a fixed finite proxy returns, so the limsup of the recovery error is one minus d to the minus two. thm:BH-conditional is conditional and does not establish its gravitational hypotheses. thm:release leaves unitarity of quantum gravity, a generic interacting recovery window, and a gravitational endpoint unproved.
• OpenAI families 227, 260, 262, 264, 265, 272, and 273 are a documentary catalogue. They are not premises. Hawk01-B, Hawk02-D, Hawk02-E, Hawk03-A, Em03-C, Em05-A, Em05-B, En02-B, and En02-E are source records and are not premises. Landmark I is optional semantic input after the carrier is qubits and is not a premise. No horizon, no infalling diary, no coherent local radiation receiver, and no gravitational backreaction is constructed.
• This is not metric reconstruction, not Einstein dynamics, not holographic identification, not a Page curve, and not spacetime emergence. H2, I3, and J2 stay unresolved. O.1 stays NOT_CLOSED. The series Route B is not discharged. XVI-N is not discharged. XV-B is not opened. XVI-P is registered and is not a premise. No quantum coefficient is admitted. No compilation is asserted.

Open Hawk04-A · Emergence problem · Page curve · Separations

Hawk04-B version 2 separates readout from quantum recovery and does not delete the residual

A finite acyclic typed fragment denotes a reference-preserving channel. Quantum recovery returns a quantum register through a decoder from radiation to the code. Enter on that radiation register returns a classical record and is not that decoder. Discard of residual outcomes is operational forgetting, not physical annihilation.

• thm:global proves a CPTP left inverse of the complete unitary channel, with every external reference retained. thm:exact recovers the code from one output if and only if the complete complement is constant, and supplies the decoder. cor:nohiding interchanges the outputs. A nonconstant complement shows that some logical information is present in the residual. It does not show that the residual alone recovers the entire code. Hawk04-A states the complement criterion for a different formulation and is not a premise.
• thm:adequacy gives a reference-preserving CPTP semantics for the declared finite acyclic fragment. The programs that return the complete output, the local quantum decoder, the joint recovered code and residual, the radiation-only marginal, and an explicit readout-and-drop are distinct. Allowing a specified finite unitary as a semantic constant does not prove its compilation over a fixed gate library. En03-A is a source record of a minimal interface and is not a premise. Landmark I supplies the destructive Born residual as optional semantic input after the carrier is qubits and is not a premise of thm:main.
• thm:classical proves that any process retaining only classical outcomes has quantum recovery error at least one minus one over d. prop:records says a quantum decoder certifies a later prescribed measurement, and the converse for one selected measurement is false. prop:measurement-dilation keeps a coherent apparatus factor that the classical record omits.
• thm:drop proves that destructive readout of the residual, followed by discarding its outcomes, equals the partial trace, including external references. The channel to radiation is unchanged. Conditioning on a supplied outcome is a different access task. This is not a claim that the residual has physically disappeared.
• thm:regulator reconstructs a finite-time approximation of the regulated quartic source--scalar architecture of Hawk02-E and does not prove the small residual. Hawk02-E is not a premise. thm:control evaluates one frozen four-Majorana realization. Radiation recovery error is (3 minus z_R(t)) over 4, at least one half. Residual recovery error is (1 minus c_R(t)) over 2. Complete leakage is the maximum of one half and (1 plus 2 c_R(t)) over 4. The complete output recovers the diary exactly. Neither output alone need recover it. Appendix comparisons do not transfer the quadratic Hawk02-D identity. Hawk02-D is not a premise.
• thm:endpoint requires access-preserving output identifications. A unitary that mixes radiation and residual changes the recovery task. prop:recurrence says a fixed finite proxy returns, so the limsup of the recovery error is one minus d to the minus two. cor:gravity is conditional and does not establish its gravitational hypotheses. sec:release leaves a positive noncommuting interacting recovery window, a physical receiver, unitarity of quantum gravity, and a gravitational endpoint unproved. Finite-program termination is not that endpoint.
• OpenAI is a documentary catalogue. Families 279, 227, 274, 276, and 119 by OpenAI are documentary labels and are not premises. Family 227 is not a scrambling estimate for the four-Majorana control. The companion does not verify those proofs. Hawk04-A, Hawk01-B, Em03-C, Em05-A, En02-B, En02-E, En03-A, XIV-H, XIV-I, and XIV-J are source records and are not premises. No horizon, no infalling diary, no coherent local radiation receiver, and no gravitational backreaction is constructed.
• This is not metric reconstruction, not Einstein dynamics, not holographic identification, not a Page curve, and not spacetime emergence. H2, I3, and J2 stay unresolved. O.1 stays NOT_CLOSED. The series Route B is not discharged. XVI-N is not discharged. XV-B is not opened. XVI-P is registered and is not a premise. No quantum coefficient is admitted. No compilation is asserted.

Open Hawk04-B · Emergence problem · Page curve · Separations

Hawk04-C states finite access analogues and does not solve evaporation

A complete finite interface restores the code from the joint output. Exact recovery from one factor holds only when the complete complement is constant. Destructive readout returns a classical record. Readout-and-drop is partial trace, not annihilation. The title page names Ngo Cheung. These are operational analogues, not black-hole evaporation.

• thm:global restores the code from the complete output, including external references. thm:exact recovers the whole code from the accessible factor if and only if the complete complement is constant. cor:nohiding says the two factors cannot each recover the whole code. cor:strict is a finite-dimensional obstruction when the complement is nonconstant. Hawk04-A states the complement criterion for a different formulation and is not a premise.
• thm:classical keeps classical-record recovery error at least one minus one over d. thm:drop equates residual readout-and-drop with the partial trace and leaves the accessible channel unchanged. That equality is not physical annihilation. prop:recurrence gives arbitrarily late return of a fixed finite proxy and is not permanent release. Hawk04-B is a source record and is not a premise.
• prop:thermal says identical thermal observations can disagree on recovery. prop:entropy says a selected entropy does not determine recovery and is not a Page curve. Oai265-A is a documentary comparison and is not a premise. En02-D's finite entropy sequence is not imported. En02-C's one-live-qubit error is not a premise.
• thm:endpoint is conditional on a same-model package that is not constructed. prop:toy is a register-level transfer schedule, not a black hole. En07-A, En07-B, En07-C, and En04-A are source records and are not premises. No metric, no island, and no gravitational endpoint is constructed.
• OpenAI is a documentary catalogue and is not a premise. This comparison is not an exhaustive audit. Companion manuscripts are not premises.
• This is not metric reconstruction, not Einstein dynamics, not holographic identification, not a Page curve, and not spacetime emergence. O.1 stays NOT_CLOSED. XVI-N is not discharged. XV-B is not opened. No quantum coefficient is admitted. No compilation is asserted.

Open Hawk04-C · Page curve · Tests · Separations

Hawk04-D states a conditional certificate and does not solve evaporation

A complete finite interface restores the code from the joint output. Exact recovery from one factor holds only when the complete complement is constant. A supplied luminosity law yields a cutoff lifetime and stops at a positive mass. The title page names Ngo Cheung. These are conditional certificates, not black-hole evaporation.

• thm:exact restores the code from the complete output and recovers it from one factor if and only if the complete complement is constant. prop:drop equates readout-and-drop with the partial trace and is not annihilation. lem:benchmarks keeps classical-record error at least one minus one over d. Hawk04-A and Hawk04-B state related distinctions and are not premises.
• thm:swap and thm:flagged are exact calibration identities for a partial-SWAP schedule and a flagged transfer. They are not a universal Page-time law. Hawk04-C is a source record and is not a premise.
• thm:regulator bounds one finite-band source-reservoir model and is not a collapsing-shell Bogoliubov theorem. thm:lifetime is a cutoff-lifetime consequence of a supplied inverse-square luminosity and stops at a positive mass cutoff. It is not a Planck-scale endpoint and not a metric. Hawk02-A is a source record and is not a premise.
• prop:spectral-separation says selected entropy and thermal marginals do not determine recovery. thm:endpoint is conditional on an access-preserving package that is not constructed. prop:recurrence blocks permanent release by a fixed finite proxy. Hawk01-B, En07-A, En07-B, En07-C, and En02-C are source records and are not premises.
• thm:main is a conditional extrapolation certificate. It does not construct a gravitational evaporation channel. OpenAI is a documentary catalogue and is not a premise. This comparison is not an exhaustive audit.
• This is not metric reconstruction, not Einstein dynamics, not holographic identification, not a Page curve, and not spacetime emergence. O.1 stays NOT_CLOSED. XVI-N is not discharged. XV-B is not opened. No quantum coefficient is admitted. No compilation is asserted.

Open Hawk04-D · Page curve · Tests · Separations

Hawk05-A separates the classical album from coherent radiation

A complete finite interface preserves the code on the joint output. Exact recovery from the accessible factor holds only when the complete complement is constant. A destructive record is a different object: its whole-code error stays at least one minus one over d, and an unedited album does not become less random as photographs are appended. The supplied author field is empty and authorship is not inferred.

• thm:global restores the code from the complete output, including external references. thm:exact recovers the whole code from the accessible factor if and only if the complete complement is constant. A constant mixed complement can still leave raw radiation mixed. Hawk04-A states the complement criterion for a different formulation and is not a premise.
• thm:classical keeps classical-record recovery error at least one minus one over d, including an arbitrarily long adaptive record. thm:recordentropy shows that the Shannon entropy of an unedited cumulative record cannot fall. Conditional uncertainty about a separate message can fall. Those are different ledgers.
• thm:flagged gives a conserving flagged schedule whose pure-input radiation entropy is the binary entropy of the survival weight, while recovery error decreases monotonically. That designed turnover is not a Page curve of gravitational evaporation. Hawk04-D's calibration identities are source records and are not premises.
• thm:drop equates residual readout-and-drop with the partial trace and leaves the already-returned accessible channel unchanged. That equality is not physical annihilation and not an energetic final burst. thm:endpoint is conditional on four same-model obligations that are not constructed.
• thm:main is a corrected operational analogy. It does not construct a gravitational evaporation channel. OpenAI is a documentary catalogue and is not a premise. This comparison is not an exhaustive audit.
• This is not metric reconstruction, not Einstein dynamics, not holographic identification, not a Page curve, and not spacetime emergence. O.1 stays NOT_CLOSED. XVI-N is not discharged. XV-B is not opened. No quantum coefficient is admitted. No compilation is asserted.

Open Hawk05-A · Page curve · Tests · Separations

Hawk05-B derives a finite Haar mean and does not derive gravitational evaporation

One logical-input-independent Haar unitary scrambles a finite code, and a conserving sequence moves cells into a growing radiation register. For every fixed pure input chosen independently of that unitary, the mean radiation entropy is the Page-Sen value. The title page names Ngo Cheung. This is a declared non-gravitational model, not black-hole evaporation.

• thm:page derives the exact finite Page-Sen mean. The value depends on the radiation and residual dimensions and not on the fixed pure input. thm:uniform gives a simultaneous all-prefix leading law for one sampled unitary. The Haar hypothesis is an extra assumption, not a consequence of Enter.
• thm:classicalpage gives the exact mean Shannon entropy of the destructive record. That mean is monotone and does not turn over. A classical album is not the coherent Page history. Hawk05-A states the record obstruction for a different schedule and is not a premise. Its supplied author field is empty and authorship is not inferred.
• thm:exact recovers the whole code only when the complete complement is constant. thm:fullcode and thm:decoupling separate that whole-code quantifier from the fixed-input entropy mean. thm:retain exhibits entropy histories with opposite endpoint recoverability. The mean does not certify the code.
• thm:flagged corrects residual leakage in the flagged model. thm:endpoint stays inside the same finite model and is not a gravitational endpoint. Em03-A's fixed-background emission law is not imported. Hawk04-D's conditional certificate is not a premise.
• thm:main keeps a conditional route to a gravitational comparison and does not construct it. No island, no quantum extremal surface, and no microscopic evaporation channel is constructed. OpenAI is a documentary catalogue and is not a premise. This comparison is not an exhaustive audit.
• This is not metric reconstruction, not Einstein dynamics, not holographic identification, not a Page curve of gravitational evaporation, and not spacetime emergence. O.1 stays NOT_CLOSED. XVI-N is not discharged. XV-B is not opened. No quantum coefficient is admitted. No compilation is asserted.

Open Hawk05-B · Page curve · Tests · Separations

Hawk05-C states a conditional two-curve extrapolation and does not derive gravitational evaporation

One finite cell-release proxy has two exact means. Coherent readout follows the Page-Sen formula. Destructive readout builds an append-only classical record whose Shannon mean does not turn over. A compatible inverse-square clock can cross those capacities only before a positive cutoff. The title page names Ngo Cheung. This is a conditional finite sketch, not black-hole evaporation.

• thm:two gives the exact coherent mean and the exact record mean for one logical-input-independent unitary. The coherent mean can turn over if the capacity crossing is traversed. The classical mean increases at every release. If the schedule stops before a crossing, no turnover is guaranteed.
• thm:compatibility says a fixed tensor-release proxy needs a constant sum of its two logarithmic capacities. A coarse entropy-production ratio different from one is not a reparametrization of Hawk05-B. Hawk05-B is a source record and is not a premise.
• thm:crossover and thm:sketch give a rounded two-curve clock for a supplied inverse-square luminosity. The clock can stop on the increasing branch. A capacity schedule is an input, not a horizon area. Hawk04-D's cutoff lifetime is not imported.
• thm:sector is an exact direct-sum mean for one conserved additive charge. thm:transfer prices entropy transfer and does not transfer recovery. thm:recovery and lem:petz complete a deterministic channel on the declared access interface. That decoder is not an island and not a gravitational receiver.
• prop:classical keeps a record-only endpoint at recovery error at least one minus one over d. thm:main is a conditional extrapolation certificate. The five missing obligations of Hawk05-B remain unconstructed. OpenAI is a documentary catalogue and is not a premise. This comparison is not an exhaustive audit.
• This is not metric reconstruction, not Einstein dynamics, not holographic identification, not a Page curve of gravitational evaporation, and not spacetime emergence. O.1 stays NOT_CLOSED. XVI-N is not discharged. XV-B is not opened. No quantum coefficient is admitted. No compilation is asserted.

Open Hawk05-C · Page curve · Tests · Separations

Hawk06-A states an operational island and does not derive gravitational evaporation

One finite vault holds a diary, an old register purified by an accessible early register, and a blank factor. A known unitary scrambles the vault, and a nested schedule releases cells. After a declared threshold, a decoder on the augmented radiation can reconstruct the diary. The physical residual stays a tensor factor. The title page names Ngo Cheung. This is an operational island, not a gravitational island.

• def:island is a reference-preserving reconstruction certificate for a logical factor that starts outside the receiver's access. The qubits do not leave the laboratory. Calling that certificate an island is a definition of this manuscript, not a gravitational surface.
• thm:exact equates exact whole-code recovery with a constant complete complement. thm:moment is the exact complementary Haar moment of the early-entangled preparation. For an old-vault dimension greater than one, that radiation entropy is not the pure Page-Sen mean.
• thm:threshold uses one cut, together with nested access, to certify every later retained cut. thm:decoder is a deterministic finite program. prop:workspace prices its quantum workspace. A mathematical recovery map is not a claim of efficient decoding.
• thm:entropy bounds the coherent entropy of the early-entangled radiation. prop:record keeps the destructive Enter record append-only. thm:joint is a positive-measure family on which accurate recovery and strict coherent turnover both occur before a cutoff that retains one physical qubit.
• thm:exactexample is an exact certificate with a positive-dimensional residual and an exhibited decoder. prop:residual says the physical residual remains the complement. prop:noduplicate produces no second commuting copy of the logical algebra. prop:EB obstructs a purely classical returned interface. A record plus a surviving quantum early register is a different interface.
• thm:cutoff stops at a predeclared positive residual. No later drain is included. thm:main is the operational-island certificate. Hawk05-B, Hawk05-C, and the OpenAI catalogue are source records and are not premises. Authorship of the supplied Hawk05-B file is not inferred here. This comparison is not an exhaustive audit.
• This is not metric reconstruction, not Einstein dynamics, not holographic identification, not a gravitational island, not a quantum extremal surface, not a replica wormhole, not a Page curve of gravitational evaporation, and not spacetime emergence. O.1 stays NOT_CLOSED. XVI-N is not discharged. XV-B is not opened. No quantum coefficient is admitted. No compilation is asserted.

Open Hawk06-A · Page curve · Tests · Separations

I-B records a finite Enter spacetime and does not derive it from records

The background is a prescribed conical product. Destructive Enter consumes a finite clock factor and returns a classical code with the surviving matter. The geometric time axis, the worldsheet defect, and the future cone remain. The title page names Ngo Cheung. This is a spacetime model with an Enter interface, not emergence of spacetime from records.

• def:experiment fixes the external geometry, finite names, accessible algebras, and a complete control interface. Geometry is supplied. prop:geometry gives signature (-,+,+,+) and unit-lapse proper time for static observers. The defect after adjoining z is a worldsheet, not a worldline.
• thm:instrument is the complete destructive clock instrument. prop:interfaces keeps destructive Enter, coherent recording, and represented nondestructive readout apart. Only the destructive instrument removes the clock names from the returned quantum context.
• def:calibration separates event-time agreement from history-label calibration. prop:fixed-event says exact agreement at one fixed event forces a deterministic clock outcome. A stochastic reading cannot equal several distinct coordinates of that same event. prop:basis says a general clock-basis change is not a spacetime coordinate transformation.
• prop:no-return refuses a universal quantum return. prop:record-residual says the classical record does not certify the residual. prop:no-ccr is a finite canonical-commutator obstruction. Enter consumes the clock encoding, not the geometric time axis.
• thm:locality and thm:metric-containment keep scheduled influence inside the prescribed metric causal relation. Ancestors of an output lie in its metric past. prop:scheduler does not select the Lorentz cone from scheduler consistency. thm:transport is exact reference-preserving SWAP transport on a declared target-adapted chain, with a resource ledger. It is not an exact-attainment claim for a previously fixed lattice.
• prop:not-source says conservation and a trace condition do not impose Einstein dynamics. prop:constant-flat requires spacetime-constant components, not mere spatial homogeneity. prop:signature records the Lorentzian signature as an extra choice. thm:lapse-composition is a classical second-order shape. A lapse jet is not the metric. prop:rod-witness detects a rod prescription and does not quantize it.
• Landmark I, En03-A, En09-A, VII-F, VIII-B, XIX-A, En08-A, En08-B, and the OpenAI catalogue are source records and are not premises. No catalogue family is a premise. This comparison is not an exhaustive audit. This is not metric reconstruction from entanglement, not Einstein dynamics, not holographic identification, not a Page curve, and not quantized relational time without an external clock. O.1 stays NOT_CLOSED. XVI-N is not discharged. XV-B is not opened. No quantum coefficient is admitted. No compilation is asserted.

Open I-B · Time · Separations

II-B adapts a finite contact certificate onto a prescribed cone and does not derive it

Manuscript II's SEP-finite fit stays an algebraic input. I-B's conical product stays a prescribed background. A complete destructive two-qubit clock supplies four outcomes, and a declared dictionary sends them to the frozen contact labels. The title page names Ngo Cheung. This is a Grade S operational adaptation, not emergence of spacetime from records.

• def:grade is the Grade S contract: prescribed geometry, a finite named experiment, a complete destructive clock, the frozen response certificate, and reference-preserving transport. Grade E, in which records determine the geometry, is not constructed.
• thm:frozen reproduces the finite certificate: target (0, 16/3, 16/3), rank 2, original minor 64, and coefficients 2/3 and 2/3. thm:pullback preserves that certificate under the declared dictionary. A finite fit is not a global contact identity and not a counterterm matrix.
• thm:instrument is the complete destructive clock. prop:no-return refuses a universal quantum return. A clock record is not the geometric time coordinate. Enter consumes the clock encoding, not the time axis.
• thm:operational-embedding is an exact finite table probe of the response vector. It is a lookup-table realization, not a measurement of a gravitational field. rem:not-convex says the linear fit is not a convex mixture of instruments.
• thm:locality keeps scheduled ancestors inside the prescribed metric past. thm:transport is exact reference-preserving SWAP transport on a target-adapted chain. En08-B's lattice resource formula is not imported. The metric and the speed remain inputs.
• prop:lapse is the optional classical second-order composition. It is not used in the conical release, which fixes unit lapse. Em02-E and XX-A are comparisons, not premises. No quantum composite lapse follows.
• II, I-B, En09-A, En03-A, En05-A, En08-B, VII-F, VIII-B, XIX-A, Em02-E, XX-A, and the OpenAI catalogue are source records and are not premises. No catalogue family is a premise. This comparison is not an exhaustive audit. This is not metric reconstruction, not Einstein dynamics, not holographic identification, not a Page curve, and not quantized relational time without an external clock. O.1 stays NOT_CLOSED. XVI-N is not discharged. XV-B is not opened. No quantum coefficient is admitted. No compilation is asserted.

Open II-B · Emergence · Separations

III-B adapts classical descent onto a supported laboratory and does not derive the cone

Manuscript III's classical descent stays an algebraic input. I-B's conical product stays a prescribed background. The laboratory is a supported regular developing chart: the punctured product is not globally hyperbolic, and evolution does not meet the singular worldsheet. A destructive clock consumes finite clock names, not the geometric time axis. A three-qubit evaluation encoding reads selected descended values and is not a continuum field instrument. The sourced successor S1–S3 is not constructed. The source is formatted as an anonymous submission. Citation of N. Cheung does not by itself assign authorship. This is a local Grade S adaptation, not emergence of spacetime from records.

• def:grade is the local Grade S contract: prescribed geometry, named classical equations, a complete destructive clock, a finite encoding of selected evaluations, and reference-preserving transport. Grade E, in which records determine the metric, is not constructed. def:laboratory is the support contract. prop:notGH shows the punctured conical product is not globally hyperbolic.
• thm:product obstructs one exhibited Poisson symbol. thm:killing classifies local massive free-shell tangency by Killing fields. thm:jet-descent retains the forced correction and supplies a past-trivial harmonic section. thm:reduced is a Hausdorff vacuum-metric triangular quotient. The metric equation stays vacuum linearized gravity. thm:compact-pair constructs a nonzero compact coupled Ward pair. prop:exact-zero says an adjoint-exact repair can vanish without every compact Ward observable vanishing.
• thm:instrument is the complete destructive clock. def:calibration separates event-time agreement from history-label calibration. prop:deterministic says exact event-time calibration with distinct labels is deterministic. Enter consumes the clock encoding, not the geometric time axis.
• thm:pilot is a three-qubit evaluation encoding of selected descended values. It is not a representation of the continuum field quotient and not a quantized gravitational observable.
• thm:locality keeps scheduled influence inside the prescribed cone. thm:transport is a target-adapted endpoint channel. A remote record-controlled operation needs a causal classical record wire. Neither theorem derives the metric.
• III, I-B, I, En09-A, En03-A, En05-A, En08-B, II, VII-E, VIII-B, XIX-A, Em02-E, XX-A, and the OpenAI catalogue are source records and are not premises. No catalogue family is a premise. This comparison is not an exhaustive audit. This is not metric reconstruction, not Einstein dynamics, not holographic identification, not a Page curve, and not quantized relational time without an external clock. O.1 stays NOT_CLOSED. XVI-N is not discharged. XV-B is not opened. No quantum coefficient is admitted. No compilation is asserted.

Open III-B · Time · Emergence · Separations

IV-B attaches three represented instruments to a prescribed cone and does not derive it

Manuscript IV's three instruments stay algebraic inputs. I-B's conical product stays a prescribed background. The field models are evaluated on a declared flat completion and pulled back through a developing chart. Local flatness is not a global cone field theory, and a timestamp is not a compact causal implementation of the global apparatus. A destructive clock consumes finite clock names, not the geometric time axis. The source is formatted as an anonymous submission. Citation of N. Cheung does not by itself assign authorship. This is a Grade-S interface, not emergence of spacetime from records.

• def:grades is the Grade-S contract: prescribed geometry, three separately represented models, a finite destructive clock, explicit dictionaries, and the stated regulator estimates. An intrinsic-cone field adaptation is not constructed. Grade E, in which records determine the metric, is not constructed.
• prop:geometry records signature (-,+,+,+), unit-lapse proper time, and a worldsheet defect. prop:no-global-transfer says a local developing isometry does not supply a global mode representation, an intrinsic Newton inverse, or a local implementation of a global controlled unitary. def:completion and lem:patch keep the models on an auxiliary Minkowski spacetime and agree only on compact pairings inside the patch.
• thm:model1, thm:model2, and thm:model3 stay separate. Model 1 removes a smooth initial edge with pointwise complete trace-norm convergence. thm:spectral-channel gives diamond-norm spectral convergence at each fixed finite particle cutoff. Model 3 retains selected finite cutoffs. A prescribed Newton-wave response is not Einstein dynamics.
• thm:instrument is the complete destructive clock. thm:composition attaches the Ramsey-Enter channel and retains untouched references. prop:event keeps exact event-time agreement distinct from a stochastic reading of several coordinates. Enter consumes the clock encoding, not the geometric time axis.
• thm:locality keeps scheduled influence inside the prescribed cone. thm:transport is exact complete transport of a finite payload on a target-adapted route. Neither theorem derives the metric or the speed. A Ramsey contrast and reference-preserving transport are not a gravity-generated entanglement test.
• IV, I-B, I, V, III, II, II-B, III-B, En09-A, En03-A, En05-A, En08-A, En08-B, VII-E, VII-F, VIII-B, XIX-A, Em02-E, XX-A, and the OpenAI catalogue are source records and are not premises. No catalogue family is a premise. This comparison is not an exhaustive audit. This is not metric reconstruction, not Einstein dynamics, not holographic identification, not a Page curve, and not quantized relational time without an external clock. O.1 stays NOT_CLOSED. XVI-N is not discharged. XV-B is not opened. No quantum coefficient is admitted. No compilation is asserted.

Open IV-B · Time · Emergence · Separations

V-B adapts admissible currents on a prescribed cone and does not derive it

Manuscript V's fixed-time response, raw current, and Newton-wave cubic are reproduced on a supported presentation. I-B's conical product stays a prescribed background. The regular product is not globally hyperbolic, and the flat Green operator is not intrinsic on the cone. A destructive clock consumes finite clock names, not the geometric time axis. Finite compression is not a finite-qubit field instrument. The source is formatted for anonymous review. Citation of N. Cheung does not assign authorship. This is local Grade S, not emergence of spacetime from records.

• def:grade is the local Grade S contract: a prescribed spacetime, the declared responses, a finite clock instrument, event dictionaries, and a reference-preserving transport ledger. Grade E, in which records determine the metric, the lapse, or the cone, is not constructed.
• prop:nonGH says the regular product is not globally hyperbolic. def:presentation is a supported regular developing chart. There is no incoming boundary data and no interaction with the singular worldsheet. A local flat chart is not a global conical Green theorem.
• thm:raw keeps the distributional current, including the initial-surface measure. thm:defect is the complete Ward defect. thm:classification separates raw and harmonic-prescription admissibility. thm:plane interpolates one admitted two-dimensional transverse-traceless plane and is not dense-TT representability. Removed Green terms are not tensorial.
• thm:external and thm:ESA are selected first retarded coefficients. thm:cubicform is a separate Newton-wave cubic, not those coefficients, not Einstein dynamics, and not the inherited characteristic coefficient. thm:cubicwitness distinguishes states that agree through degree two. A joint cutoff limit is not ultraviolet completion.
• thm:instrument compresses the represented responses and cubic forms before destructive clock readout. Enter consumes a finite clock encoding, not the geometric time axis. Exact event-time calibration with distinct labels is deterministic. Finite number compression is not a finite-dimensional one-particle space and not a finite-qubit field instrument.
• thm:locality keeps scheduled influence inside the prescribed cone. thm:transport is a target-adapted endpoint channel. A remote record-controlled operation needs a causal classical record wire. Neither theorem derives the metric or the speed.
• V, I, I-B, En09-A, En03-A, En05-A, En08-A, En08-B, III, IV, II, II-B, III-B, IV-B, VIII-B, XIX-A, Em02-E, XX-A, Oai282-A, and the OpenAI catalogue are source records and are not premises. No catalogue family is a premise. This comparison is not an exhaustive audit. This is not metric reconstruction, not Einstein dynamics, not holographic identification, not a Page curve, and not quantized relational time without an external clock. O.1 stays NOT_CLOSED. XVI-N is not discharged. XV-B is not opened. H2, I3, and J2 stay unresolved. No quantum coefficient is admitted. No compilation is asserted.

Open V-B · Time · Emergence · Separations

VI-B adapts harmonic descent on a prescribed cone and does not derive it

Manuscript VI's second-order harmonic relational descent and compact-switch defect are reproduced on a supported presentation. I-B's conical product stays a prescribed background. The regular product is not globally hyperbolic, and the flat Green operator is not intrinsic on the cone. A destructive clock consumes finite clock names, not the geometric time axis. A finite evaluation table is not a continuum field instrument. The quantum certificate remains RG-open. The source is formatted for anonymous review. Citation of N. Cheung does not assign authorship. This is local Grade S, not emergence of spacetime from records.

• def:grade is the local Grade S contract: a prescribed spacetime, named classical coefficient equations, a finite destructive clock, a finite encoding of selected evaluations, and reference-preserving transport. Grade E, in which records determine the metric, the lapse, or the cone, is not constructed.
• prop:nonGH says the regular product is not globally hyperbolic. def:presentation fixes the chart, compact tests, coefficient Cauchy data, and truncated past cones. There is no incoming boundary data and no interaction with the singular worldsheet. The defect is a worldsheet, not a worldline. A local flat chart is not a global conical Cauchy theorem. The flat Green operator is not intrinsic on the cone.
• thm:descent is second-order descent of a finite-time harmonic relational scalar. def:jet stipulates the Einstein-scalar coefficient equations, including the sourced metric row. Those equations are not derived from the clock record. A positive second-order coefficient is not Einstein dynamics derived from records.
• thm:switch-defect is an exact first-order gauge defect of a compactly switched retarded response. thm:plateau-obstruction keeps a normalized smeared gap. cor:order-obstruction says no correction beginning at second coupling order, or at positive hbar-order, removes that classical gap while the lower-order prescription is held fixed. That gap is not a quantum anomaly and not a renormalization separator.
• thm:sourced-nonzero gives a strictly positive second-order relational coefficient on a constraint-compatible sourced family. That example is not compact metric Cauchy data and is not physical backreaction. thm:certificate is a finite membership or separation alternative, not a global functional identity and not a quantum response classification.
• thm:instrument is a complete destructive clock. Enter consumes a finite clock encoding, not the geometric time axis. Finite compression of already defined evaluations is not a finite-qubit field instrument. The quantum certificate remains RG-open. No quantum Ward identity or radiative calculation is constructed.
• thm:locality keeps scheduled influence inside the prescribed cone. thm:transport moves a finite payload on a target-adapted route. Neither theorem derives the metric or the speed. A prescribed route is not a derived light cone.
• VI, I, I-B, En09-A, II, II-B, III, III-B, IV, IV-B, V, V-B, VII-A, En03-A, En05-A, En08-A, En08-B, VIII-B, XIX-A, Em02-E, XX-A, En10-A, XVI-A, Oai282-A, and the OpenAI catalogue are source records and are not premises. No catalogue family is a premise. This comparison is not an exhaustive audit. This is not metric reconstruction, not Einstein dynamics, not holographic identification, not a Page curve, and not quantized relational time without an external clock. O.1 stays NOT_CLOSED. XVI-N is not discharged. XV-B is not opened. H2, I3, and J2 stay unresolved. No quantum coefficient is admitted. No compilation is asserted.

Open VI-B · Time · Emergence · Separations

VII-A-ST adapts the plateau intertwiner on a prescribed cone and does not derive it

Manuscript VII-A's first-order plateau cancellation and second-order classical intertwiner are reproduced on a supported presentation. I-B's conical product stays a prescribed background. The regular product is not globally hyperbolic, and the flat Green operator is not intrinsic on the cone. The repair stays plateau-restricted. A larger compact gauge support keeps a negative classical gap that no higher coupling order removes. A destructive clock consumes finite clock names, not the geometric time axis. A finite evaluation table encodes already defined evaluations and does not acquire a field. The quantum certificate remains RG-open. The source is formatted for anonymous review. Citation of N. Cheung does not assign authorship. This is local Grade S, not emergence of spacetime from records.

• def:grade is the local Grade S contract: a prescribed spacetime, named classical coefficient equations, a finite destructive clock, a finite encoding of selected evaluations, and reference-preserving transport. Grade E, in which records determine the metric, the lapse, or the cone, is not constructed.
• prop:nonGH says the regular product is not globally hyperbolic. def:presentation is a supported developing chart: no incoming boundary data and no interaction with the singular worldsheet. The plateau is relatively compact and open. The defect is a worldsheet, not a worldline. A local flat chart is not a global conical Cauchy theorem. The flat Green operator is not intrinsic on the cone.
• thm:first is the first-order plateau cancellation. thm:second is the complete second-order scalar and coordinate intertwiner, including the density transformation and every switch derivative. No field equation is imposed on the metric coefficients. def:jet is a nonempty Einstein-scalar coupling jet. Those equations are stipulated, not derived from records.
• prop:defect is the exact first-order residual for a larger compact gauge support. prop:witness constructs a strictly negative smeared witness. cor:nohigherrepair says no higher coupling coefficient or positive hbar-order removes that fixed classical gap. The repair stays plateau-restricted. That gap is not a quantum anomaly and not a renormalization separator.
• A common observation plateau does not imply response equality. prop:classicalcomparison is a unique Cauchy-data-preserving comparison cocycle. Finite readout encodes already defined evaluations and does not acquire a field.
• thm:instrument is a complete destructive clock. Enter consumes a finite clock encoding, not the geometric time axis. The quantum certificate remains RG-open. No quantum product, quantum Ward identity, radiative coefficient, or counterterm separator is constructed.
• thm:locality keeps scheduled influence inside the prescribed cone. thm:transport moves a finite payload and its classical control record on a target-adapted route. Neither theorem derives the metric or the speed. A prescribed route is not a derived light cone.
• VII-A, I, I-B, En09-A, VI, VI-B, II, II-B, III, III-B, IV, IV-B, V, V-B, VII-E, VII-F, VII-G, VII-J, En03-A, En05-A, En08-A, En08-B, VIII-A, VIII-B, VIII-C, XIX-A, Em02-E, XX-A, XVI-A, Oai282-A, and the OpenAI catalogue are source records and are not premises. No catalogue family is a premise. This comparison is not an exhaustive audit. This is not metric reconstruction, not Einstein dynamics, not holographic identification, not a Page curve, and not quantized relational time without an external clock. O.1 stays NOT_CLOSED. XVI-N is not discharged. XV-B is not opened. H2, I3, and J2 stay unresolved. No quantum coefficient is admitted. No compilation is asserted.

Open VII-A-ST · Time · Emergence · Separations

VII-E-ST adapts observation boundaries and finite hybrid feedback on a prescribed cone and does not derive them

Manuscript VII-E's observation boundary and Manuscript VII-G's finite hybrid channel are reproved together on a supported presentation. I-B's conical product stays a prescribed background. The regular product is not globally hyperbolic, and the flat Green operator is not intrinsic on the cone. Record compatibility is not residual agreement. An informative classical record excludes recovery of every unknown quantum input. A four-face transverse marking is not the conical worldsheet and not a particle-link event. Matter-controlled slicing is not matter-driven gravitational dynamics. A destructive clock consumes finite clock names, not the geometric time axis. The quantum certificate remains RG-open. The source is formatted for anonymous review. Citation of N. Cheung does not assign authorship. This is local Grade S, not emergence of spacetime from records.

• def:grade is the local Grade S contract: a prescribed spacetime, named observation and evolution contracts, a finite destructive clock, a finite encoding of labels and selected residuals, and reference-preserving transport. Grade E, in which records determine the metric, the lapse, or the cone, is not constructed.
• prop:nonGH says the regular product is not globally hyperbolic. def:presentation is a supported developing chart: no incoming boundary data and no interaction with the singular worldsheet. The defect is a worldsheet, not a worldline. A local flat chart is not a global conical Cauchy theorem. The flat Green operator is not intrinsic on the cone.
• thm:pullback is the effect-pullback and full residual criterion. thm:residual-obstruction separates ideal residual targets with identical records by trace distance one half. thm:luders removes fine coherence inside a coarse outcome and need not remove coherence between coarse outcomes. Record compatibility is not residual agreement.
• thm:structure is a complete state-independent branch representation. thm:histories closes observation under declared histories. cor:informative says an informative classical record excludes recovery of every unknown quantum input, even when the declared residual is also available. A named effect or a specified code may still be preserved.
• thm:certificate is a compactly supported four-face transverse marking and its 3+1 lift, with an exact event guard. It is not VII-F's three-to-six particle event and not the conical worldsheet. thm:finite-model selects strictly ordered slices and changes no conical metric. thm:coarse-gap keeps the exact half-diamond residual gap after coarse aggregation.
• thm:instrument is a complete destructive clock. Enter consumes a finite clock encoding, not the geometric time axis. The quantum certificate remains RG-open. No quantum Ward identity or radiative coefficient is constructed.
• thm:locality-typed is a typed interface bound. thm:locality-cone keeps scheduled ancestors inside the prescribed cone once the ports are embedded. thm:transport moves payload and classical control on a target-adapted route. Neither theorem derives the metric or the speed. A prescribed route is not a derived light cone. A remote zero-duration SWAP is not admitted.
• VII-E, VII-G, I, I-B, En09-A, VII-F, VII-J, En03-A, En05-A, En08-A, En08-B, VII-A, VII-A-ST, VI, VI-B, II, II-B, III, III-B, IV, IV-B, V, V-B, VIII-A, VIII-B, VIII-C, XIX-A, Em02-E, XX-A, XVI-A, Oai282-A, and the OpenAI catalogue are source records and are not premises. No catalogue family is a premise. This comparison is not an exhaustive audit. This is not metric reconstruction, not Einstein dynamics, not holographic identification, not a Page curve, and not quantized relational time without an external clock. O.1 stays NOT_CLOSED. XVI-N is not discharged. XV-B is not opened. H2, I3, and J2 stay unresolved. No quantum coefficient is admitted. No compilation is asserted.

Open VII-E-ST · Time · Emergence · Separations

VII-F-ST adapts a particle-supported slicing certificate on a prescribed cone and does not derive it

Manuscript VII-F's three-to-six incidence is lifted to a prescribed 3+1 conical product. I-B's cone stays a background. The singular set is a worldsheet, and the laboratory stays off the defect. The regular product is not globally hyperbolic. Framed affine holonomy matches on the collar, the core, and both germs. Record compatibility is not residual agreement. An informative classical record is not recovery of every unknown quantum input. A destructive clock consumes finite clock names, not the geometric time axis, and does not measure the worldsheet. Matter-controlled slicing is not matter-driven gravitational dynamics. The quantum certificate remains RG-open. The source is formatted for anonymous review. Citation of N. Cheung does not assign authorship. This is local Grade S, not emergence of spacetime from records.

• def:grade is the local Grade S contract: a prescribed spacetime, a classical incidence certificate, a finite destructive clock, a finite encoding of already defined evaluations, and reference-preserving transport. Grade E, in which records determine the metric, the lapse, or the cone, is not constructed.
• prop:nonGH says the regular product is not globally hyperbolic. def:support is a finite sector atlas plus a compact regular laboratory whose closure is disjoint from the worldsheet. The defect is a worldsheet, not a worldline. A local flat chart is not a global conical Cauchy theorem.
• thm:spacelike lifts the transverse family to embedded uniformly spacelike markings. thm:event is the unique parameter at which the normal transverse particle link changes from three faces to six. cor:product keeps that change inside one transverse section of the worldsheet. The event changes a marking, not the ambient metric.
• thm:holonomy is one common positively primitive, reference-framed affine peripheral holonomy on the collar, the core, the outgoing star, and both zero germs. thm:reversible is an exact guarded metadata update with a forward decoder and an explicit gate bound.
• thm:pullback separates record compatibility from residual agreement. cor:residual leaves a possible residual discrepancy of trace distance one half. prop:informative says an informative classical record excludes recovery of every unknown quantum input. Intrinsic lengths and areas do not determine the event guard.
• thm:instrument is a complete destructive clock. Enter consumes a finite clock encoding, not the geometric time axis. The event code is not a detector at the worldsheet. prop:table-probe encodes a known evaluation table. The quantum certificate remains RG-open. No quantum Ward identity or radiative coefficient is constructed.
• thm:locality keeps scheduled influence inside the prescribed cone. thm:transport moves the surviving payload, location and history data, and the classical control record on a buffered target-adapted route. Neither theorem derives the metric or the speed. A prescribed route is not a derived light cone.
• VII-F, I, I-B, VII-E, VII-G, VII-J, En03-A, En05-A, En08-A, En08-B, En09-A, VIII-A, VIII-B, VIII-C, VI-B, VII-A-ST, VII-E-ST, and the OpenAI catalogue are source records and are not premises. No catalogue family is a premise. This comparison is not an exhaustive audit. This is not metric reconstruction, not Einstein dynamics, not holographic identification, not a Page curve, and not quantized relational time without an external clock. O.1 stays NOT_CLOSED. XVI-N is not discharged. XV-B is not opened. H2, I3, and J2 stay unresolved. No quantum coefficient is admitted. No compilation is asserted.

Open VII-F-ST · Time · Emergence · Separations

VII-J-ST adapts scheduled dependencies and certified causality on a prescribed cone and does not derive them

Manuscript VII-J's scheduled support, signalling criterion, and causal embedding are reproved on a supported presentation of I-B's prescribed cone. VII-F's three-to-six incidence stays an input. The singular set is a worldsheet, and no quantum register meets it. The regular product is not globally hyperbolic. A destructive clock reads an installed finite encoding, not an unknown geometry, and does not consume the geometric time axis. One buffered regular-part exchange preserves a retained reference and has a unit signalling witness on an allowed route. A cycle-velocity inclusion is not short-time causal safety. A Hamiltonian tail is not an exact Lorentzian cutoff. Matter-controlled slicing is not matter-driven gravitational dynamics. The quantum certificate remains RG-open. The source is formatted for anonymous review. Citation of N. Cheung does not assign authorship. This is local Grade S, not emergence of spacetime from records.

• def:grade is the local Grade S contract: a prescribed spacetime, complete finite channels, a finite destructive clock, proved support and causal-embedding statements, and one nonempty transport realization. Grade E, in which records determine the metric, the lapse, or the cone, is not constructed.
• prop:nonGH says the regular product is not globally hyperbolic. def:support keeps the laboratory off the worldsheet. The defect is a worldsheet, not a worldline. lem:slices is the transverse three-to-six incidence. The event changes a marking, not the ambient metric. No apex quantum register is used.
• thm:nosignal is the exact finite no-signalling criterion, including an untouched reference. A joint output can reveal a signal hidden in the marginals. thm:schedule bounds every jointly observed output by the complete scheduled ancestor set, including controllers, records, encoders, and decoders.
• thm:physical gives exact containment once dependency edges are causally embedded. thm:polytope keeps a finite-time directional remainder that an asymptotic velocity inclusion can miss. thm:signal-stability changes signalling by at most twice the half-diamond error. thm:tail is reference-stable and not an exact Lorentzian cutoff.
• thm:clock is a complete destructive clock. Enter consumes a finite clock encoding, not the geometric time axis. prop:calibration keeps the geometric incidence timestamp distinct from metadata completion. The quantum certificate remains RG-open. No quantum Ward identity or radiative coefficient is constructed.
• thm:benchmark is an exact buffered regular-part Target B exchange. lem:benchmark-causal keeps the route off the worldsheet. A unit signalling witness is a declared transport operation, not gravity-generated entanglement. A finite evaluation table encodes already defined evaluations and does not acquire a field.
• thm:release is the local Grade S package. VII-J, VII-F, I, I-B, VII-E, VII-G, En03-A, En05-A, En08-A, En08-B, En09-A, VIII-A, VIII-B, VIII-C, VI-B, VII-A-ST, VII-E-ST, VII-F-ST, and the OpenAI catalogue are source records and are not premises. No catalogue family is a premise. This comparison is not an exhaustive audit. This is not metric reconstruction, not Einstein dynamics, not holographic identification, not a Page curve, and not quantized relational time without an external clock. O.1 stays NOT_CLOSED. XVI-N is not discharged. XV-B is not opened. H2, I3, and J2 stay unresolved. No quantum coefficient is admitted. No compilation is asserted.

Open VII-J-ST · Time · Emergence · Separations

VIII-ST unifies affine matching, persistent cellulation, and certified flow on a prescribed cone and does not derive them

Series VIII matching, variable-deficit cellulation, and guarded flow are assembled on a supported presentation of I-B's prescribed cone. The singular set is a worldsheet, and the laboratory stays off it. The regular product is not globally hyperbolic. A catalogue of prescribed deficits is not the host metric: replacing a source table does not evolve the laboratory geometry. The source token is supplied, not acquired. Computational ancestry is not a physical causal past. A destructive clock reads an installed finite encoding and does not consume the geometric time axis. Reference-preserving transport moves an unknown payload with its certificate history and is not gravity-generated entanglement. The quantum certificate remains RG-open. The source is formatted for anonymous review. Citation of N. Cheung does not assign authorship. This is local Grade S, not emergence of spacetime from records.

• def:grade is the local Grade S contract: a prescribed spacetime, complete finite channels, a finite destructive clock, proved support and causal-embedding statements, and one nonempty transport realization. Grade E, in which records determine the metric, the lapse, or the cone, is not constructed.
• prop:nonGH says the regular product is not globally hyperbolic. def:support keeps the laboratory off the worldsheet. The defect is a worldsheet, not a worldline. thm:event is the unique transverse three-to-six particle-link incidence. The event changes a marking, not the ambient metric.
• def:host separates the catalogue from the fixed host. prop:fixedhost says a selected deficit does not replace the apparatus metric. thm:matching is the five-component affine certificate. prop:residual separates equal classical records from residual source functionals. prop:affine separates packet selection from expectation acquisition. The source token is supplied, not acquired.
• thm:C5 is a computational support bound, not a physical causal past. thm:physical gives containment only after a separately certified causal embedding. thm:instrument is a complete destructive clock. Enter consumes a finite clock encoding, not the geometric time axis. The quantum certificate remains RG-open. No quantum Ward identity or radiative coefficient is constructed.
• thm:transport is exact reference-preserving buffered transport of an unknown payload together with its classical certificate history. A unit signalling witness is a declared transport operation, not gravity-generated entanglement. prop:no-einstein says symmetry, conservation, and zero trace do not imply Einstein dynamics. A finite evaluation table encodes already defined evaluations and does not acquire a field.
• thm:release is the local Grade S package. VIII-A, VIII-B, VIII-C, I, I-B, VII-F, VII-F-ST, VII-J, VII-J-ST, VII-E, VII-G, VI-B, En03-A, En05-A, En08-A, En08-B, En09-A, and the OpenAI catalogue are source records and are not premises. No catalogue family is a premise. This comparison is not an exhaustive audit. This is not metric reconstruction, not Einstein dynamics, not holographic identification, not a Page curve, and not quantized relational time without an external clock. O.1 stays NOT_CLOSED. XVI-N is not discharged. XV-B is not opened. H2, I3, and J2 stay unresolved. No quantum coefficient is admitted. No compilation is asserted.

Open VIII-ST · Time · Emergence · Separations

IX-A-ST admits a sharp insertion on a prescribed cone and does not construct a quantum product

The IX-A admission domain is placed on a causally saturated regular chart of I-B's prescribed cone. The singular set is a worldsheet, and the laboratory stays off it. The regular product is not globally hyperbolic. Auxiliary Minkowski inverses are not a global conical Green operator. A normalized separator shows that unchanged regular approximants do not converge to the sharp insertion. Classical multiplication is separately continuous and is not a renormalized quantum product. A finite table encodes supplied evaluations and does not acquire a field. A destructive clock reads an installed finite encoding and does not consume the geometric time axis. Reference-preserving transport is not gravity-generated entanglement. The free quantum-product gate stays unresolved. The quantum certificate remains RG-open. The source is formatted for anonymous review. Citation of N. Cheung does not assign authorship. This is local Grade S, not emergence of spacetime from records.

• prop:nonGH says the regular product is not globally hyperbolic. def:support keeps the laboratory off the worldsheet. The defect is a worldsheet, not a worldline. lem:saturation makes the local zero-Cauchy response independent of auxiliary extensions. No global conical inverse is constructed.
• prop:adjoint and prop:trace keep the boundary term intrinsic to the actual off-shell functional. thm:separator is one on the sharp insertion and zero on every unchanged regular approximant. Faithful admission does not identify the sharp element with that regularization limit.
• thm:closure keeps bulk polynomials, exact sharp insertions, and finite classical words in the carrier. thm:separate says pointwise multiplication is separately continuous. That continuity is not joint continuity, not hypocontinuity, and not quantum associativity.
• thm:transfer locates selected already-defined free coefficients in the classical carrier. Membership of one output is not a quantum-product gate. The free quantum-product gate stays unresolved. The quantum certificate remains RG-open.
• thm:instrument is a complete destructive clock. Enter consumes a finite clock encoding, not the geometric time axis. prop:table encodes supplied evaluations and does not acquire an unknown continuum field. prop:compatibility separates equal records from residual agreement.
• thm:locality is scheduled ancestry, not a physical causal past. thm:operational is exact reference-preserving transport of an unknown payload with its certificate history. A unit signalling witness is a declared transport operation, not gravity-generated entanglement. prop:noeinstein says symmetry, conservation, and zero trace do not imply Einstein dynamics.
• thm:release is the local Grade S package. IX-A, I-B, VII-C, VII-D, VII-E, VII-G, VII-E-ST, VI-B, VII-J, VII-J-ST, En03-A, En05-A, En08-A, En08-B, En09-A, VIII-A, VIII-ST, IX-B, IX-D, and the OpenAI catalogue are source records and are not premises. No catalogue family is a premise. This comparison is not an exhaustive audit. This is not metric reconstruction, not Einstein dynamics, not holographic identification, not a Page curve, and not quantized relational time without an external clock. O.1 stays NOT_CLOSED. XVI-N is not discharged. XV-B is not opened. H2, I3, and J2 stay unresolved. No quantum coefficient is admitted. No compilation is asserted.

Open IX-A-ST · Time · Products · Emergence · Separations

IX-B-ST calibrates a numerical triangle on a prescribed cone and does not construct a sharp product

IX-B-ST certifies a source-locked numerical triangle, a derivative-spectator finite part, and one admitted partial coefficient on a prescribed conical chart, with a destructive clock and reference-preserving transport. The singular set is a worldsheet, and the laboratory stays off it. The regular product is not globally hyperbolic. Covariance blocks and the parent finite part are supplied chart data, not a conical Green operator. Regulator replacement does not evolve the host metric. It does not factor that finite part through a sharp binary multiplication or establish spacetime emergence. The source is formatted for anonymous review. Citation of N. Cheung does not assign authorship. This is local Grade S, not emergence of spacetime from records.

• prop:nonGH says the regular product is not globally hyperbolic. def:support keeps the laboratory off the worldsheet. The defect is a worldsheet, not a worldline. prop:saturation uses the IX-A-ST saturation contract and does not construct a global conical Green operator.
• prop:fixedhost says replacing a regulator or subtraction-scale label leaves the host metric unchanged. Observation differentiation is not host-metric evolution. Covariance blocks are supplied chart data.
• thm:skeletons retains eight contraction skeletons. prop:unique says H_ww=0 does not imply K=0. The residue lies on a reflected observation relation, not on an observation equality diagonal. thm:descendants transfers the parent finite part with test-order loss 64 to 64+d. The ultraviolet analysis is not re-proved.
• thm:independence says the observation-derivative orbit is not the parent conversion class. thm:regularassociation equates two regularized parenthesizations as one numerical coefficient. Neither sharp second multiplication is constructed. prop:obstruction retains the VII-C obstruction. The quantum certificate remains RG-open.
• thm:instrument is a complete destructive clock. Enter consumes a finite clock encoding, not the geometric time axis. prop:table encodes supplied evaluations and does not acquire an unknown continuum field. thm:transport is exact reference-preserving transport and is not gravity-generated entanglement.
• thm:locality is scheduled ancestry, not a physical causal past. prop:noeinstein says symmetry, conservation, and zero trace do not imply Einstein dynamics. A unit signalling witness is a declared transport operation, not gravity-generated entanglement.
• thm:release is the local Grade S package. IX-B, IX-A-ST, IX-A, I-B, VII-D, VII-C, VIII-ST, VII-J-ST, IX-C, IX-Free, IX-Free-2, IX-D, Em01-B, Em01-C, VII-H, VII-I, En05-A, En08-A, En08-B, En09-A, En10-A, En10-B, and the OpenAI catalogue are source records and are not premises. No catalogue family is a premise. This comparison is not an exhaustive audit. This is not metric reconstruction, not Einstein dynamics, not holographic identification, not a Page curve, and not quantized relational time without an external clock. O.1 stays NOT_CLOSED. XVI-N is not discharged. XV-B is not opened. H2, I3, and J2 stay unresolved. No quantum coefficient is admitted. No compilation is asserted.

Open IX-B-ST · Time · Products · Emergence · Separations

IX-C-ST certifies one partial product on a prescribed cone and does not construct a causal lift

IX-C-ST places the sequential IX-C, IX-Free, and IX-Free-2 programme on a supported chart of the prescribed cone. The singular set is a worldsheet, and the laboratory stays off it. The regular product is not globally hyperbolic. The first stage certifies products and descent criteria and does not construct either sharp second multiplication. The degree-two stage admits tree outputs and does not release either complete association. The last stage certifies degree-four descent, vanishing old overlap, and one truncated partial product through order hbar^3, with a destructive clock and reference-preserving transport. Wordwise coherence is not unspecified-triple associativity, not a causal lift, and not spacetime emergence. The source is formatted for anonymous review. Citation of N. Cheung does not assign authorship. This is local Grade S, not emergence of spacetime from records.

• IX-C-ST certifies both admitted first stages and the exact descent and coherence criteria on a prescribed chart. At this stage neither sharp second multiplication is constructed, and no metric is derived.
• IX-Free-ST, retained as the second stage of this one file, certifies presentation kernels, full mixed-kernel support, degree-two scalar descent, and three admitted tree outputs. Complete associations are not released at this stage. The cone remains prescribed.
• IX-Free-2-ST, retained as the third stage, certifies degree-four descent, vanishing overlaps, and one declared truncated partial product through order hbar^3. Wordwise coherence is not unspecified-triple associativity, a causal lift, or spacetime emergence.
• prop:nonGH says the regular product is not globally hyperbolic. def:support keeps the laboratory off the worldsheet. The defect is a worldsheet, not a worldline. prop:saturation uses the IX-A-ST saturation contract and does not construct a global conical Green operator. prop:fixedhost says regulator replacement is not host-metric evolution.
• thm:separation separates every nonzero sharp generator from the partial contractions and the old microcausal algebra. thm:oldgluing eliminates the old overlap of the whole new-domain sum. C_desc and C_glue are all of R only relative to the stated inputs. prop:obstruction retains the VII-C obstruction. The quantum certificate remains RG-open.
• thm:instrument is a complete destructive clock. Enter consumes a finite clock encoding, not the geometric time axis. thm:table encodes supplied evaluations and does not acquire an unknown continuum field. thm:transport is exact reference-preserving transport and is not gravity-generated entanglement.
• thm:locality is scheduled ancestry, not a physical causal past. prop:noeinstein says symmetry, conservation, and zero trace do not imply Einstein dynamics. thm:release is the local Grade S package. IX-C, IX-Free, IX-Free-2, IX-A-ST, I-B, VII-D, VII-C, IX-B-ST, VIII-ST, VII-J-ST, IX-D, V, Em01-B, Em01-C, VII-H, VII-I, En05-A, En08-A, En08-B, En09-A, En10-A, En10-B, and the OpenAI catalogue are source records and are not premises. No catalogue family is a premise. This comparison is not an exhaustive audit. This is not metric reconstruction, not Einstein dynamics, not holographic identification, not a Page curve, and not quantized relational time without an external clock. O.1 stays NOT_CLOSED. XVI-N is not discharged. XV-B is not opened. H2, I3, and J2 stay unresolved. No quantum coefficient is admitted. No compilation is asserted.

Open IX-C-ST · Time · Products · Emergence · Separations

IX-D-ST organizes causal interfaces on a prescribed cone and does not construct a time-ordered product

IX-D-ST places the ordered IX-D, IX-E, IX-E-2, and IX-E-3 programme on a supported chart of the prescribed cone. The singular set is a worldsheet, and the laboratory stays off it. The regular product is not globally hyperbolic. Free coherence is not time ordering. The commutator vanishes on the strongly separated class, and a nonzero observation-spacelike control is not, by itself, a two-way obstruction. The null-sphere bridge holds under the boundary-trace certificate. That certificate stays unverified for the weak inherited adjoint, and a specified flat realization does not identify it. A support bridge is not a sharp time-ordered product. No sharp time-ordered product is constructed. The source is formatted for anonymous review. Citation of N. Cheung does not assign authorship. This is local Grade S, not emergence of spacetime from records.

• IX-D-ST, the first stage, certifies causal interfaces, support bounds, the scalar non-lift, and conditional subtraction. At this stage no sharp time ordering and no normalized retarded map are constructed, and no metric is derived.
• IX-E-ST, retained as the second stage of this one file, certifies the ordering geometry, the first-stage commutator identity, the fixed-domain obstruction criterion, and the algebraic extension criterion. The criterion is not a universal obstruction, and the analytic extension is not released.
• IX-E-2-ST, retained as the third stage, evaluates the imaginary part of the locked kernel. The commutator vanishes on the entire strongly separated class. A nonzero observation-spacelike control is not a certified two-way pair of actual functional supports.
• IX-E-3-ST, retained as the fourth stage, proves exact support of the quadratic slot and the null-sphere bridge under the boundary-trace certificate. A solid-ball lower-support assertion is false in the specified flat realization. The weak inherited certificate stays unverified.
• prop:nonGH says the regular product is not globally hyperbolic. def:chartcausal keeps chart causal sets inside the retained laboratory. The defect is a worldsheet, not a worldline. ass:carrier uses the IX-A-ST carrier and does not construct a global conical Green operator. prop:fixedhost says regulator replacement is not host-metric evolution.
• thm:instrument is a complete destructive clock. Enter consumes a finite clock encoding, not the geometric time axis. prop:table encodes supplied evaluations and does not acquire an unknown continuum field. thm:transport is exact reference-preserving transport and is not gravity-generated entanglement.
• thm:locality is scheduled ancestry, not a physical causal past. thm:release is the local Grade S package and keeps the causal-product verdict Unresolved. IX-D, IX-E, IX-E-2, IX-E-3, IX-C-ST, IX-Free-2, IX-A-ST, I-B, VII-D, VII-C, IX-B, IX-B-ST, VIII-ST, VII-J-ST, En05-A, En08-A, En08-B, En09-A, En10-A, En10-B, and the OpenAI catalogue are source records and are not premises. No catalogue family is a premise. This comparison is not an exhaustive audit. This is not metric reconstruction, not Einstein dynamics, not holographic identification, not a Page curve, and not quantized relational time without an external clock. O.1 stays NOT_CLOSED. XVI-N is not discharged. XV-B is not opened. H2, I3, and J2 stay unresolved. No quantum coefficient is admitted. No compilation is asserted.

Open IX-D-ST · Time · Products · Emergence · Separations

Hawk07-A states an operational wormhole and does not derive a geometric bridge

One finite vault holds a diary, an old register purified by accessible early memory, and a blank factor. A nested schedule names an accessible register and a positive residual. After a declared threshold, one decoder on the accessible side returns the diary. The physical residual stays a tensor factor. The title page names Ngo Cheung. This is an operational wormhole, not an Einstein-Rosen bridge.

• def:wormhole is a two-mouth reconstruction certificate: an isometry into an accessible register and a residual, a deterministic decoder, and a reference-preserving error allowance. Mouths are named output factors. The throat is the complete complementary channel, not a tunnel. The qubits do not leave the laboratory.
• prop:global restores the code from the complete output. thm:exact equates exact whole-code recovery with a constant complete complement. lem:KSW separates the two directions: a nearly constant complement is an upper bound, and a nearly constant accessible channel is a lower bound.
• prop:nested says recovery error and complete leakage are nonincreasing under this release. An intermediate entropy maximum is not their maximum. thm:threshold uses one cut to certify every later retained cut. thm:decoder is one fixed deterministic core. A mathematical recovery map is not a claim of efficient decoding.
• thm:entropy bounds the coherent entropy of the early-entangled radiation. prop:record keeps the destructive Enter record append-only. thm:joint is a positive-measure family on which accurate recovery and a strict three-cut coherent turnover both occur before a cutoff that retains one physical qubit.
• prop:classical keeps a purely classical returned interface from beating the record-only bound. prop:noduplicate produces no second commuting code-preserving copy of the logical algebra. prop:residual says the physical residual remains the complement. prop:drop and prop:physicaldiscard equate terminal readout and forgetting with partial trace on the returned interface, not physical annihilation.
• thm:cone is a finite release schedule, not a causal curve through a throat. prop:nosignal does not construct a gravitational signal crossing. thm:main is the operational-wormhole certificate. Hawk06-A, Hawk05-B, Hawk05-C, and the OpenAI catalogue are source records and are not premises. Authorship of the supplied Hawk05-B file is not inferred here. This comparison is not an exhaustive audit.
• This is not metric reconstruction, not Einstein dynamics, not holographic identification, not an Einstein-Rosen bridge, not a Morris-Thorne throat, not ER=EPR as geometry, not a Page curve of gravitational evaporation, and not spacetime emergence. O.1 stays NOT_CLOSED. XVI-N is not discharged. XV-B is not opened. No quantum coefficient is admitted. No compilation is asserted.

Open Hawk07-A · Page curve · Tests · Separations

Hawk07-B states operational functions and does not derive a geometric wormhole

The finite certificate is scaled. A sufficient threshold prices the released dimension by an inverse square, not the entire receiver. Whole-code return is stronger than a beacon. Square-power dimensions can show recovery together with coherent entropy turnover, and the destructive album does not fall. A convoy needs separately prepared resources. Leakage does not supply memory reset. The title page names Ngo Cheung. This is an operational function certificate, not a geometric wormhole.

• def:certificate names a complete isometry, a deterministic quantum-return map, a diamond error, a physical residual, and no second commuting code-preserving copy. Mouths are named output factors. The throat is the complete complementary channel, not a tunnel. The qubits do not leave the laboratory.
• thm:correction equates exact whole-code recovery with a constant complete complement. The two recovery inequalities are not swapped. A record-only interface keeps the classical floor. prop:noduplicate produces no second commuting copy of the logical algebra.
• thm:moment rederives the complementary Choi moment at the declared payload dimension. Hawk07-A is not silently reused. thm:threshold gives a sufficient released dimension with inverse-square scaling. thm:design prices the payload against the resource before a positive cutoff. prop:decoder prices batch occupancy. Sequential occupancy is a different question.
• thm:functions certifies referenced return, entanglement transfer, a classical message, and logical postprocessing. A beacon is weaker than the payload. thm:privacy is privacy against the complete residual. thm:teleport needs a classical label plus surviving quantum early memory. prop:nosignal says a Bell resource alone cannot signal.
• thm:turnover and cor:scaledturnover show square-power coexistence of recovery and strict coherent entropy turnover, with measure at least one over 4d, and one physical residual qubit. The destructive album is nondecreasing. thm:convoy bounds a finite convoy of separately prepared sessions, including mutually entangled payloads. thm:resetcomposition says small previous leakage does not supply memory reset.
• thm:noise reserves error headroom for channel and decoder error. prop:discard equates terminal Enter and dropBit with partial trace. That equality leaves the already-returned accessible channel unchanged. It is not annihilation and not a fuel bill. thm:main is the operational function certificate.
• Hawk07-A, Hawk05-A, Hawk05-B, Hawk05-C, and the OpenAI catalogue are source records and are not premises. Authorship of the supplied Hawk05-B file is not inferred here. Entanglement assistance is an input. This comparison is not an exhaustive audit. This is not metric reconstruction, not Einstein dynamics, not holographic identification, not a geometric wormhole, not an Einstein-Rosen bridge, not a Morris-Thorne throat, not ER=EPR as geometry, not material spacecraft transport, not a fuel bill, not a Page curve of gravitational evaporation, and not spacetime emergence. O.1 stays NOT_CLOSED. XVI-N is not discharged. XV-B is not opened. No quantum coefficient is admitted. No compilation is asserted.

Open Hawk07-B · Page curve · Tests · Separations

En04-A separates magic from residual response and does not derive geometric backreaction

After a finite quantum carrier exists, residual response means the complete complementary channel is not constant on the logical code. Exact whole-code recovery from radiation is that constancy. A non-Clifford resource does not force the response, and a responding residual is not geometric backreaction.

• def:response says the complete residual responds when the complementary channel is not a replacement channel on the logical code. Dependence of a fixed replacement state on an external coupling is not, by itself, logical-input response. No rigid geometry is defined by Cliffordness.
• thm:global proves a CPTP left inverse of the complete unitary channel. The restore map returns the code from the complete output RB. It does not relocate the diary into the residual. Residual-only recovery needs its own condition. Hawk04-A states the same restore structure for a different formulation and is not a premise.
• thm:exact recovers the entire code from radiation if and only if the complete complement is constant, and supplies the decoder. cor:nohiding says both outputs cannot independently recover the whole unknown code. A positive residual witness shows that the residual distinguishes some logical inputs. It does not prove residual-only recovery of the entire code.
• cor:noimplication separates the claims. A Clifford copying circuit responds, with leakage and radiation recovery error one half, and with no magic. A local non-Clifford gate, and even a fixed syndrome containing bipartite non-local magic, can leave the logical code exactly recoverable. Magic is not leakage. thm:cliffordcriterion is a Pauli-compression test for Clifford encoders, not a geometric label.
• thm:rotation constructs one controlled-rotation family. Complete leakage is sin theta over 2, and radiation recovery error is (1 minus cos theta) over 2, for theta from 0 to pi over 2. Those formulas are model-specific. thm:linearresponse is a first-order sufficient witness under a declared deformation, not a universal magic law.
• thm:majorana retains the four-Majorana recovery obstruction and does not read it as a magic certificate. Radiation recovery error is already one half at zero coupling, and coupling can only increase that error. Family 227 is not a scrambling estimate for that control. Hawk04-A is a source record and is not a premise.
• thm:drop equates residual readout followed by dropBit with the partial trace. The radiation channel is unchanged. That equality is operational forgetting, not permanent physical deletion. prop:readoutdilation keeps a coherent apparatus factor that the classical record omits. thm:classical keeps a classical-output process from reconstructing an unknown quantum code, with error at least one minus one over d. Enter is destructive readout, not the decoder and not deletion. Landmark I is optional semantic input after the carrier is qubits and is not a premise.
• prop:recurrence says a fixed finite proxy returns arbitrarily late, so the limsup of the recovery error is one minus d to the minus two. That is not persistent leakage at every time, and it does not identify the origin as magic. thm:endpoint requires access-preserving output identifications. Mixing radiation and residual changes the task. cor:bridge leaves geometric backreaction conditional on a same-model dictionary: identified degrees of freedom, a declared geometric observable, a coupling, an interval, and a limit. A nonconstant residual is not backreaction. sec:conclusion leaves a metric, a field-to-memory receiver, and a gravitational endpoint unproved.
• OpenAI is a documentary catalogue. Families 227, 279, 274, and 276 by OpenAI are documentary labels and are not premises. Family 227 is not a scrambling or OTOC evaluation. Family 279 is not a compilation theorem for the controlled rotation. Hawk04-A, Hawk04-B, Hawk02-E, En03-A, En02-B, En02-C, En02-E, Em03-C, XIV-H, XIV-I, XIV-J, XV-B, and XVI-N are source records and are not premises.
• This is not metric reconstruction, not Einstein dynamics, not holographic identification, not a Page curve, and not spacetime emergence. H2, I3, and J2 stay unresolved. O.1 stays NOT_CLOSED. The series Route B is not discharged. XVI-N is not discharged. XV-B is not opened. XVI-P is registered and is not a premise. No quantum coefficient is admitted. No compilation is asserted.

Open En04-A · Emergence problem · Page curve · Separations

En05-A states an exact causal cone and does not derive an invariant speed

Partitioned updates of diameter at most r have an exact schedule cone. The schedule past upper-bounds influence. A relay attains that lattice speed. Neither fact is a Euclidean metric, an invariant physical speed, or spacetime emergence.

• lem:comparison equates snapshot factorization, equal output snapshots, and adjoint support containment. Reference stability needs the joint cone-reference reductions to agree. Equality on the cone alone is not enough.
• thm:cone and cor:influence make the schedule past an upper bound, not an equality with influence. The metric envelope is d(x,Y) at most r times (T minus s). En03-A lem:one-layer is a source comparison and is not a premise.
• prop:attain gives an explicit relay with c_lat equal to r on the stated lattices. The universal upper bound stays at most r. Finite-program soundness needs a compositional interface. Simulation needs routing from every starting tick.
• prop:drop separates destructive Enter from unrestricted coherent recording. Operational discard is the partial trace, not permanent deletion. def:response is non-constancy of the complete complement. prop:restore does not relocate the diary into the residual. prop:classical says a classical record is not a quantum decoder. En04-A and Hawk04-B are source records and are not premises.
• thm:isotropyobstruction and prop:diamond keep a fixed finite periodic model inside a velocity polytope. The cardinal model is an ell-one diamond, not a Euclidean ball. VII-J thm:polytope is a source comparison and is not a premise.
• thm:boostobstruction shows that unrestricted boost-closure, together with composition and well-founded executability, excludes ordinary bidirectional one-tick relays. Fixed-gate retiming is not device boost-closure. Physical retiming-stability is withdrawn. VII-E thm:retiming is not a premise.
• thm:teleport states entanglement-assisted transfer with its Bell resource, communication, and charged ticks. A constant overhead does not prove super-cone transport. thm:longrange keeps long-range completely positive channels affine and unable to clone.
• Continuum domain of dependence, operational no-signalling, algebraic microcausality, and a frame-invariant speed are proved only under hypotheses C1 through C7. Algebraic microcausality needs localized observables, not merely commuting superoperators. conj:family and conj:opcov remain open. No invariant physical speed is claimed. Anisotropy is not a contradiction of no-signalling relative to the anisotropic cone.
• prop:approx is an approximate cone certificate with a diamond allowance. A finite-graph check with N at most 20 is a programme, not an execution. VIII-B thm:dictionary is not the scheduled past. Em02-E thm:lapse is not the frame group in C7. XIV-I's I2 amplitude is not the full joint map at I3 and J2. The H2 stop in XIV-H is not that later advance.
• OpenAI is a documentary catalogue. Families 279, 227, 274, 276, 212, and 356 by OpenAI are documentary labels and are not premises. Family 279 is not a compilation theorem for the relay or the block instruments. Family 227 is not a scrambling estimate. Family 356 is not the Alexandrov-Zeeman theorem. Landmark I is optional semantic input after the carrier is qubits and is not a premise.
• This is not metric reconstruction, not Einstein dynamics, not holographic identification, not a Page curve, and not spacetime emergence. H2, I3, and J2 stay unresolved. O.1 stays NOT_CLOSED. The series Route B is not discharged. XVI-N is not discharged. XV-B is not opened. XVI-P is registered and is not a premise. No quantum coefficient is admitted. No compilation is asserted.

Open En05-A · Emergence problem · Page curve · Separations

En05-B constructs one isotropic operational limit and does not derive a metric

One declared family of partitioned substrates makes the Euclidean envelope and the scheduled past converge under one clock. The operational speed equals the prescribed c. That speed is an input of the construction, not a metric extracted from entanglement, and not spacetime emergence.

• thm:main separates transport lanes from junction interfaces. Every junction is one block. Lane interiors are disjoint nearest-neighbor pairs, so increasing directional resolution does not add a direction-by-direction service delay.
• thm:metric controls every intermediate site, not only hubs. thm:routing charges routes from every starting tick. Excess time vanishes on bounded journeys. En05-A's conditional continuum hypotheses are not premises and are not discharged.
• thm:identity transports a finite quantum register as the logical identity, including untouched references. thm:relay gives classical relays with total-variation gap one in every Euclidean direction. Destructive Enter is not that identity channel. Hawk04-B and En04-A are source records and are not premises.
• thm:realization and thm:matched realize the declared finite-circuit class and local replacements on a common schedule. thm:completion retains local channels and intervention slots. prop:weakC4 does not infer a unique instrument from one terminal law.
• cor:maxspeed equals the prescribed c for this class. No uniform degree, block cardinality, or interface-dimension bound is claimed. No spacetime observable algebra and no frame group are constructed. VII-J's velocity polytope is a comparison and is not a premise.
• OpenAI is a documentary catalogue and is not a premise. Landmark I is optional semantic input after the carrier is qubits and is not a premise. XIV-I's I2 amplitude is not the full joint map at I3 and J2.
• This is not metric reconstruction, not Einstein dynamics, not holographic identification, not a Page curve, and not spacetime emergence. H2, I3, and J2 stay unresolved. O.1 stays NOT_CLOSED. The series Route B is not discharged. XVI-N is not discharged. XV-B is not opened. XVI-P is registered and is not a premise. No quantum coefficient is admitted. No compilation is asserted.

Open En05-B · Emergence problem · Page curve · Separations

En06-A separates proved layers from an invariant speed

Discrete cones, an increasing-stencil Euclidean envelope, and one restricted outcome-law theory are kept apart. Unrestricted device closure stays withdrawn. None of those layers is an invariant physical speed or spacetime emergence.

• lem:comparison equates snapshot factorization, equal snapshots, and adjoint support. The proof is self-contained. En05-A's comparison is a source record and is not a premise.
• thm:order and thm:metric give scheduled ancestry and its metric envelope. thm:foliation is legal reordering of one finite network and is not a boost. VII-E thm:retiming is not a premise.
• thm:coneconv is a Euclidean limiting envelope for changing word metrics. thm:relays attain speed c in every direction for admissible relays of that geometry. A fixed periodic model remains inside a velocity polytope. VII-J is not a premise.
• thm:coarseDOD, prop:coarseNS, and cor:coarsespeed hold only for one full-tail fixed-wire outcome-law theory. That is not an instrument-level scaling limit. The common-final-tick source class is not boost closed.
• thm:algmicro does not promote commuting channels to algebraic microcausality. thm:withdrawal keeps unrestricted device resynchronization withdrawn because it excludes ordinary bidirectional relays. prop:lanecounter and prop:innercounter record failed predecessor shortcuts.
• The registered En05-B construction is a separate existence theorem and is not a premise of this audit. The working designation En05-B in the combination plan is not that sheet. OpenAI is a documentary catalogue and is not a premise. Landmark I is optional semantic input and is not a premise.
• This is not metric reconstruction, not Einstein dynamics, not holographic identification, not a Page curve, and not spacetime emergence. H2, I3, and J2 stay unresolved. O.1 stays NOT_CLOSED. The series Route B is not discharged. XVI-N is not discharged. XV-B is not opened. XVI-P is registered and is not a premise. No quantum coefficient is admitted. No compilation is asserted.

Open En06-A · Emergence problem · Page curve · Separations

En05-C separates state restriction from a relativistic gauge theory

Equal state restrictions, local factorization, and Heisenberg containment are equivalent without a spatial tensor factor. A finite gauge net and a finite-mode refinement are constructed. Neither is a relativistic field theory or spacetime emergence.

• thm:comparison equates snapshot determinacy, a unique UCP local channel, and containment of the pulled-back output algebra. lem:separation uses Jordan decomposition. No complementary state and no spatial complement are used. cor:tensorcase recovers the hybrid comparison of En05-A, En05-B, and En06-A as a special case. Those sheets are source records and are not premises.
• prop:centers keeps sector probabilities in the affine snapshot. Equal conditional states do not determine the center. prop:relative makes a restricted preparation class equivalent to an annihilator, not automatically to the regional algebra. cor:reference amplifies an independent matrix factor. A charge-linked reference needs a joint constrained algebra.
• prop:extensiongap shows that two global devices can agree on a regional algebra and disagree across the boundary. prop:sharedcenter obstructs independently changing shared flux. Exterior fixation is not membership in the declared regional algebra.
• thm:onelayer and thm:ancestry hold for specified internal Kraus devices in a locally commuting net. They do not hold for an arbitrary regional UCP map. thm:nosignalling is unconditioned no-signalling for a device that fixes the declared algebra. cor:influence keeps ancestry as an upper bound, not equality with influence. VII-G and VII-J are source records and are not premises.
• thm:normal is the von Neumann version for all normal states. A normal conditional expectation is not assumed. thm:sequence and thm:refinementnet construct a product-preserving bounded-sequence limit and an exact finite-mode spatial gauge refinement. That refinement keeps four physical dimensions. It is not a continuum Yang-Mills theory.
• OpenAI is a documentary catalogue and is not a premise. Landmark I is optional semantic input after a measured register is selected and is not a premise. Enter remains destructive readout. A nontrivial center is not geometric backreaction. XIV-I's I2 amplitude is not the full joint map at I3 and J2.
• This is not metric reconstruction, not Einstein dynamics, not holographic identification, not a Page curve, and not spacetime emergence. H2, I3, and J2 stay unresolved. O.1 stays NOT_CLOSED. The series Route B is not discharged. XVI-N is not discharged. XV-B is not opened. XVI-P is registered and is not a premise. No quantum coefficient is admitted. No compilation is asserted.

Open En05-C · Emergence problem · Page curve · Separations

En06-B constructs one finite transport and does not derive a field theory

Every finite future-causal fixed-wire network is realized on one increasing-stencil family. Residue lanes stay disjoint, the complete instrument is preserved, and one Bell specimen has a commuting observable net. None of that is a quantum field theory or spacetime emergence.

• lem:midpoint replaces each calibrated block by a causal midpoint graph. The coarse Hausdorff error is independent of the number of vertices. Extra declared-support points stay metadata and are not the minimal physical support.
• lem:residues reserves disjoint residue classes inside one ordinary lattice, including in one spatial dimension. Geometric crossings do not identify sites. lem:pacing controls every prefix of a rounded affine path, not only the endpoint. A boosted idle wire is paced, not sent early and then parked.
• lem:junction charges a finite swap-payload-swap frame a vanishing physical time. thm:schedule runs long routes in parallel. Serialization is not used as a global slowdown. The coarse coefficient does not grow with source-network complexity.
• thm:identity preserves the complete logical instrument exactly, including every untouched reference. thm:T is the transport contract for this family. thm:diagonal is the full-tail argument after that contract. En06-A's conditional contract and En05-B's junction-clique family are source records and are not premises.
• prop:Bellinstrument keeps local setting inputs, retained quantum outputs, and an untouched quantum memory. thm:microcausality proves spacelike commutation at a common circuit cut, not by disjoint ancestors. thm:observablelimit uses product-preserving logical identifications. thm:pairing equates instrument probabilities with observable-state pairings. The prepared Bell law has CHSH value 2 times the square root of 2, and unconditioned marginals do not depend on the remote setting.
• prop:obstruction shows that a fixed cardinal stencil still fails. The constant c is an input. cor:transportedBell moves one finite specimen. It is not an exact microscopic boost symmetry. En05-A's velocity polytope and En05-C's tensor-free comparison are source records and are not premises. OpenAI is a documentary catalogue and is not a premise. Landmark I is optional semantic input and is not a premise. Enter remains destructive readout.
• This is not metric reconstruction, not Einstein dynamics, not holographic identification, not a Page curve, and not spacetime emergence. H2, I3, and J2 stay unresolved. O.1 stays NOT_CLOSED. The series Route B is not discharged. XVI-N is not discharged. XV-B is not opened. XVI-P is registered and is not a premise. No quantum coefficient is admitted. No compilation is asserted.

Open En06-B · Emergence problem · Page curve · Separations

En07-A frames a complete residual and does not derive a Landauer cost

Complete restoration, exact complement constancy, and readout-and-drop as partial trace are restated locally. Channel equality does not fix heat, work, or reset cost. None of that is holographic identification or spacetime emergence.

• thm:global restores a complete isometry on the joint output. That map is a complete-access decoder, not a radiation-only decoder. thm:exact equates whole-code recovery from the accessible factor with constancy of the complete complement. cor:nohiding says the two complementary outputs cannot independently recover the entire unknown code.
• lem:erasure-interface equates destructive readout followed by classical discard with partial trace, including external references. The coherent dilation is isometric. It is not a thermodynamic implementation certificate. prop:local says an ignored local operation leaves untouched outputs unchanged. Reset of a completed record is a different type.
• thm:classical bounds record-only reconstruction by one minus one over d. prop:featureless bounds deterministic recovery error by the maximum of zero and one minus d to the minus two minus eta. prop:flagged is an exact flagged transfer whose destination is the complete output, not physical deletion.
• prop:no-landauer-from-channel says equality with partial trace does not determine heat, work, or reusable-memory reset cost. Conservation of a declared Hamiltonian is a separate assertion. cor:dimension is a Hilbert-space count, not an area law. prop:entropy shows that selected zero radiation entropy does not identify recovery. cor:gravity stays conditional on four same-model hypotheses that are not constructed.
• rem:holography-refusal withholds area laws, islands, Page curves, and bulk-boundary dictionaries. Hawk04-B, Hawk04-A, En04-A, En06-B, En05-C, XVII-A, and Landmark I are source records and are not premises. This registered note is not the gauge-theory designation refused by En05-C. OpenAI is a documentary catalogue and is not a premise. Enter remains destructive readout.
• This is not metric reconstruction, not Einstein dynamics, not holographic identification, not a Page curve, and not spacetime emergence. H2, I3, and J2 stay unresolved. O.1 stays NOT_CLOSED. The series Route B is not discharged. XVI-N is not discharged. XV-B is not opened. XVI-P is registered and is not a premise. No quantum coefficient is admitted. No compilation is asserted.

Open En07-A · Emergence problem · Page curve · Separations

En07-B certifies a finite endpoint and does not construct a gravitational one

Outgoing recovery follows when four same-model obligations are supplied. A nearly constant complete complement is an upper bound on recovery error. A nearly constant accessible output is a lower bound. Neither direction is spacetime emergence.

• thm:global restores the complete output, including references. That map is not a radiation-only decoder. thm:exact equates outgoing recovery with constancy of the complete complement and writes an explicit deterministic decoder. cor:nohiding says the two outputs cannot both recover the whole unknown code.
• conv:normalization uses half-diamond distance. The corresponding unhalved diamond bounds are twice the stated values. lem:erasure-interface equates destructive readout followed by drop with partial trace. thm:classical bounds a classical record by one minus one over d. prop:not-annihilation says that equality is not physical annihilation.
• thm:approx imports the Kretschmann–Schlingemann–Werner theorem and converts it. If the complete complement is within half-diamond distance zeta of a replacement channel, recovery error is at most the minimum of 1 and the square root of 2 zeta. prop:featureless says that if the accessible output is within eta of a replacement channel, recovery error is at least the maximum of zero and one minus d to the minus two minus eta. Those hypotheses cannot be interchanged.
• thm:endpoint is the access-preserving certificate. def:four names complete preparation, complete evolution, outgoing access with an endpoint, and a complement allowance. None of the four is constructed here. cor:gravity stays conditional. Finite-program termination is not an evaporation endpoint. Channel equality does not fix a Landauer cost.
• Hawk04-B, En07-A, Hawk04-A, Hawk03-A, En06-B, En05-C, XVII-A, and Landmark I are source records and are not premises. OpenAI is a documentary catalogue and is not a premise. Enter remains destructive readout.
• This is not metric reconstruction, not Einstein dynamics, not holographic identification, not a Page curve, and not spacetime emergence. H2, I3, and J2 stay unresolved. O.1 stays NOT_CLOSED. The series Route B is not discharged. XVI-N is not discharged. XV-B is not opened. XVI-P is registered and is not a premise. No quantum coefficient is admitted. No compilation is asserted.

Open En07-B · Emergence problem · Page curve · Separations

En07-C types Hawking radiation and does not construct an evaporation channel

Hawking's late-time occupation formula and temperature are external semiclassical inputs. Outgoing recovery still requires a constant complete complement. A thermal spectrum is not spacetime emergence.

• thm:global restores the complete output, including references. That map is not a radiation-only decoder. thm:exact equates outgoing recovery from the accessible factor with constancy of the complete complement and writes an explicit deterministic decoder. cor:dimension is a residual-rank bound, not an area law. cor:nohiding says the two outputs cannot both recover the whole unknown code.
• lem:erasure-interface equates destructive basis readout followed by forgetting with partial trace. The coherent dilation is isometric. It is not a thermodynamic certificate. thm:classical bounds a classical record. prop:not-annihilation says that equality is not physical annihilation.
• prop:featureless says that if the accessible channel is within half-diamond distance eta of a replacement channel, recovery error is at least the maximum of zero and one minus d to the minus two minus eta. thm:approx imports the Kretschmann–Schlingemann–Werner theorem. A nearly constant complete complement is a recovery upper bound. Those hypotheses cannot be interchanged. A thermal occupation number is not itself that replacement channel.
• prop:entropy says selected entropy does not identify recovery. prop:no-landauer-from-channel says channel equality does not fix heat, work, or reset cost. prop:insufficiency separates thermal data, energy drain, and termination from outgoing recovery. thm:endpoint and cor:gravity stay conditional on four same-model obligations that are not constructed.
• En07-B, En07-A, Hawk04-B, Hawk04-A, Hawk03-A, En06-B, and Landmark I are source records and are not premises. OpenAI is a documentary catalogue and is not a premise. Family 265’s area law is not this thermal input and not a Page curve. Enter remains destructive readout.
• This is not metric reconstruction, not Einstein dynamics, not holographic identification, not a Page curve, and not spacetime emergence. H2, I3, and J2 stay unresolved. O.1 stays NOT_CLOSED. The series Route B is not discharged. XVI-N is not discharged. XV-B is not opened. XVI-P is registered and is not a premise. No quantum coefficient is admitted. No compilation is asserted.

Open En07-C · Emergence problem · Page curve · Separations

Oai265-A prices a conditional area law and does not verify Family 265

Oai265-A is the supplied 14 October 2026 development. The identifier is Oai265-A. The source withholds a Cheung endorsement, and the companion does not resolve that conflict. It freezes the induced-graph boundary and the full-system gap, proves a terminal two-family entropy certificate, and names the missing information charges that would price an area-law constant. 265-01 and 265-02 are not verified. No graph cut is a horizon, an island, or a time-dependent radiation entropy. This is not a Page curve and not spacetime emergence.

• lem:boundary converts the cut, the inner boundary, and both endpoint sets. The factor 2 needs endpoints on both sides. lem:components handles a zero boundary without assuming the external area law. lem:cancellation proves the two-family entropy bound and does not construct the partition or the mutual-information charges.
• thm:terminal prices S at most a stated combination of depth, local dimension, and supplied information charges, times the boundary size. Those charges are not derived from the gap. A decoder ledger and a diamond error budget do not supply them. The single active successor is quantitative constant extraction. Formalization, algorithmic PEPS, unrestricted degeneracy, and a strict area law stay blocked.
• prop:cut keeps a PEPS cut bound separate from tensor production, contraction, and preparation. 265-02 remains an existence record. Dropping uniqueness permits a volume-law ground vector. A full-system gap does not imply a uniform restricted gap. An entropy upper bound is not a strict area-law equality. Complementary mutual information and Renyi entropies of order greater than one do have elementary bounds once a von Neumann area law is assumed. Those corrections are not a verification of Family 265.
• thm:recovery equates reference-preserving recovery with the complete complement. lem:constant gives the replacement-channel error one minus d to the minus two. Complete isometries can agree on every pure-input accessible spectrum and still have recovery errors 0 and one minus d to the minus two. Selected spectra are not recovery. Uniformly gapped bond-dimension-two ground states permit both turnover and no turnover. Their preparation dynamics are separate data.
• prop:forty is a procedure-dependent forty-shot nonacceptance. It is not a universal sample lower bound. Oai265-B remains a separate finite-sample certificate and is not a calibration of this area law. Canonical265.lean canonicalizes moments. It is not an area-law formalization. No Lean execution is claimed.
• thm:separation and thm:release keep the record from a horizon, an island, a quantum extremal surface, a replica wormhole, and a radiation history. En02-A, En02-B, En02-C, En07-A, En07-B, En07-C, Hawk04-A, Hawk04-B, Oai283-A, XXII-B, and Landmark I are source records and are not premises. The ledger is scoped. It is not an exhaustive audit of every catalogue manuscript. Enter remains destructive readout.
• Against the standing problems the audit is a boundary, not an answer. It does not complete Einstein gravity in the ultraviolet. It does not derive spacetime. It does not exclude classical gravity. It is not a Page curve. De Sitter, autonomous time, cosmological singularities, vacuum energy, and the aligned-null contraction are not reached. No standing problem is solved.
• This is not metric reconstruction, not Einstein dynamics, not holographic identification, not a Page curve, and not spacetime emergence. H2, I3, and J2 stay unresolved. O.1 stays NOT_CLOSED. The series Route B is not discharged. XVI-N is not discharged. XV-B is not opened. XVI-P is registered and is not a premise. No quantum coefficient is admitted. No compilation is asserted.

Open Oai265-A · Family 265 · Emergence problem · Page curve · Decisive test · Separations

Oai265-B certifies one implemented decoder and does not calibrate a laboratory

Three Bell correlations bound the normalized Choi overlap of a specified qubit memory. That overlap bounds half-diamond error, with coverage at least one minus alpha. The interval is not decoder optimality and not spacetime emergence.

• def:contract names dimensions, the implemented decoder, calibration allowances, the complete outcome alphabet, and the acceptance rule before validation data are collected. lem:branches keeps every decoder branch inside the tested channel. A successful branch alone need not be trace preserving. Destructive readout is an analyzer, not a decoder.
• lem:choi converts normalized Choi states into half-diamond bounds. prop:bellbounds turns the Bell overlap into a recovery interval. A transfer allowance b stays outside the square root. Direct laboratory certification would set b to zero. prop:three recovers the overlap from X, Y, and Z correlations. An implemented upper bound is not optimal recovery.
• thm:main is a repeated-experiment coverage guarantee, not a posterior on one dataset. thm:binomial and the Hoeffding procedure are finite-sample bounds. Calibration failure risk is included in alpha. The upper endpoint controls every input and untouched reference.
• A supplied report covers 140 simulated datasets: 20 repetitions of seven channels, 40 shots per setting, and zero invalid acceptances at threshold 0.1. That count cannot accept the threshold even on perfect data. The identity upper endpoint is approximately 0.8226864813. The report is supplied evidence, not an independent rerun. Optional arithmetic checks are written and not asserted as executed.
• Oai265-A, En07-C, Hawk04-B, En02-B, En01-C, and Landmark I are source records and are not premises. OpenAI Family 265 is not this certificate. No laboratory calibration, device-independent guarantee, or gravitational identification is claimed.
• This is not metric reconstruction, not Einstein dynamics, not holographic identification, not a Page curve, and not spacetime emergence. H2, I3, and J2 stay unresolved. O.1 stays NOT_CLOSED. The series Route B is not discharged. XVI-N is not discharged. XV-B is not opened. XVI-P is registered and is not a premise. No quantum coefficient is admitted. No compilation is asserted.

Open Oai265-BOpen Oai290-A · Open Oai265-A · Emergence problem · Page curve · Separations

Oai290-A types a finite recovery decision and does not reconstruct the bulk

A declared finite channel, a specified decoder, and a modular-band witness are three different statements. Exact full-code recovery is a constant complete complement. A named observable can survive when that complement is not constant. Neither statement is bulk reconstruction or spacetime emergence.

• thm:exact equates exact full-code recovery with a constant complete complement and counts residual rank. cor:nonconstant says a nonconstant complement blocks exact full-code recovery. prop:erasure shows that residual rank is not a stable approximate-error parameter. prop:classical keeps a classical record from reconstructing an unknown quantum code, with error at least one minus one over d.
• thm:effect equates exact reconstruction of one binary readout with an adjoint identity. prop:dephasing keeps an exact computational-basis effect while the identity decoder has error one half. A named observable is not a diamond-norm object. Failure of full-code recovery is not failure of that effect.
• thm:certificate uses a confidence event that supplies a normalized Choi overlap between F_L and F_U and a half-diamond transfer allowance b. The specified target then has error between the maximum of zero and one minus F_U minus b, and the minimum of one and d times the square root of one minus F_L, plus b. The allowance stays outside the square root. This certifies the specified decoder, not every decoder. thm:leakage is an information-theoretic bound, not an implemented resource certificate.
• thm:bounded restates the modular-band witness of OpenAI preprint 290-02 under a scalar centralizer. A positive averaged defect on bands shrinking to s yields uniformly bounded algebra elements whose images stay in a band of width at most four delta. cor:boundeddefect is one direction only. prop:finitecentralizer says a finite factor with scalar centralizer is the scalars. No decoder and no finite-sample count are supplied. 290-01 is not imported. The Lean note names 290-02 only.
• prop:thermal shows two complete isometries with the same selected marginal and recovery errors 0 and one minus d to the minus two. A thermal occupation number is not a complete channel. def:endpoint names four operational obligations that are not constructed. prop:geometrytest rejects a declared geometric class only when the confidence region misses every permitted law. Consistency is not uniqueness. prop:copies obstructs two commuting exact copies of a noncommutative code and does not resolve a firewall.
• thm:assembly allows certified, excluded, and inconclusive outcomes. An unsuccessful sufficient certificate is not an obstruction. The six characteristic gates stay open. Oai265-A, Oai265-B, En07-C, En07-B, Hawk04-B, XIV-I, XIV-J, and the OpenAI catalogue are source records and are not premises. Enter remains destructive readout.
• This is not metric reconstruction, not Einstein dynamics, not holographic identification, not a Page curve, and not spacetime emergence. H2, I3, and J2 stay unresolved. O.1 stays NOT_CLOSED. The series Route B is not discharged. XVI-N is not discharged. XV-B is not opened. XVI-P is registered and is not a premise. No quantum coefficient is admitted. No compilation is asserted.

Open Oai290-A · Open Oai265-B · Family 290 · Emergence problem · Page curve · Separations

Oai211-A marks a block tree and does not construct spacetime

A conditioned finite-variance tree, a path-averaged channel, and a metric scaling limit are three different statements. Exact full-code recovery is still a constant complete complement. Neither a path sum nor the Brownian continuum random tree is spacetime emergence.

• thm:path gives a uniform ancestral-path law for labels bounded by offspring number, using only finite variance. cor:boundedpath excludes shallow paths from the relative conclusion. prop:root shows that the root mark need not concentrate.
• thm:channel defines a path-averaged channel and compares it in half-diamond distance with the size-biased spine average. A sum of local errors is not that comparison. cor:loss keeps loss labels distinct from channel errors.
• thm:serial constructs a designed weak depolarizing family with strength N to the minus one half. Its compositions have an excursion-indexed error profile. Those steps are not dynamics inferred from a Gromov--Hausdorff limit.
• thm:experiment keeps tree law, experimental sampling, calibration, and implementation comparison separate. Acceptance, exclusion, and an inconclusive outcome are different decisions. The supplied 140-dataset report is not rerun here.
• thm:blockrepresentation and prop:corners transfer the statements only under the printed corner-substitution and endpoint contracts. Corner mass transports to degree measure exactly. That identity is not an entropy and not a horizon. cor:FK keeps the supplied q>4 Fortuin--Kasteleyn limit conditional. Family 211 is not verified.
• thm:exact equates exact full-code recovery with a constant complete complement. prop:goodbad shows that the same metric or entropy record can disagree on recovery. The Brownian continuum random tree has Hausdorff dimension two. That dimension is not manifold dimension and not a gravitational surface. prop:descent does not close the characteristic map. The four endpoint obligations are not constructed. Family 290-02 is not instantiated.
• thm:assembly certifies only the named operations. Oai290-A, Oai265-A, Oai265-B, En07-C, En07-B, Hawk04-B, XIV-I, XIV-J, and the OpenAI catalogue are source records and are not premises. Enter remains destructive readout.
• This is not metric reconstruction, not Einstein dynamics, not holographic identification, not a Page curve, and not spacetime emergence. H2, I3, and J2 stay unresolved. O.1 stays NOT_CLOSED. The series Route B is not discharged. XVI-N is not discharged. XV-B is not opened. XVI-P is registered and is not a premise. No quantum coefficient is admitted. No compilation is asserted.

Open Oai211-A · Open Oai280-A · Open Oai280-B · Open Oai290-A · Family 211 · Emergence problem · Page curve · Separations

Oai280-A records a VOA-net claim and does not construct spacetime

Family 280 is a source record. A sector-label certificate, a tensor-free snapshot comparison, and a Q-system extension record are three different statements. None is a derivation of a metric.

• record:correspondence records Family 280-01 Theorem 1.1 as a source claim. record:extensions records Corollary 9.3. Neither is verified. The Lean scope note names VertexAlgebraNet.lean for 280-01 only.
• prop:scalar calculates the scalar VOA. That calculation is not a gravitational example and does not supply a qubit inside the one-dimensional vacuum space.
• thm:comparison is a tensor-free snapshot comparison. thm:exact equates exact recovery with a constant complete complement. prop:effect shows that a named observable can survive when full-code recovery fails.
• thm:main is a simultaneous three-correlation half-diamond certificate. prop:forty shows that forty shots cannot accept the 0.1 threshold under this Hoeffding procedure. A sector tag is not sector identification.
• thm:extensionseparation says a Q-system is not a gravitational dictionary. thm:separation says sector data do not determine recovery, a radiation history, or a metric. A circle net is not a derived gravitational spacetime.
• The four endpoint obligations of En07-B are not constructed. Family 290-02 is not instantiated. Oai211-A, Oai290-A, En07-C, and the OpenAI catalogue are source records and are not premises.
• This is not metric reconstruction, not Einstein dynamics, not holographic identification, not a Page curve, and not spacetime emergence. H2, I3, and J2 stay unresolved. O.1 stays NOT_CLOSED. The series Route B is not discharged. XVI-N is not discharged. XV-B is not opened. XVI-P is registered and is not a premise. No quantum coefficient is admitted. No compilation is asserted.

Open Oai280-A · Open Oai211-A · Family 280 · Emergence problem · Page curve · Separations

Oai280-B certifies a printed five-qubit channel and does not construct spacetime

One printed encoding, one audited access interface, and one complete decoder are one channel. A single pentagon is not an extended holographic geometry.

• prop:encoding prints the isometry and the Clifford circuit. prop:stabilizers identifies the range with the HaPPY stabilizer convention used in En02-B. En02-B is a source record and is not a premise.
• lem:privacy proves privacy of every boundary set of at most two qubits. thm:idealaccess constructs accessible decoders for every set of at least three and gives optimal half-diamond error 3/4 below that. prop:perfect proves the six-leg perfect state.
• thm:main certifies the connected implemented channel. Calibration sits inside the fidelity interval. Transfer sits outside the square root. cor:forty keeps the forty-shot limitation certificate-specific. No validation dataset is supplied.
• prop:effecttrap keeps a named effect from being full-code recovery. prop:spectatortrap shows that a fixed spectator is not arbitrary-spectator recovery. thm:patchrecovery constructs subsystem decoders for a named two-pentagon patch.
• thm:assembly separates the finite code statements from a gravitational duality. Family 280 is not verified and is not this encoding. Family 290-02 is not instantiated. XVII-A rem:no-wedge stands.
• This is not metric reconstruction, not Einstein dynamics, not holographic identification, not a Page curve, and not spacetime emergence. H2, I3, and J2 stay unresolved. O.1 stays NOT_CLOSED. The series Route B is not discharged. XVI-N is not discharged. XV-B is not opened. XVI-P is registered and is not a premise. No quantum coefficient is admitted. No compilation is asserted.

Open Oai280-B · Open Oai280-A · Open En02-B · Emergence problem · Page curve · Separations

Oai280-C certifies a logical algebra and does not construct spacetime

One declared decoder, one declared accessible interface, and one complete channel are the recovery claim. A logical code, a subsystem, and a finite algebra are different targets. None is a gravitational dictionary.

• con:main freezes the target, the accessible channel, the complete tested channel, and the validation contract before measurements are chosen. The external validation reference is never a decoder input.
• prop:EB shows that a classical record is entanglement-breaking. For a qubit identity the half-diamond error is at least one half. prop:effect keeps an exact computational-basis effect while the dephasing channel sits at error one half from the identity.
• thm:complement equates exact full-code recovery with a constant complete complement. Partial trace of a spectator is a counterexample: subsystem recovery does not require that criterion. thm:snapshot equates informational determination with adjoint containment and does not produce a CPTP decoder.
• lem:privacy and thm:block re-prove two-share privacy and the ideal five-qubit access table. Optimal error is 3/4 on at most two qubits and exact recovery begins at three. thm:patch and thm:accessmap construct the connected two-cell subsystem and hybrid-algebra decoders. Changing a drawn region label is not geometry-dependent access.
• thm:programme turns a declared programme into a complete channel, with failure branches kept inside the tested map. thm:stream and thm:messages bound one specified three-share model. Those bounds are not universal live-memory lower bounds.
• thm:simultaneous gives simultaneous reference-preserving intervals for complete implemented channels. prop:forty shows that forty shots cannot accept the 0.1 threshold under this Hoeffding procedure. Exact binomial counts are a different contract. prop:optimal separates failure of one decoder from an all-decoder obstruction.
• Oai280-B, En02-B, En05-C, Oai265-B, Oai290-A, Em05-B, VII-G, and XVII-A are source records and are not premises. Family 280 is not verified and is not this encoding. Families 283, 290, and 365 are not decoder premises. En07-B’s four endpoint obligations are not invoked. A connected two-cell code is not an entanglement wedge.
• This is not metric reconstruction, not Einstein dynamics, not holographic identification, not a Page curve, and not spacetime emergence. H2, I3, and J2 stay unresolved. O.1 stays NOT_CLOSED. The series Route B is not discharged. XVI-N is not discharged. XV-B is not opened. XVI-P is registered and is not a premise. No quantum coefficient is admitted. No compilation is asserted.

Open Oai280-C · Open Oai280-B · Open En02-B · Open En05-C · Emergence problem · Page curve · Separations

Oai282-A certifies a finite local Ward residual and does not construct spacetime

Family 282 is a source record. Conservation of a conformal-Killing current, a finite defect certificate, and a global conformal action are three different statements. None is a derivation of a metric.

• record:main records Family 282-01 as a local traceless improvement and local Ward identities. Integration to a global action on the bounded net is left open. The catalogue reports no Lean scope note. The claim is not verified.
• thm:improvement and prop:current conserve conformal-Killing currents from declared improvement data. prop:affine-ward preserves a declared local polynomial under a spacelike-collar contract. That contract is not special-conformal implementation on every field.
• thm:ward and prop:finitefit are an exact finite defect certificate. prop:coverage says finite vanishing is not a distributional identity unless coverage is proved independently. prop:invisible shows a finite test family can miss a nonzero conserved perturbation in the unrestricted class.
• prop:free calculates L equal to minus Q over 2 on a supplied Wick domain. Deleting the label Q does not delete its derivative. No new physical scalar is reconstructed from the Family 282 hypotheses. VII-H’s susceptibility is not L. Em02-E’s lapse is not L.
• prop:einstein says symmetry, conservation, and zero trace do not imply the Einstein equation. The Minkowski metric is an input. prop:flow and prop:nonintegrable separate a local current from a global unitary action. A special conformal flow can leave the chart.
• thm:snapshot restates a tensor-free comparison and does not construct a stress tensor. thm:recovery separates a Ward or scaling record from full-code recovery. prop:history says a fixed scaling record is not an entropy history. prop:standard says cyclic and separating is not a unique invariant vector.
• prop:descent is a necessary factorization condition and is not the joint characteristic map. En05-C, III, VI, II, and the OpenAI catalogue are source records and are not premises. Enter remains destructive readout.
• This is not metric reconstruction, not Einstein dynamics, not holographic identification, not a Page curve, and not spacetime emergence. H2, I3, and J2 stay unresolved. O.1 stays NOT_CLOSED. The series Route B is not discharged. XVI-N is not discharged. XV-B is not opened. XVI-P is registered and is not a premise. No quantum coefficient is admitted. No compilation is asserted.

Open Oai282-A · Open Oai282-BOpen Oai069-A · Open Oai280-A · Open VII-H · Family 282 · Emergence problem · Page curve · Low-energy completion · Separations

Oai282-B constructs a free Ward action and does not construct spacetime

The improvement scalar, the local conformal currents, and coverage of one homogeneous class are three statements about one free scalar. None is a general scale-to-conformal theorem, and none is a derivation of a metric.

• prop:physicalL constructs L equal to minus Q over 2 in the original Weyl net. Mixed products exist on a common invariant domain that contains the old vacuum-word domain. Compact smearings of L are affiliated with the algebra of their support. The net is not enlarged to make that true.
• prop:improvement gives the symmetric, conserved, traceless tensor. prop:elementarycontact calculates the elementary retarded contact. thm:localaction implements translations, Lorentz transformations, dilations, and special conformal transformations on every compact Wick polynomial and every finite ordered product. prop:brackets keeps the stated Lie brackets.
• thm:classification leaves a two-dimensional residual family in the declared homogeneous class. thm:coverage shows that the translation probe and the trace probe separate that family. Finite vanishing is then the full local Ward conclusion inside the class, not only on the two probe vectors. prop:invisible shows that the same finite probes can miss a nonzero conserved tensor outside the class.
• prop:flow shows that a special conformal flow can leave the Minkowski chart. prop:nonintegrable is a deficiency-index example, not a calculation for these charges. Global integration is not attempted. Oai282-A’s finite-fit certificate is a source record and is not a premise.
• prop:einstein says symmetry, conservation, zero trace, and the local Ward theorem do not imply the Einstein equation. The Minkowski metric is an input. VII-H’s susceptibility is not L and not the stress current. Em02-E’s lapse is not L.
• prop:descent is a factorization criterion and is not the joint characteristic map. The symbol L in the XIV programme is not this improvement scalar. Family 290-02 is not instantiated. III, V, VI, II, and the OpenAI catalogue are source records and are not premises.
• This is not metric reconstruction, not Einstein dynamics, not holographic identification, not a Page curve, and not spacetime emergence. H2, I3, and J2 stay unresolved. O.1 stays NOT_CLOSED. The series Route B is not discharged. XVI-N is not discharged. XV-B is not opened. XVI-P is registered and is not a premise. No quantum coefficient is admitted. No compilation is asserted.

Open Oai282-BOpen Oai069-A · Open Oai282-A · Open VII-H · Family 282 · Emergence problem · Page curve · Low-energy completion · Separations

Oai069-A certifies a finite-monodromy decoder and does not construct spacetime

The dagger equivalence, the receiver-only decoder, and the independent free-scalar Ward audit are three statements about one finite benchmark. None is a specialization of Family 069, and none is a derivation of a metric.

• thm:category is a dagger equivalence of unitary local systems whose monodromy factors through a specified finite cyclic quotient. It is not the connected-simple Family 069 theorem. prop:fourier is a finite Fourier matrix, not the source central-torsor theorem.
• prop:nopositive shows a complex-linear equivalence need not preserve positivity. A DG equivalence is not a positive channel and not an AdS dual.
• thm:exact returns the named local-system label and the qubit multiplicity from the receiver-only programme, uniformly over references and gauge correlations. That return is not full-code recovery.
• thm:loss gives sharp all-decoder errors after a coefficient leg is removed and still recovers a named effect. A failed sufficient certificate is not an all-decoder exclusion. A receiver leg is not an entanglement wedge.
• thm:simultaneous gives simultaneous finite-confidence intervals for complete implemented channels. Two stress probes are not process tomography. Oai280-C is a source record and is not a premise.
• prop:improvement, thm:stresscoverage, and prop:ward identify one normalized traceless stress and a finite Ward defect in a declared homogeneous class. That audit is independent of Oai282-B and of VII-H. It is not a chiral-to-four-dimensional bridge. Two probes do not cover unrestricted tensors.
• def:bridge and prop:source-separation name the missing localization–Whittaker bridge. A category record without that bridge does not select the channel. No gravitational dictionary is inferred. A traceless matter tensor is not an Einstein equation. A finite recovery error is not a Page curve.
• This is not metric reconstruction, not Einstein dynamics, not holographic identification, not a Page curve, and not spacetime emergence. H2, I3, and J2 stay unresolved. O.1 stays NOT_CLOSED. The series Route B is not discharged. XVI-N is not discharged. XV-B is not opened. XVI-P is registered and is not a premise. No quantum coefficient is admitted. No compilation is asserted.

Open Oai069-A · Family 069 · Emergence problem · Page curve · Low-energy completion · Separations

VIII-A through VIII-C, version 3, certify cones and do not construct spacetime

The three sheets now prove their comparison statements locally. A citation is a locator, not a premise. The matching packet, the sourced family, and the guarded schedule stay three different objects.

• VIII-A A:thm:A1 through A:thm:A4 certify one fixed cone of deficit π/2. A:thm:residual separates equal classical records from residual source functionals. A:thm:classical and A:thm:complement are finite recovery safeguards, not a decoder for the cone. A:prop:no-einstein shows that symmetry, conservation, and zero trace do not imply Einstein dynamics.
• VIII-B thm:dictionary and thm:persistence construct the family on a compact interval before any source is substituted. prop:matching-unique and prop:rejections hold at every admitted deficit. prop:obstruction and prop:affine keep the token promised. prop:no-einstein is not a mass law. Zero source recovers the reference family. VIII-C is not a premise.
• VIII-C prop:complete-output rejects a stale rotation and a time shift at every installed deficit. prop:token-obstruction does not acquire the expectation. thm:C5 is an adjoint inclusion for prescribed block channels, not a light cone. prop:recovery is not quantum recovery. prop:not-einstein is not Einstein dynamics.
• Four interfaces stay outside the schedule: a mixed incidence–source germ, a token-acquisition instrument, an independently certified directional inclusion, and a polygon Hamiltonian. En05-A, En06-A, VII-J, Em02-E, XVII-A, Hawk04-B, Oai280-C, and Oai282-A/B are source records where cited and are not premises.
• This is not metric reconstruction, not Einstein dynamics, not holographic identification, not a Page curve, and not spacetime emergence. H2, I3, and J2 stay unresolved. O.1 stays NOT_CLOSED. The series Route B is not discharged. XVI-N is not discharged. XV-B is not opened. XVI-P is registered and is not a premise. No quantum coefficient is admitted. No compilation is asserted.

Open VIII-A · Open VIII-B · Open VIII-C · Emergence problem · Page curve · Geometry map

XVIII-A states the interface and does not evaluate the coefficient

Version 2 is a contract for a prepared relational observable. It proves non-identifications. It does not evaluate the companion one-loop coefficient, and it does not replace the finite-matrix XVII-A sheet.

• thm:witness and cor:smoothwitness show that a pure-trace witness does not determine the compact three-slot kernel, its microcausal admission, or its free-shell class. The gap already exists among smooth compact kernels. XVI-H is a source record and is not a premise.
• prop:weighted retains preparation derivatives. prop:lateresponse says late source agreement is not retarded-response agreement. XVI-B is not a premise.
• thm:forest says a balanced forest is not a loop. prop:hbar says a positive formal order in Planck's constant cannot cancel a classical formal coefficient. X-F and X-G are not premises.
• thm:ward equates exact affine cancellation with vanishing in the quotient by the actual counterterm image. That quotient is not ambient BRST cohomology and not Oai282-B's homogeneous coverage.
• prop:truncation says a projected fixed point is not a fixed point. thm:matching is conditional and does not reconstruct spacetime, a wedge, a Page curve, or an island.
• eq:readout is a finite readout convention. It consumes the measured name and returns a classical record. It is not a field instrument, not a decoder, and not Born uniqueness. Hawk04-B and Landmark I are source records and are not premises.
• This is not metric reconstruction, not Einstein dynamics, not holographic identification, not a Page curve, and not spacetime emergence. H2, I3, and J2 stay unresolved. O.1 stays NOT_CLOSED. The series Route B is not discharged. XVI-N is not discharged. XV-B is not opened. XVI-P is registered and is not a premise. No quantum coefficient is admitted. No compilation is asserted.

Open XVIII-A · Open XVIII-B · Emergence problem · Low-energy completion · Page curve · Separations

XVIII-B evaluates one massive stress response and does not construct spacetime

Version 2 evaluates one external-source kernel. The metric is classical. The quantum field is one free scalar of positive mass. The result is not the companion relational observable and not Einstein dynamics.

• thm:spectral evaluates the spin-two and spin-zero vacuum spectral densities. thm:retarded constructs a once-subtracted causal kernel of scaling degree at most eight. The polynomial tensors stay defined at zero momentum.
• thm:contacts classifies one quadratic and two quartic transverse contacts. cor:unique fixes them by the zero-momentum jet through degree four. The massive reference starts at degree six.
• thm:ward is linear transversality on compact tests. It is not Oai282-B's homogeneous coverage and not an interacting BRST identity. thm:nonlocal keeps a contact-independent discontinuity.
• prop:ctp is quadratic-source closed-time-path bookkeeping, not an Enter channel. prop:prepared multiplies the source by a fixed ramp. thm:residual computes the unrestricted residual and kills it on a plateau.
• prop:detector detects spectral weight by a vacuum norm. It is not a measurement instrument, not a classical record, and not a decoder. Hawk04-B and Landmark I are not premises. VII-H's massless susceptibility is not this kernel.
• XVIII-A is a sibling contract, not a parent. A comparison map is not supplied by shared projector notation. Positive mass does not discharge XVI-N and is not a massless limit. No match to Fröb is asserted.
• This is not metric reconstruction, not Einstein dynamics, not holographic identification, not a Page curve, and not spacetime emergence. H2, I3, and J2 stay unresolved. O.1 stays NOT_CLOSED. The series Route B is not discharged. XVI-N is not discharged. XV-B is not opened. XVI-P is registered and is not a premise. No quantum coefficient is admitted. No compilation is asserted.

Open XVIII-B · Open VII-H · Emergence problem · Low-energy completion · Page curve · Separations

The revised Landmark I keeps companion records out of Born uniqueness

thm:main still identifies the Born strategy inside the stated class. The revision separates that theorem from later record, decoder, instrument, and cutoff interfaces. Those interfaces are source records, not premises.

• prop:pullback and ex:equal-records separate classical record compatibility from residual instruments. Equal records need not fix the residual state. En03-A thm:obstruction is a source record and is not a premise.
• prop:process records one direction: complete-process equality implies equal adaptive record laws. The converse is not claimed. Psy02-B thm:process is a source record and is not a premise.
• En02-B thm:B1 is decoder soundness under already fixed Born semantics. Hawk01-A thm:completion, Hawk01-B thm:number, Hawk02-A cor:spectrum, Hawk02-B thm:B3, Hawk02-C thm:C4, Hawk02-D thm:erasure, Hawk02-E thm:certificate, Hawk03-A thm:partner, Hawk04-A thm:global, Hawk04-B thm:classical, En04-A thm:classical, and En05-A prop:classical, En05-B thm:identity, En06-A prop:drop, En05-C thm:comparison, and En06-B thm:identity, and En07-A thm:classical, and En07-B thm:classical, and En07-C thm:classical are channel or algebra comparisons. Oai265-A thm:separation and Oai265-B thm:main are a record separation and a finite-sample certificate. Oai290-A thm:assembly is a typed recovery decision. Oai211-A thm:assembly is a path-sum certificate. Oai280-A thm:main is a sector-label certificate. Oai280-B thm:assembly is a five-qubit certificate. Oai280-C thm:simultaneous is a logical-algebra certificate. Oai282-A thm:main is a finite local-Ward certificate. Oai282-B thm:release is a free local Ward action. Oai069-A thm:main is a finite-monodromy certificate. XVIII-A eq:readout and thm:release are a finite readout convention and an interface release. XVIII-B prop:detector is a vacuum norm. None is a measurement axiom for Enter.
• Em03-C and Em03-E do not construct an interior algebra or resolve horizon physics. XIV-I constructs the named I2 amplitude and leaves the joint map unresolved at I3. None of these is a premise of thm:main.
• This is not a physical Frauchiger-Renner no-go, not a microscopic evaporation channel, and not a horizon construction. OpenAI’s full preprint sources and Lean scope notes are not premises of thm:main. This is not metric reconstruction, not Einstein dynamics, not holographic identification, not a Page curve, and not spacetime emergence. H2, I3, and J2 stay unresolved. O.1 stays NOT_CLOSED. The series Route B is not discharged. XVI-N is not discharged. XV-B is not opened. XVI-P is registered and is not a premise. No quantum coefficient is admitted. No compilation is asserted.

Open I · Emergence problem · Separations

XV-B version 2 proves local lifting tests and does not construct the joint map

Version 2 is the technical continuation of the unresolved six-branch characteristic map. It is not the downstream admission exit. Relative lifting, a jet-null criterion, closed-set extension, and a one-point puncture correction are local interface theorems. They do not construct the inherited map.

• thm:lifting gives an exact affine relative-lifting criterion: a reconstruction-descending candidate exists exactly when the relative obstruction vanishes. lem:null and prop:descent keep factorization separate from extension. XIV-J leaves the map unresolved at J2 and is not a premise of the local criterion.
• thm:contact says contact-supported corrections cannot cancel a null defect detected off their support. XIII-E is a comparison only and is not a premise. No regulator or characteristic limit is imported.
• thm:jetnull is a complete null criterion for one specified finite normal-jet module. thm:jetextension equates supported extension at a fixed normal order with coefficient extension. XV-C states a related test and is not a premise. The local module is not the inherited presentation space.
• thm:closedextension is a uniform local finite-order criterion across a relatively closed set. It does not supply the estimates for the actual supported-sector coefficients.
• lem:jetdefect and thm:pointcorrection correct one point puncture by finitely many derivatives of a delta distribution, and only after an existing coefficient extension. The result is not asserted for a positive-dimensional characteristic locus. XV-E is not a premise. The inherited dimension-eight set is not that puncture.
• thm:release keeps the application unresolved at B1. No graph-specific preliminary lift or permitted cancellation of its null defect is constructed. No nonzero obstruction is evaluated in a family proved exhaustive for the frozen graph. Descent is not quantum admission. The admission condition is not established.
• OpenAI is a documentary catalogue and is not a premise. Families 279, 227, 274, 276, 212, 356, and 119 are labels, not theorems. Family 279 is not a compilation theorem. Family 356 is not the Alexandrov–Zeeman theorem. XIV-I, XIV-J, XV-C, XV-E, and XIII-E are source records and are not premises.
• This is not metric reconstruction, not Einstein dynamics, not holographic identification, not a Page curve, and not spacetime emergence. The inherited full map is not constructed. H2, I3, and J2 stay unresolved. O.1 stays NOT_CLOSED. The series Route B is not discharged. XVI-N is not discharged. XV-B is not opened. XVI-P is registered and is not a premise. No quantum coefficient is admitted. No compilation is asserted.

Open XV-B · Emergence problem · Page curve · Separations

Em04-A is the analytical chain. It is not an executed certificate

Every registered sheet was walked from I, I-B, II-B, III-B, IV-B, V-B, VI-B, VII-A-ST, VII-E-ST, VII-F-ST, and VII-J-ST, and VIII-ST, and IX-A-ST, and IX-B-ST, and IX-C-ST, and IX-D-ST through Hawk02-D, Hawk02-E, Hawk03-A, Hawk04-A, Hawk04-B, Hawk04-C, Hawk04-D, Hawk05-A, Hawk05-B, Hawk05-C, Hawk06-A, Hawk07-A, Hawk07-B, En04-A, En05-A, En05-B, En06-A, En05-C, and En06-B, and En07-A, and En07-B, and En07-C, and Oai265-A, and Oai265-B, and Oai290-A, and Oai211-A, and Oai280-A, and Oai280-B, and Oai280-C, and Oai282-A, and Oai282-B, and Oai069-A, and XVIII-A, and XVIII-B, and XIX-A, and XIX-B, and XIX-C, and XIX-D, and XIX-E, and XX-A, and XX-B, and XX-C, and XX-D, and XX-E, and XX-F, and En08-A, and En08-B, and En09-A, and En10-A, and En10-B, and XXII-A, and XXII-B, and XXII-C, and XXII-D, and XXII-E, and XXII-F, and Oai212-A, and Oai365-A, and Oai283-A, and Oai272-A, and Oai276-A, and Oai279-A, and Oai227-A, and Oai119-A. 215 sheets. Em04-A proves the exact vacuum-plus-single-excitation reduction, the concurrence and logarithmic-negativity formulas, the two-coordinate scaling, the local instruments, and the compressed-position bounds. Em05-A is a different signed extractor. Em05-B restates that extractor and proves complementary leakage and an improved sandwich. Neither supplies that generator. Em05-A is not a premise of Em05-B. VII-G is a finite hybrid instrument on that walk, not the XY reduction and not gravitational dynamics. VII-H is a free-field susceptibility on that walk. It is not the XY reduction, not that instrument, and not the inherited gravitational coefficient. VII-I is a finite-width free algebra on that walk. It is not the XY reduction and not the original sharp interacting observable. VII-J is a finite causal network on that walk. It is not the XY reduction and not matter-driven evolution of the cone. Em06-A is a scalar-only classical limit on that walk. It is not the XY reduction and not spacetime emergence. XVII-A is a finite-model sine effect on that walk. It is not the XY reduction, not a Page curve, and not holographic emergence. Em06-B is a scalar-only family concentration on that walk. It is not the XY reduction, not spacetime emergence, and not the metric gate B6. Psy02-A is a conditional carrier ledger on that walk. It is not the XY reduction, not a derivation of Orch-OR, and not spacetime emergence. Psy01-A is an analytic pruning framework on that walk. It is not the XY reduction, not a biological mechanism, and not spacetime emergence. Psy02-B is a branch-matched finite pilot on that walk. It is not the XY reduction, not a derivation of Orch-OR, and not spacetime emergence. Psy03-A is an intervention-budget framework on that walk. It is not the XY reduction, not an antidepressant mechanism, and not spacetime emergence. Psy03-B is a longitudinal structural-memory framework on that walk. It is not the XY reduction, not a kindling mechanism, and not spacetime emergence. Psy03-C is a recurrent-stability framework on that walk. It is not the XY reduction, not a cognitive construct, and not spacetime emergence. Psy03-D is a hidden-rule observability framework on that walk. It is not the XY reduction, not a cognitive construct, and not spacetime emergence. Psy04-A is a delayed random-access framework on that walk. It is not the XY reduction, not quantum environmental memory, and not spacetime emergence. Psy04-B is a causal-cut framework on that walk. It is not the XY reduction, not a physical causal cone, and not spacetime emergence. En03-A is a destructive-readout and external-geometry interface on that walk. It is not the XY reduction, not a field equation, and not spacetime emergence. Hawk01-A is a fixed-background Hawking retrieval framework on that walk. It is not the XY reduction, not a recovery derivation, and not spacetime emergence. Hawk01-B is a finite sequential code-preservation model on that walk. It is not the XY reduction, not a microscopic evaporation law, and not spacetime emergence. Hawk02-A is a conditional evaporation interface on that walk. It is not the XY reduction, not a microscopic Hamiltonian, and not spacetime emergence. Hawk02-B is a Hamiltonian-derived finite emission model on that walk. It is not the XY reduction, not a microscopic evaporation law, and not spacetime emergence. Hawk02-C is an autonomous source-field bridge on that walk. It is not the XY reduction, not gravitational Hawking radiation, and not spacetime emergence. Hawk02-D is a quadratic fermionic residual on that walk. It is not the XY reduction, not interacting SYK, not gravitational backreaction, and not spacetime emergence. Hawk02-E is a regulated interacting SYK--scalar diary on that walk. It is not the XY reduction, not a small dynamical residual, not a gravitational correspondence, and not spacetime emergence. Hawk03-A is a finite firewall-interface package on that walk. It is not the XY reduction, not a smooth horizon, and not spacetime emergence. Hawk04-A is a complete-complement formulation on that walk. It is not the XY reduction, not radiation recovery from unitarity alone, and not spacetime emergence. Hawk04-B version 2 is a typed readout and discard ledger on that walk. Enter on radiation is a record, not the quantum decoder. It is not the XY reduction, not a decoder, and not spacetime emergence. En04-A separates non-Clifford resources from residual response. Magic is not leakage, the restore map does not move the diary into the residual, and a nonconstant residual is not geometric backreaction. It is not the XY reduction and not spacetime emergence. En05-A proves an exact schedule cone and a sharp relay speed r on stated lattices. The schedule past is an upper bound, not influence. A fixed periodic model has a velocity polytope, not a Euclidean ball. Unrestricted boost-closure excludes ordinary bidirectional relays, and physical retiming-stability is withdrawn. Continuum existence stays open. It is not an invariant physical speed, not the XY reduction, and not spacetime emergence. En05-B constructs one finite-experiment family whose operational speed equals a prescribed c. That speed is an input, not a derived metric. It is not the XY reduction and not spacetime emergence. En06-A keeps discrete cones, an increasing-stencil envelope, and one restricted outcome-law theory apart. Unrestricted device closure stays withdrawn. It is not an invariant physical speed, not the XY reduction, and not spacetime emergence. En05-C equates state restriction with Heisenberg containment and does not use a spatial tensor factor. A finite-mode gauge refinement is not a relativistic field theory. It is not the XY reduction and not spacetime emergence. En06-B realizes one finite transport contract and one Bell instrument on an increasing-stencil family. The constant c is an input. It is not the XY reduction and not spacetime emergence. En07-A restates complete restoration and readout-and-drop as partial trace. Channel equality is not a Landauer cost. It is not the XY reduction, not holographic identification, and not spacetime emergence. En07-B certifies outgoing recovery only under four unconstructed same-model obligations. A nearly constant complement is an upper bound, and a nearly constant accessible output is a lower bound. It is not the XY reduction, not a gravitational endpoint, and not spacetime emergence. En07-C types Hawking's thermal occupation as an external input. A thermal spectrum is not a replacement channel. It is not the XY reduction, not a gravitational endpoint, and not spacetime emergence. Oai265-A separates a static area-law record from recovery and from a radiation history. Selected entropy is not a Page curve. It is not the XY reduction, not a verification of Family 265, and not spacetime emergence. Oai265-B certifies one implemented decoder from three Bell correlations. Forty shots cannot accept the 0.1 threshold. It is not the XY reduction, not a laboratory calibration, and not spacetime emergence. Oai290-A separates full-code recovery from a named observable and from a modular-band witness. It is not the XY reduction, not bulk reconstruction, and not spacetime emergence. XV-B version 2 proves relative lifting, a jet-null criterion, closed-set extension, and a point-puncture correction. The point correction is not the characteristic locus. XV-C and XV-E are not premises. The inherited full map is not constructed. It is not the XY reduction and not spacetime emergence. II version 2 is a finite contact-span certificate on that walk. A finite fit is not a global contact identity, not a Page curve, and not spacetime emergence. I version 2 is a finite Enter characterization on that walk. It is not the XY reduction, not a field instrument, and not spacetime emergence. The lines below are separations. They are not a declared path. Earlier sheets do not supply that generator.

• I thm:main, IV’s binary instruments, En02-A thm:I, and X-Enter’s four-live-qubit bound do not construct the chain. Lindblad dynamics are an assumption of Em04-A, not a theorem of I.
• Em03-H remains a fermionic channel. It is not this XY reduction and not a gravitational dictionary. Reported P8 numbers are not validated. The new v8 programs are unexecuted. Em05-A restates a signed extractor independently. It is not this XY reduction, and Em03-H is not a premise of Em05-A. Em05-B restates complementary leakage and an improved sandwich independently. It is not this XY reduction, and Em05-A is not a premise of Em05-B. VII-G thm:finite-model is a finite hybrid instrument on a fixed cone. It is not this XY reduction and not gravitational dynamics. VII-H thm:release is a free-field vacuum susceptibility. It is not this XY reduction, not an instrument for the Wick square, and not gravitational dynamics. VII-I thm:release is a finite-width free algebra and a sharp incompatibility. It is not this XY reduction and not gravitational dynamics. VII-J thm:release is a finite causal network on a fixed cone. It is not this XY reduction and not gravitational dynamics. Em06-A thm:main is a scalar-only classical limit. It is not this XY reduction and not spacetime emergence. XVII-A thm:main is a finite-model sine effect. It is not this XY reduction, not a Page curve, and not holographic emergence. Em06-B thm:release is a scalar-only family concentration. It is not this XY reduction and not gravitational dynamics. Psy02-A thm:main is a conditional scalar-carrier ledger. It is not this XY reduction and not a derivation of Orch-OR. Psy01-A thm:release is an analytic pruning framework. It is not this XY reduction and not gravitational dynamics. Psy02-B thm:release is a branch-matched finite pilot. It is not this XY reduction and not a derivation of Orch-OR. Psy03-A thm:release is an intervention-budget framework. It is not this XY reduction and not an antidepressant mechanism. Psy03-B thm:release is a longitudinal structural-memory framework. It is not this XY reduction and not a kindling mechanism. Psy03-C thm:release is a recurrent-stability framework. It is not this XY reduction and not a cognitive construct. Psy03-D thm:release is a hidden-rule observability framework. It is not this XY reduction and not a cognitive construct. Psy04-A thm:release is a delayed random-access framework. It is not this XY reduction and not quantum environmental memory. Psy04-B thm:release is a causal-cut framework. It is not this XY reduction and not a physical causal cone. En03-A thm:exchange is a fixed-spacetime observation interface. It is not this XY reduction and not a field equation. Hawk01-A thm:release is a fixed-background Hawking retrieval framework. It is not this XY reduction and not a recovery derivation. Hawk01-B thm:release is a finite sequential emission model. It is not this XY reduction and not a microscopic evaporation law. Hawk02-A thm:main is a conditional certification interface. It is not this XY reduction and not a microscopic Hamiltonian. Hawk02-B thm:B3 is an exact recovery error for a finite pulse sequence. It is not this XY reduction and not a microscopic evaporation law. Hawk02-C thm:C2 is an autonomous source-field Hamiltonian on excitation sectors. It is not this XY reduction and not gravitational Hawking radiation. Hawk02-D thm:main is a quadratic fermionic residual bound. It is not this XY reduction, not interacting SYK, and not gravitational backreaction. Hawk02-E thm:release is a regulated interacting certification framework. It is not this XY reduction, not a small dynamical residual, and not gravitational backreaction. Hawk03-A thm:release constructs a finite partner algebra and leaves the physical firewall unresolved. It is not this XY reduction and not a smooth horizon. Hawk04-A thm:release proves global preservation and a constant-complement recovery criterion and leaves unitarity of quantum gravity unproved. It is not this XY reduction and not radiation recovery from unitarity alone. Hawk04-B cor:gravity separates destructive readout and operational discard from quantum recovery and leaves physical annihilation unproved. It is not this XY reduction and not an evaporation endpoint. Hawk04-C thm:classical keeps classical-record error at least one minus one over d and equates readout-and-drop with partial trace. It is not this XY reduction, not evaporation, and not a Page curve. Hawk04-D lem:benchmarks keeps classical-record error at least one minus one over d, and prop:drop equates readout-and-drop with partial trace. A supplied luminosity is not this XY reduction, not evaporation, and not a Page curve. Hawk07-A thm:main is an operational-wormhole certificate in one finite model. It is not this XY reduction, not an Einstein-Rosen bridge, not a Page curve of gravitational evaporation, and not spacetime emergence. Hawk07-B thm:main is an operational function certificate in one finite model. It is not this XY reduction, not a geometric wormhole, not a Page curve of gravitational evaporation, and not spacetime emergence. En04-A cor:noimplication separates non-Clifford resources from residual response. Magic is not leakage, and cor:bridge does not establish geometric backreaction. En05-A thm:cone is a scheduled metric envelope, not this XY reduction and not an invariant physical speed. thm:isotropyobstruction keeps the cardinal model an ell-one diamond. thm:boostobstruction withdraws physical retiming-stability. En05-B thm:main is one isotropic operational limit. cor:maxspeed is a prescribed speed, not this XY reduction and not a derived metric. En06-A thm:withdrawal keeps unrestricted device closure withdrawn. It is not this XY reduction and not an instrument-level scaling limit. En05-C thm:comparison is a tensor-free local-algebra comparison. It is not this XY reduction and not a relativistic field theory. En06-B thm:identity is exact instrument transport on one increasing-stencil family. It is not this XY reduction and not a quantum field theory. En07-A thm:release is a local channel framing. It is not this XY reduction, not a Landauer bound, and not holographic identification. En07-B thm:endpoint is a conditional finite certificate. It is not this XY reduction, not a gravitational endpoint, and not holographic identification. En07-C thm:release is a finite comparison of an external thermal input. It is not this XY reduction, not a gravitational endpoint, and not holographic identification. En08-A thm:main separates scheduler consistency from a Lorentz cone. It is not this XY reduction, not Einstein dynamics, and not spacetime emergence. En08-B thm:main approximates a prescribed null boundary by finite local SWAP protocols. The metric and the speed are inputs. It is not this XY reduction, not a derived cone, and not spacetime emergence. En09-A thm:main reads a finite clock by destructive Enter. It is not this XY reduction and not spacetime emergence. En10-A thm:main estimates a source weight from destructive records. It is not this XY reduction and not spacetime emergence. En10-B thm:release leaves the unconditional positron identification unconstructed. It is not this XY reduction and not spacetime emergence. Oai265-A thm:separation is a record-only separation. It is not this XY reduction, not a verification of Family 265, and not a Page curve. Oai265-B thm:main is a finite-sample decoder certificate. It is not this XY reduction, not a laboratory calibration, and not spacetime emergence. Oai290-A thm:assembly is a typed recovery decision. It is not this XY reduction, not a verification of Family 290, and not bulk reconstruction. Oai280-B thm:assembly is a five-qubit certificate. It is not this XY reduction and not a gravitational dictionary. Oai280-C thm:simultaneous is a logical-algebra certificate for complete implemented channels. A constant complement is a full-code criterion. It is not this XY reduction, not a Page curve, and not spacetime emergence. Oai282-A thm:ward is a finite local-Ward certificate. It is not this XY reduction, not a verification of Family 282, and not spacetime emergence. Oai069-A thm:main is a finite-monodromy decoder and an independent Ward defect. It is not this XY reduction, not a verification of Family 069, and not spacetime emergence. XVIII-A thm:witness is a witness non-determination. It is not this XY reduction and not spacetime emergence. XVIII-B thm:spectral is a massive stress response. It is not this XY reduction and not spacetime emergence. XV-B version 2 thm:lifting, thm:jetnull, thm:closedextension, and thm:pointcorrection are local interface theorems. They are not this XY reduction, not spacetime emergence, and not a constructed characteristic map.
• XIV-A’s relative classical master is not this Lindblad generator. V and Em03-D are not this compressed-position measurement.
• Source alignment remains unresolved. Reported correspondences are not validated. Independent execution is not asserted. The verification appendix is unexecuted. O.1 stays NOT_CLOSED. The series Route B is not discharged. XVI-N is not discharged. XV-B is not opened. XVI-P is registered and is not a premise. H2, I3, and J2 stay unresolved. No quantum coefficient is admitted. No compilation is asserted.

Tests problem · Emergence problem · Separations

Draw a packet

The packet is assembled locally either way. Packet only does not call Grok. Quick asks for three candidates. Discovery adds one challenge and, when the budget remains, one revision.