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• When local-only is off and a key is configured, Grounded and Develop send the question and the retrieved excerpts — not the whole corpus. Plain passes the question through and also sends a ledger of every registered N. Cheung manuscript and the OpenAI catalogue.
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The corpus is the registered manuscripts: I, I-B, II, II-B, III, III-B, IV, IV-B, V, V-B, VI, VI-B, VII-A, VII-A-ST, VII-B, VII-C, VII-D, VII-E, VII-E-ST, VII-F, VII-F-ST, VII-G through VII-J, VII-J-ST, VIII-A through VIII-C, VIII-ST, IX-A, IX-A-ST, IX-B, IX-B-ST, IX-C, IX-Free, IX-Free-2, IX-C-ST, IX-D, IX-E through IX-E-3, IX-D-ST, X-A-conv, X-A through X-G, X-B-ii, X-Enter, XI-A through XI-G, XII-A through XII-F, XIII-A through XIII-E, XIV-A through XIV-J, XV-A through XV-F, XV-F-patch, XV-F-patch-ii, XVI-A, XVI-B, XVI-D, XVI-H, XVI-I, XVI-J, XVI-K, XVI-L, XVI-M, Em01-A, Em01-B, Em01-C, Em01-D, Em01-E, Em01-F, Em01-G, En01-A, En01-B, En01-C, Em02-A, Em02-B, Em02-D, Em02-E, XVI-N, XVI-O, En02-A, En02-B, En02-C, En02-D, Em03-A, En02-E, Em03-B, Em03-C, Em03-D, Em03-E, Em03-F, Em03-G, Em03-H, Em04-A, Em05-A, Em05-B, Em06-A, XVII-A, Em06-B, Psy02-A, Psy01-A, Psy02-B, Psy03-A, Psy03-B, Psy03-C, Psy03-D, Psy04-A, Psy04-B, En03-A, Hawk01-A, Hawk01-B, Hawk02-A, Hawk02-B, Hawk02-C, 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, En06-B, En07-A, En07-B, En07-C, Oai265-A, Oai265-B, Oai290-A, Oai211-A. The OpenAI manuscripts are stored in the OpenAI section and are not part of this registered list. Their authors are OpenAI. No successful compilation of those sources is asserted. The patches do not pass F0, and XVI-A, XVI-B, XVI-D, XVI-H, and XVI-I do not admit a quantum coefficient. XVI-J does not admit a quantum coefficient of the fuller graph. XVI-K does not admit a quantum coefficient of the complete interaction. XVI-L does not admit a quantum coefficient of a complete one-loop correction. XVI-M does not achieve broad matched-scale release, does not identify the scale variation with a Wilson coefficient, and does not admit a quantum coefficient. Em01-A does not construct the joint graph. Em01-B does not admit a quantum coefficient. Em01-C does not evaluate the physical characteristic coefficient, including the aligned-null contraction, and does not admit a quantum coefficient. Em01-D does not evaluate the designated physical graph: its decision stays conditional on an unverified origin-germ certificate, and the appendix powers are not physical inputs. Em01-E does not identify the physical Einstein–scalar graph: its evaluated specialization sets the observation to zero, and the authorized class forbids that subtraction. Em01-F does not identify the inherited weighted observable, does not decide the raw limit, and does not admit a quantum coefficient. Em01-G does not classify every datum, does not match the residual tip, and does not admit a quantum coefficient. En01-A does not turn a question-level order into a physical no-go, does not identify its agreement down-set with a gravitational path, and does not admit a quantum coefficient. En01-B does not turn a sphere contrast into an experimental exclusion, does not derive a metric, and does not admit a quantum coefficient. En01-C does not turn a diffusion certificate into source identification, does not derive a metric, and does not admit a quantum coefficient. Em02-A does not evaluate a physical singular-data sector: its localization powers are not the physical smoothing scale, the inherited package is not supplied, and it does not admit a quantum coefficient. Em02-B does not release a physical row: its atomic quadrature is not the seven-dimensional seed integral, the simulated numbers are not a physical coefficient, and no quantum coefficient is admitted. Em02-D does not turn the fixed-model leading coefficient into the physical characteristic limit: the model is not the designated physical package, the raw family does not converge, the remainder is not a finite part, and no quantum coefficient is admitted. Em02-E does not turn the classical relational lapse into regulator removal: the quantum audit is incomplete, the background is not a de Sitter state, the kernel is not spacetime emergence, and no quantum coefficient is admitted. XVI-N does not turn one massless instance into a universal completion: Route B is not discharged, arbitrary prescribed mass stays unresolved, the prepared theory is not a BV complex, and no quantum coefficient is admitted. XVI-O does not turn a kernel counterterm into bulk BV restoration: O.1 stays NOT_CLOSED, the insertion stays frozen, the archived scripts are package evidence rather than a certificate, and no quantum coefficient is admitted. En02-A does not turn finite capacity into spacetime emergence: cut conservation is not a gravitational current, the four-live-qubit class is not the register cost, the instrument ledger is not IV's three models, the embedded listing is package evidence rather than a certificate, and no quantum coefficient is admitted. En02-B does not turn a perfect-code decoder into an entanglement wedge: the two-live-qubit optimum is not a bulk–boundary map, the module-class bound is not unrestricted optimality, the checks are package evidence rather than a certificate, and no quantum coefficient is admitted. En02-C does not turn a finite radiation decoder into a Page curve: exact information-theoretic recovery is not executable recovery, the one-live-qubit error is not an island, the appendix checks are package evidence rather than a certificate, and no quantum coefficient is admitted.
• I-B records a finite Enter spacetime on a prescribed conical product. thm:instrument consumes a finite clock encoding and returns a classical code. The geometric time axis remains. prop:fixed-event makes exact event-time agreement deterministic. thm:metric-containment keeps scheduled influence inside the prescribed causal relation. thm:transport is a target-adapted chain, not a previously fixed lattice. The defect is a worldsheet, not a worldline. A lapse jet is not the metric. The title page names Ngo Cheung. Cited sheets and the OpenAI catalogue are not premises. This is not spacetime emergence, not Einstein dynamics, not a Page curve, and not quantized relational time without an external clock.
• II-B records a Grade S adaptation of the SEP-finite contact certificate onto that prescribed cone. thm:frozen keeps rank 2, minor 64, and coefficients 2/3 and 2/3. thm:pullback preserves the finite certificate under a declared dictionary. A finite fit is not a global contact identity. thm:instrument consumes clock names. A clock record is not the geometric time coordinate. thm:transport is a target-adapted chain and does not import a lattice resource formula. prop:lapse is not used in the conical release. The title page names Ngo Cheung. Cited sheets and the OpenAI catalogue are not premises. This is not spacetime emergence, not Einstein dynamics, not a Page curve, and not quantized relational time without an external clock.
• III-B records a local Grade S adaptation of classical descent onto a supported laboratory inside that prescribed cone. The punctured product is not globally hyperbolic. thm:reduced is a Hausdorff vacuum-metric triangular quotient. thm:instrument consumes a finite clock encoding and leaves the geometric time axis. thm:pilot is a three-qubit evaluation encoding, 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. Cited sheets and the OpenAI catalogue are not premises. This is not spacetime emergence, not Einstein dynamics, 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.
• IV-B records a Grade-S interface for three represented instruments on that prescribed cone, through a declared flat completion. prop:no-global-transfer says a local developing chart is not an intrinsic cone field theory. thm:model1 removes a smooth edge in trace norm. thm:spectral-channel gives diamond-norm spectral convergence at fixed finite particle number. Model 3 retains finite cutoffs. thm:instrument consumes a finite clock encoding and leaves the geometric time axis. thm:transport is a target-adapted finite payload route. The source is formatted as an anonymous submission. Citation of N. Cheung does not by itself assign authorship. Cited sheets and the OpenAI catalogue are not premises. This is not spacetime emergence, not Einstein dynamics, 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.
• V-B records a local Grade S adaptation of admissible currents and a finite destructive clock onto a supported presentation of that prescribed cone. prop:nonGH says the regular product is not globally hyperbolic. def:presentation admits no incoming boundary data and no interaction with the singular worldsheet. thm:raw and thm:defect keep the current and the complete Ward defect. thm:cubicform is a separate Newton-wave cubic, not Einstein dynamics and not the inherited characteristic coefficient. thm:instrument consumes a finite clock encoding and leaves the geometric time axis. Finite compression is not a finite-qubit field instrument. thm:transport is a target-adapted endpoint channel. The source is formatted for anonymous review. Citation of N. Cheung does not assign authorship. Cited sheets and the OpenAI catalogue are not premises. This is not spacetime emergence, not Einstein dynamics, 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.
• VI-B records a local Grade S adaptation of harmonic Einstein-scalar descent and a compact-switch defect onto a supported presentation of that prescribed cone. prop:nonGH says the regular product is not globally hyperbolic. The flat Green operator is not intrinsic on the cone. thm:descent is second-order descent of a finite-time harmonic relational scalar. thm:switch-defect retains the first-order gap. A second-order correction, or a positive hbar-order correction, does not remove that gap while the lower-order prescription is held fixed. thm:instrument consumes a finite clock encoding and leaves 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. Cited sheets and the OpenAI catalogue are not premises. This is not spacetime emergence, not Einstein dynamics, 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.
• VII-A-ST records a local Grade S adaptation of the plateau intertwiner onto a supported presentation of that prescribed cone. prop:nonGH says the regular product is not globally hyperbolic. 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 intertwiner. prop:defect retains the larger-support gap. A higher coupling order does not remove that gap. The repair stays plateau-restricted. thm:instrument consumes a finite clock encoding and leaves the geometric time axis. Finite readout encodes 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. Cited sheets and the OpenAI catalogue are not premises. This is not spacetime emergence, not Einstein dynamics, 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.
• VII-E-ST records a local Grade S assembly of the observation-boundary contract and the finite hybrid channel onto a supported presentation of that prescribed cone. prop:nonGH says the regular product is not globally hyperbolic. The flat Green operator is not intrinsic on the cone. thm:pullback separates record compatibility from residual agreement. thm:residual-obstruction keeps a trace-distance gap of one half between ideal residuals with the same record. cor:informative says an informative classical record excludes recovery of every unknown quantum input. thm:coarse-gap keeps an exact half-diamond residual gap after coarse aggregation. A four-face marking is not the worldsheet. thm:instrument consumes a finite clock encoding and leaves the geometric time axis. 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. Cited sheets and the OpenAI catalogue are not premises. This is not spacetime emergence, not Einstein dynamics, 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.
• VII-F-ST records a local Grade S lift of the three-to-six particle-link event onto a supported presentation of that prescribed cone. prop:nonGH says the regular product is not globally hyperbolic. def:support keeps the quantum laboratory off the worldsheet. thm:event is the unique transverse incidence. thm:holonomy is one framed affine peripheral holonomy. thm:pullback separates record compatibility from residual agreement. cor:residual leaves a trace-distance gap of one half. prop:informative says an informative classical record excludes recovery of every unknown quantum input. thm:instrument consumes a finite clock encoding and leaves the geometric time axis. The event code is not a detector at 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. Cited sheets and the OpenAI catalogue are not premises. This is not spacetime emergence, not Einstein dynamics, 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.
• VII-J-ST records a local Grade S adaptation of scheduled dependencies and certified causality onto a supported presentation of that prescribed cone. prop:nonGH says the regular product is not globally hyperbolic. def:support keeps the laboratory off the worldsheet. No apex quantum register is used. thm:schedule bounds every jointly observed output by the complete ancestor set. thm:nosignal is the exact finite no-signalling criterion. thm:physical embeds those dependencies in the prescribed causal relation. thm:polytope keeps a finite-time directional remainder. thm:benchmark is one buffered regular-part exchange. thm:clock consumes a finite clock encoding and leaves the geometric time axis. A cycle velocity 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. Cited sheets and the OpenAI catalogue are not premises. This is not spacetime emergence, not Einstein dynamics, 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.
• VIII-ST records a local Grade S unification of affine matching, persistent three-to-six cellulation, and guarded description flow onto a supported presentation of that prescribed cone. prop:nonGH says the regular product is not globally hyperbolic. def:support keeps the laboratory off the worldsheet. def:host keeps catalogue replacement from changing the host metric. thm:event is the transverse three-to-six incidence. thm:matching is the five-component certificate. prop:residual separates equal records from residual source functionals. prop:affine separates packet selection from expectation acquisition. The source token is supplied, not acquired. thm:C5 is computational support, not a physical causal past. thm:instrument consumes a finite clock encoding and leaves the geometric time axis. thm:transport is reference-preserving 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. Cited sheets and the OpenAI catalogue are not premises. This is not spacetime emergence, not Einstein dynamics, 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.
• IX-A-ST records a local Grade S adaptation of the sharp-admission domain onto a causally saturated regular presentation of that prescribed cone. prop:nonGH says the regular product is not globally hyperbolic. def:support keeps the laboratory off the worldsheet. lem:saturation uses auxiliary Minkowski inverses and does not construct a global conical Green operator. thm:separator shows that unchanged regular approximants do not converge to the sharp insertion. thm:separate keeps classical multiplication separately continuous and does not construct a renormalized quantum product. Finite tables encode supplied evaluations, not acquired field values. thm:instrument consumes a finite clock encoding and leaves the geometric time axis. thm:operational is reference-preserving transport and 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. Cited sheets and the OpenAI catalogue are not premises. This is not spacetime emergence, not Einstein dynamics, 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.
• IX-B-ST records a local Grade S adaptation of the source-locked numerical triangle onto a supported chart of that prescribed cone. prop:nonGH says the regular product is not globally hyperbolic. def:support keeps the laboratory off the worldsheet. 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:skeletons retains eight contraction skeletons. prop:unique says H_ww=0 does not imply K=0. thm:descendants transfers the parent finite part with test-order loss 64 to 64+d. thm:independence says the observation-derivative orbit is not the parent class. thm:regularassociation equates two regularized parenthesizations and does not construct either sharp second multiplication. The VII-C obstruction remains. Finite tables encode supplied evaluations, not acquired field values. thm:instrument consumes a finite clock encoding and leaves the geometric time axis. thm:transport is reference-preserving transport 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. Cited sheets and the OpenAI catalogue are not premises. This is not spacetime emergence, not Einstein dynamics, 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.
• IX-C-ST records a local Grade S adaptation of the sequential IX-C, IX-Free, and IX-Free-2 partial product onto a supported chart of that prescribed cone. prop:nonGH says the regular product is not globally hyperbolic. def:support keeps the laboratory off the worldsheet. 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:Crelease certifies first-stage products and descent criteria and does not construct either sharp second multiplication. thm:Freerelease admits degree-two maps and does not release either complete association. thm:oldgluing and thm:coherence give one truncated partial product through order hbar^3. Wordwise coherence is not unspecified-triple associativity and not a causal lift. The VII-C obstruction remains. Finite tables encode supplied evaluations, not acquired field values. thm:instrument consumes a finite clock encoding and leaves the geometric time axis. thm:transport is reference-preserving transport 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. Cited sheets and the OpenAI catalogue are not premises. This is not spacetime emergence, not Einstein dynamics, 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.
• IX-D-ST records a local Grade S adaptation of the ordered IX-D, IX-E, IX-E-2, and IX-E-3 causal-interface programme onto a supported chart of that prescribed cone. prop:nonGH says the regular product is not globally hyperbolic. def:chartcausal keeps chart causal sets inside the retained laboratory and off the worldsheet. 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:Drelease separates free coherence from causal factorization and does not construct a sharp time-ordered product. thm:Erelease is the commutator criterion and is not a universal obstruction. thm:E2release evaluates the imaginary part and vanishes on the strongly separated class. thm:E3release is the conditional null-sphere bridge. The weak inherited trace certificate stays unverified. A specified flat realization does not identify that adjoint. The causal-product release stays Unresolved. The VII-C obstruction remains. Finite tables encode supplied evaluations, not acquired field values. thm:instrument consumes a finite clock encoding and leaves the geometric time axis. thm:transport is reference-preserving transport 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. Cited sheets and the OpenAI catalogue are not premises. This is not spacetime emergence, not Einstein dynamics, 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.
• XV-B version 2 proves relative lifting, a jet-null criterion, closed-set extension, and a one-point puncture correction. The point correction is not a positive-dimensional characteristic locus. XV-C and XV-E are not premises. The six-branch map stays unresolved at B1. The inherited full map is not constructed. This is not spacetime emergence, not a Page curve, and not holographic. The admission exit is not opened. O.1 stays NOT_CLOSED. XVI-N is not discharged. No quantum coefficient is admitted. No compilation is asserted.
• En02-D does not derive Hawking radiation: the transmission-dependent gap is not En02-C's one-live-qubit error, the prepared sequence is not a Page curve, Em02-D's inverse-cubic coefficient is not this channel, and the supplement is not reported as executed. No quantum coefficient is admitted. No compilation is asserted.
• Em03-A proves one fixed-background free-scalar emission law and does not derive quantum-gravitational evaporation. The bulk Unruh state is an external theorem. The peeling estimate is not a collapse theorem. En02-D's isometry does not select the spectrum. O.1 stays NOT_CLOSED. XV-B is not opened. No quantum coefficient is admitted. No compilation is asserted.
• En02-E constructs a finite Gaussian packet state and a flagged cutoff whose error is the discarded probability. The recovery benchmark transfers only the nonvacuum probability, which is not En02-D's transmission probability. Em03-A's packet mean is not this density operator. The implementation appendix is not reported as executed. This is not a Page curve and not a microscopic information-release mechanism. O.1 stays NOT_CLOSED. The series Route B is not discharged. XV-B is not opened. No quantum coefficient is admitted. No compilation is asserted.
• Em03-B constructs an apparatus-model readout of one Hawking packet: a passive capture kernel, coherent finite extraction, and a complete destructive instrument. The geometric density uses an inherited quasifree prescription. q_h is not En02-D's transmission probability and not En02-E's nonvacuum probability. This is not a local Schwarzschild detector and not a Page curve. Numerical execution is not reported as executed. O.1 stays NOT_CLOSED. The series Route B is not discharged. XV-B is not opened. No quantum coefficient is admitted. No compilation is asserted.
• Em03-C constructs the two-packet Gaussian baseline, a shared-port instrument, and a bounded discrimination certificate. Orthogonal packets are independent only when the off-diagonal covariance vanishes. Em03-B's one-packet budget is not this joint budget. This is not a local Schwarzschild detector, not a collapse theorem, and not a Page curve. An input-independent channel cannot recover an unknown label. Numerical execution is not reported as executed. O.1 stays NOT_CLOSED. The series Route B is not discharged. XV-B is not opened. No quantum coefficient is admitted. No compilation is asserted.
• Em03-D constructs one compact local probe for a bounded s-wave quadrature effect. The coupling region grows with the approximation, and access is a full angular shell. This is not a pointlike detector, not packet-number detection, and not channel equivalence with Em03-C. Em03-B and Em03-C effective ports are not premises. Numerical execution is not reported as executed. O.1 stays NOT_CLOSED. The series Route B is not discharged. XV-B is not opened. No quantum coefficient is admitted. No compilation is asserted.
• Em03-E constructs a finite message-dependent emission model from declared Hamiltonians. The optimal worst-case recovery error is (3-p-2p eta)/4, where p is the ciphertext pulse probability, not En02-D's transmission probability. Occupation calibration is not identification with Em03-C. No Em03-D source is assumed. Entropy is not a decoder certificate and not a Page curve. This is not unitarity restoration and not an evaporation endpoint. Numerical execution is not reported as executed. O.1 stays NOT_CLOSED. The series Route B is not discharged. XV-B is not opened. No quantum coefficient is admitted. No compilation is asserted.
• Em03-F constructs an exterior qubit coupled to the massless scalar field, with no extra radiation payload. The packet channel is entanglement breaking. The optimal diamond error is (3-d)/4 and is strictly greater than one half at every finite coupling. A sine-Weyl effect distinguishes source signs; selected number records do not. Classical source dependence is not quantum recovery. Switching work is not black-hole mass loss. Numerical execution is not reported as executed. O.1 stays NOT_CLOSED. The series Route B is not discharged. XV-B is not opened. No quantum coefficient is admitted. No compilation is asserted.
• Em03-G constructs two temporally ordered noncommuting couplings of one exterior qubit to the massless scalar field, first Z and then X. Outgoing packet restrictions are normal channels with interference, not independently assigned displaced Gaussians. An information-theoretic packet decoder has a growing-resource certificate. That decoder is not a coherent local receiver, and the growing-resource limit is not exact recovery at finite first-pulse coupling. Postprocessing Em03-F stays entanglement breaking. Em03-F does not supply the second pulse. Local access is a bounded Weyl probability only. Switching work is not black-hole mass loss. Numerical execution is not reported as executed. O.1 stays NOT_CLOSED. The series Route B is not discharged. XV-B is not opened. No quantum coefficient is admitted. No compilation is asserted.
• Em03-H version 8 specifies a fixed quartic Majorana Hamiltonian, an even spectral code, and a resonant controlled extractor, together with a declared continuum reduction. Target A replaces the quartic Hamiltonian by the number operator. Target B retains the interaction and does not discharge Target A. Ideal full transfer is exact, and the reached space for frozen instance P8 has dimension at most forty. Odd operators vanish on the initial code, and a CAR-invariant boundary subspace is the full Fock space. The specified continuum decoder has exact error one minus eta. Supplied P8-new records and a later summary report exploratory numbers, including a suggested error near 0.38687. Those reports are not validated. Independent execution is not asserted. The new v8 programs are unexecuted. The reported transmission enclosure is not a rigorous exclusion. No P8 gravitational dictionary is constructed. Quench work is not black-hole mass loss. The extractor is not passive Hawking evaporation. Em03-G does not supply this Hamiltonian. O.1 stays NOT_CLOSED. The series Route B is not discharged. XV-B is not opened. No quantum coefficient is admitted. No compilation is asserted.
• Em04-A version 2 proves an exact vacuum-plus-single-excitation reduction of one specified zero-temperature XY chain. Concurrence, the complete partial-transpose spectrum, and logarithmic negativity are explicit. Two dissipative coordinates are required. Finite local instruments and a compressed-position POVM have proved error bounds. Lindblad dynamics are an assumption of this model, not a theorem of I. I, IV, En02-A, X-Enter, and Em03-H do not supply the generator. Em03-H is not this reduction. V and Em03-D are not this position measurement. Source alignment remains unresolved. Reported correspondences are not validated. Independent execution is not asserted. The verification appendix is unexecuted. This is not a Page curve, not passive Hawking evaporation, and not a constructed gravitational dictionary. O.1 stays NOT_CLOSED. The series Route B is not discharged. XV-B is not opened. No quantum coefficient is admitted. No compilation is asserted.
• Em05-A version 1 proves exact occupation, purity, Bell-input mutual information, and reference negativity for one signed fermionic extraction channel. A specified decoder has error one minus eta and is not presumed optimal. Endpoint optimal errors are 3/4 and 0. A separate dephasing experiment retains its environment and, at full transfer, has optimal error (1-lambda)/2 while the accessible marginal stays fixed. Em03-H and Em04-A are not premises. Em03-E, Em03-F, En02-C, and En02-D do not supply this error. No numerical execution is asserted. The proposed checks are unexecuted. Independent execution is not asserted. This is not a Page curve, not passive Hawking evaporation, and not a constructed gravitational dictionary. O.1 stays NOT_CLOSED. The series Route B is not discharged. XV-B is not opened. No quantum coefficient is admitted. No compilation is asserted.
• VII-G version 1 specifies a finite completely positive hybrid instrument. Matter-controlled slicing of one fixed cone is not matter-driven gravitational dynamics. thm:observation is not a new general channel theorem. An informative classical record is incompatible with exact recovery of every input. prop:energy is not physical energy conservation. VII-E, VII-F, VIII-B, VIII-C, and En02-C are not premises. VII-A through VII-D do not supply a quantum source instrument. The pilot bound is unexecuted as a numerical certificate. This is not a Page curve, not passive Hawking evaporation, and not a constructed gravitational dictionary. O.1 stays NOT_CLOSED. The series Route B is not discharged. XV-B is not opened. No quantum coefficient is admitted. No compilation is asserted.
• VII-H version 1 constructs one connected vacuum susceptibility of a free massless scalar at first source order. thm:ambiguity leaves only a real multiple of hbar delta_0. thm:main evaluates one annular pairing at minus hbar t_0 over 2 pi squared for every admissible prescription. thm:experiment realizes that value by a delayed source and readout. This is not VII-D's reflected triangle. VII-E's dictionary does not construct the response. VII-G's finite instrument is not this distribution and is not a substitute for the missing gravitational coefficient. XII-F's classical remainder is not this susceptibility. A local counterterm is not its propagated image. H2, I3, and J2 stay unresolved. 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. XV-B is not opened. No quantum coefficient is admitted for the inherited response. No compilation is asserted.
• VII-I version 1 examines the finite-time harmonic insertion. thm:sharp excludes the original first dressing from the off-shell microcausal polynomial domain. thm:freealgebra constructs a density-prepared free polynomial algebra through second coordinate order. thm:transmission changes the sharp transmission data. thm:incompatibility separates old-product agreement from continuous triangle extraction. This is not the original sharp nonlinear interacting observable. VII-D's finite part is not a binary product. VII-H's catalogue is not this one. I3 and J2 stay open. This is not spacetime emergence. XV-B is not opened. No quantum coefficient is admitted for the inherited response. No compilation is asserted.
• VII-J version 1 separates scheduled reachability, actual influence, and an independently supplied causal relation. thm:schedule bounds influence by the complete ancestor set. thm:physical gives exact containment once edges are embedded. thm:eventbenchmark realizes one buffered transport across VII-F's fixed-cone event. Scheduled reachability is not a physical light cone. Certified matter communication is not matter-driven evolution of the cone. VII-E, VII-F, and VII-G are not premises. This is not spacetime emergence and not a Page curve. O.1 is not changed. No quantum coefficient is admitted. No compilation is asserted.
• VIII-A, VIII-B, and VIII-C are version 3. VIII-A certifies one fixed-presentation matching packet at deficit π/2 and proves a local residual obstruction and a local Einstein non-implication. VIII-B constructs the sourced family on a compact interval; the token is promised, not acquired. VIII-C returns a complete certificate after every legal command. thm:C5 is not a light cone. The mixed germ, token acquisition, directional inclusion, and polygon Hamiltonian stay unconstructed. Companion sheets are not premises. This is not spacetime emergence, not a Page curve, and not holographic identification. O.1 stays NOT_CLOSED. XV-B is not opened. No quantum coefficient is admitted. No compilation is asserted.
• Em05-B version 1 independently restates that signed extractor and proves complementary leakage, a constant-complement criterion, a flagged instrument, and an improved recovery sandwich. Exact recovery holds only at full transfer. The specified decoder still has error one minus eta and is not the improved bound. Maximal decoded Bell fidelity is (1+4 eta minus eta squared)/4. Endpoint optimal errors are 3/4 and 0. An exact intermediate half-diamond optimum is not asserted. At full transfer the dephasing error is (1-lambda)/2 while the Bell-input accessible marginal stays fixed. Identical marginals do not certify recovery. Em05-A, Em03-H, Em04-A, En02-C, and En02-D are not premises. No numerical execution is asserted. The proposed checks are unexecuted. Independent execution is not asserted. This is not a Page curve, not passive Hawking evaporation, and not a constructed gravitational dictionary. O.1 stays NOT_CLOSED. The series Route B is not discharged. XV-B is not opened. No quantum coefficient is admitted. No compilation is asserted.
• Em06-A version 1 proves a scalar-only coherent limit of the first plateau relational coefficient. The metric is a classical input. Only the free scalar is quantized. thm:main equates the mean with the named classical value for every positive classicality parameter and sets the variance to that parameter times a finite one-particle norm. prop:fixedCCR shows that unscaled coherent displacement does not make the absolute variance vanish. prop:noadmission does not repair XI-G. VII-A's first-order identity is reproduced and is not a premise of the quantum limit. VII-B, VII-H, and V are not premises. This is not metric reconstruction, not Einstein dynamics, not a holographic map, and not spacetime emergence. 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.
• XVII-A version 1 reconstructs one bounded sine effect at the central bulk point from one declared boundary time interval on an assumed global AdS2 background. thm:main supplies an exact boundary representative and an exact binary record channel. lem:timeband is a finite-cutoff completeness fact and is not an entanglement wedge. 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. This is not an identification with VII-A, V, or Em03. It is not metric reconstruction, not Einstein dynamics, not holographic emergence, not a Page curve, and not an interior partner. 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.
• Em06-B version 1 proves scalar-only gates B1 through B5 for finite families of the first plateau coefficient. The metric coefficient is a classical input. thm:estimate is a nonoptimal compact-test bound. thm:commuting and thm:ordered separate joint spectral laws from ordered Weyl expectations. thm:states makes epsilon times the observable second moment the exact concentration criterion. A residual number bound is sufficient and not necessary. thm:fluctuations keeps the residual-state CCR and does not infer a fluctuation limit from concentration. prop:noise separates measured noise from that intrinsic variance. The optional finite-mode metric gate B6 is not entered. Em06-A, VII-A, IX-A, XI-G, and XVII-A are not premises. This is not metric reconstruction, not Einstein dynamics, not holographic identification, and not spacetime emergence. 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.
• Psy02-A version 1 separates a scalar carrier, residual concentration, a coherence witness, a Wick-square response, scheduled support, one regularized reduction comparison, and a consciousness assignment. thm:concentration makes the observable-specific second moment the exact criterion. thm:witness does not infer coherence survival from concentration. thm:nonentailment does not derive experience from the stated physical premises. Em06-B, VII-H, and VII-J are source records and are not premises. This is not a derivation of Orch-OR, not metric reconstruction, not Einstein dynamics, not holographic identification, and not spacetime emergence. 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.
• Psy01-A version 1 proves cue bounds, a sparse counterexample to a universal density threshold, fixed-weight nesting, and a conditional selectivity-fragility comparison for one task-gated ReLU class. thm:nothreshold shows that density alone does not force cue loss. prop:equaldensity shows that identical masks need not determine stress tolerance. Em06-B, VII-H, and VII-J are not premises. Psy02-A is not an input. No biological pruning mechanism or treatment recommendation is asserted. This is not metric reconstruction, not Einstein dynamics, not holographic identification, and not spacetime emergence. 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.
• Psy02-B version 2 proves a branch-matched finite reduction pilot and an independent analytic interface. The same two branches determine the witness and the regularized self-energy. thm:colored is exact colored dephasing for one finite thermal bath. thm:pilot is a separate memoryless witness whose extra rate is a phenomenological input. thm:patterns and thm:massstability calculate Gaussian collective energies. thm:overlap is a complete-process obstruction. thm:pilotexample is a dimensionless gap, not a biological measurement. prop:nontransfer does not identify the pilot with the grouped map. thm:admission does not construct the map at I3, J2, or the XV-B interface. Excerpts of XII-A, XII-C, XIII-C, and XIV-H are source records and are not premises. This is not a derivation of Orch-OR, not metric reconstruction, not Einstein dynamics, not holographic identification, and not spacetime emergence. 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.
• Psy03-A version 1 proves intervention-budget certificates for one pruned network and a separately defined finite quantum extension. thm:zerodose shows that zero weight displacement need not preserve the implemented function. cor:stress is a damped path bound. thm:classicalboundary is an exact classical Markov reduction. thm:gap is a finite coherence contrast. 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, and Psy02-B are source records and are not premises. No numerical ranking and no antidepressant mechanism is asserted. This is not metric reconstruction, not Einstein dynamics, not holographic identification, and not spacetime emergence. 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.
• Psy03-B version 1 proves longitudinal structural-memory certificates for one pruned network with permanent scar masks and a separately defined finite quantum extension with a classical scar register. prop:reset shows that the gain reset forces effective gain one. thm:optimalrisk orders nested risks. The scar register is classical memory, not a quantum-memory resource. This is not a kindling mechanism and not spacetime emergence.
• Psy03-C version 1 proves recurrent-stability and probe-identifiability certificates for one scar-constrained GRU and a separately defined finite input-driven quantum model. thm:reluinvariance is an ordinary-ReLU cube, not a prediction certificate. thm:blend shows that distractor weight need not destroy information monotonically. prop:register keeps a persistent classical label from global forgetting. This is not a cognitive construct and not spacetime emergence.
• Psy03-D version 1 proves hidden-rule observability and intervention-identifiability certificates for a modular recurrent rule-switching task and a separately defined finite quantum cue pilot. thm:observability shows that point history does not reveal a stationary uncued rule. thm:ceiling gives the exact population optimum three quarters, attained by a memoryless classifier. Response repetition is not old-rule persistence. The quantum pilot does not overcome an absent observation channel. This is not a cognitive construct and not spacetime emergence.
• Psy04-A version 1 proves delayed random-access certificates for one declared two-state classical memory and a separately defined one-qubit code. thm:classical is the sharp bound of three quarters. thm:nonentailment records that a Markovian qubit can win and that a classical register can create a causal break. This is not quantum environmental memory and not spacetime emergence.
• Psy04-B version 1 proves a causal cut for that experiment. thm:schedule shows that scheduled ancestors upper-bound influence and need not equal it. ass:fresh keeps freshness separate from causal order. Enter is destructive. Neither scheduled ancestry nor a carrier-only causal break certifies quantum environmental memory. This is not a physical causal cone and not spacetime emergence.
• En03-A states an observation interface for destructive Enter and external geometry. thm:pullback is record compatibility. thm:obstruction keeps residual instruments separate. ip:networkcut is a prescribed-channel cut and is not a physical cone. thm:exchange certifies one four-face exchange on a fixed spacetime. This is not a gravitational field equation and not spacetime emergence.
• Hawk01-A states delayed-query retrieval from outgoing Hawking modes on a fixed Schwarzschild exterior. thm:source is a greybody-modified scalar emission law, not an evaporating metric. thm:null gives one half under message independence. thm:classical gives three quarters only for a trusted measure-before-query channel. thm:completion shows that equal late marginals need not agree on assisted recovery. This is not a solution of the information paradox and not spacetime emergence.
• Hawk01-B states arbitrary finite-code preservation in a declared sequential emission process. thm:exact makes recovery equivalent to a constant complete complement. thm:approximate gives the half-diamond recovery and leakage bounds. thm:entropyseparation matches radiation entropy histories and retains the code in a disclosed inaccessible memory. This is not a microscopic evaporation law and not spacetime emergence.
• Hawk02-A states a conditional certification interface for evaporation. thm:main bounds recovery error only after a stated transfer interface is supplied. cor:spectrum shows that identical late thermal states need not agree on assisted recovery. prop:massstability is a ledger allowance, not a metric theorem. This is not a microscopic black-hole Hamiltonian and not spacetime emergence.
• Hawk02-B states a Hamiltonian-derived finite sequential-emission model. thm:B2 derives the complete emission isometry from prescribed pulses. thm:B3 gives the exact single-cell recovery error. thm:B7 calculates entropy turnover and does not use it to certify recovery. This is not a microscopic evaporation law and not spacetime emergence.
• Hawk02-C states an autonomous source-field bridge. thm:C2 reduces the prepared sector to a Friedrichs operator. thm:C4 gives the exact packet recovery and residual leakage. thm:C7 separates an endpoint comparison with Hawk02-B from a predictive finite-chain remainder. A supplied diagnostic record reports 18 finite-proxy predicates. It is not an independent rerun and does not replace the proofs. This is not gravitational Hawking radiation and not spacetime emergence.
• Hawk02-D states a quadratic fermionic source-reservoir comparison. thm:main bounds K-particle recovery and complete residual leakage. thm:erasure gives the exact one-particle error. thm:endpoint derives a constant complete complement from the same Hamiltonian. thm:recurrence blocks permanent late-time recovery at fixed finite chain length. OpenAI families are documentary and are not premises. This is not interacting SYK, not a horizon, not gravitational backreaction, and not spacetime emergence.
• Hawk02-E states a regulated interacting SYK--scalar certification framework. thm:selfadjoint constructs the continuum Hamiltonian. prop:insertion loads an even-parity diary by one message-independent swap. thm:regulator bounds a finite complete-channel approximation. thm:certificate retains the code dimension. thm:release leaves the small dynamical residual, the gravitational correspondence, and the evaporation endpoint unproved. Hawk02-D and the OpenAI catalogue are not premises. This is not a horizon, not gravitational backreaction, and not spacetime emergence.
• Hawk03-A states a finite firewall-interface package. thm:partner puts the partner inside the radiation algebra. thm:commuting obstructs two commuting copies of the same noncommutative logical algebra. prop:distill changes the original pair test. req:horizon and req:diary are not discharged. This is not a firewall resolution and not spacetime emergence.
• Hawk04-A states unitary preservation and a complete-complement recovery criterion. thm:global gives a CPTP left inverse of the complete output. thm:exact recovers from radiation if and only if the complete complement is constant. thm:four-majorana keeps radiation recovery error at least one half on one frozen realization while global recovery stays exact. thm:endpoint requires access-preserving identifications. thm:release leaves unitarity of quantum gravity and a gravitational endpoint unproved. Hawk02-E and the OpenAI catalogue are not premises. This is not a horizon, not a Page curve, and not spacetime emergence.
• Hawk04-B version 2 separates quantum recovery from destructive readout and operational discard. Enter on radiation returns a classical record, not the quantum decoder. thm:classical keeps a classical record from reconstructing an unknown quantum diary, with error at least one minus one over d. thm:drop equates residual readout-and-drop with the partial trace and leaves the radiation channel unchanged. That equality is not physical annihilation. thm:control shows neither output alone need recover the diary on one frozen realization. cor:gravity is conditional. Finite-program termination is not an evaporation endpoint. Hawk04-A, Landmark I, and the OpenAI catalogue are not premises. This is not a horizon, not a Page curve, and not spacetime emergence.
• Hawk04-C states finite Enter analogues of the Hawking narrative. thm:global restores the code from the complete output. thm:exact recovers it from one factor only when the complete complement is constant. thm:classical keeps classical-record error at least one minus one over d. thm:drop equates readout-and-drop with the partial trace and is not annihilation. prop:thermal and prop:entropy do not turn thermal marginals or a selected entropy into recovery. The endpoint package is not constructed. Hawk04-A, Hawk04-B, and the OpenAI catalogue are not premises. This is not evaporation, not a Page curve, and not spacetime emergence.
• Hawk04-D states a conditional certification framework from finite Enter interfaces toward evaporation certificates. thm:exact restores the code from the complete output and recovers it from one factor only when the complete complement is constant. lem:benchmarks keeps classical-record error at least one minus one over d. prop:drop equates readout-and-drop with the partial trace and is not annihilation. thm:swap and thm:flagged are calibration identities, not a Page-time law. thm:lifetime stops at a positive mass cutoff and is not a Planck-scale endpoint. prop:spectral-separation says selected entropy and thermal marginals are not recovery. The endpoint package is not constructed. Hawk04-A, Hawk04-C, and the OpenAI catalogue are not premises. This is not evaporation, not a Page curve, and not spacetime emergence.
• Hawk05-A separates a coherent radiation history from a destructive classical record. thm:exact recovers the code from the accessible factor only when the complete complement is constant. thm:classical keeps classical-record error at least one minus one over d. thm:recordentropy keeps the Shannon entropy of an unedited record nondecreasing. thm:flagged is a designed turnover, not a Page-time law. thm:drop equates readout-and-drop with the partial trace and is not annihilation. The supplied author field is empty and authorship is not inferred. Hawk04-A, Hawk04-D, and the OpenAI catalogue are not premises. This is not evaporation, not a Page curve, and not spacetime emergence.
• Hawk05-B derives the exact finite Page-Sen mean for one Haar-scrambled coherent history. thm:classicalpage is a destructive-record mean that does not turn over. thm:fullcode and thm:decoupling separate whole-code recovery from that mean. The Haar hypothesis is an extra assumption. The title page names Ngo Cheung. Hawk05-A, Hawk04-D, and the OpenAI catalogue are not premises. This is not a Page curve of gravitational evaporation, not an island, and not spacetime emergence.
• Hawk05-C states conditional Page-curve extrapolations under Enter. thm:two gives two exact means for one cell-release proxy. thm:compatibility keeps the sum of logarithmic capacities constant. thm:crossover stops a supplied inverse-square clock at a positive cutoff. thm:sector is a direct-sum charge proxy. thm:recovery is a separate certificate and not an island. The title page names Ngo Cheung. Hawk05-A, Hawk05-B, and the OpenAI catalogue are not premises. This is not a Page curve of gravitational evaporation, not an island, and not spacetime emergence.
• Hawk06-A states an operational-island certificate in one finite Enter model. def:island is a reconstruction certificate for a logical factor that starts in an inaccessible vault. thm:threshold certifies every later retained cut. thm:decoder is a deterministic finite program. The coherent entropy can turn over. The destructive record cannot. The physical residual remains a tensor factor. The title page names Ngo Cheung. Hawk05-B, Hawk05-C, and the OpenAI catalogue are not premises. This is not a gravitational island, not a quantum extremal surface, not a replica wormhole, not a Page curve of gravitational evaporation, and not spacetime emergence.
• Hawk07-A states an operational-wormhole certificate in one finite Enter model. def:wormhole names an accessible register and a residual. The throat is the complete complement, not a tunnel. thm:threshold certifies every later retained cut. thm:decoder is a deterministic finite program. The coherent entropy can turn over. The destructive record cannot. The physical residual remains a tensor factor. The title page names Ngo Cheung. Hawk06-A, Hawk05-B, Hawk05-C, and the OpenAI catalogue are not premises. This is 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.
• Hawk07-B states operational functions and conditional predictions for one finite wormhole certificate. thm:threshold rederives a sufficient released dimension with inverse-square scaling. thm:functions makes whole-code return stronger than a beacon. thm:turnover is a square-power coexistence of recovery and strict coherent turnover, and the destructive album is nondecreasing. thm:convoy needs separately prepared resources. thm:resetcomposition says leakage does not supply memory reset. prop:discard is partial trace, not a fuel bill. The title page names Ngo Cheung. Hawk07-A is not silently reused. Hawk07-A, Hawk05-A, Hawk05-B, Hawk05-C, and the OpenAI catalogue are not premises. This is 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 Page curve of gravitational evaporation, and not spacetime emergence.
• En04-A separates quantum magic from complete residual response and from geometric backreaction. def:response is non-constancy of the complete complement. thm:exact recovers the code from radiation only when that complement is constant. The restore map returns the code from the complete output and does not relocate it into the residual. cor:noimplication shows that a Clifford copier can respond and that a non-Clifford syndrome need not. thm:rotation gives leakage sin theta over 2 and radiation recovery error (1 minus cos theta) over 2 for one family. thm:majorana is a recovery obstruction, already present at zero coupling, and not a magic certificate. thm:drop is operational partial trace, not permanent deletion. cor:bridge is conditional. Hawk04-A, Hawk04-B, Landmark I, and the OpenAI catalogue are not premises. This is not a horizon, not a Page curve, and not spacetime emergence.
• En05-A states an exact causal cone for partitioned Enter dynamics. lem:comparison equates snapshots, channels, and adjoint support. thm:cone makes the schedule past an upper bound, not influence. prop:attain gives c_lat equal to r on the stated lattices. thm:isotropyobstruction keeps a fixed periodic model inside a velocity polytope, and the cardinal model is an ell-one diamond rather than a Euclidean ball. thm:boostobstruction withdraws physical retiming-stability: unrestricted boost-closure excludes ordinary bidirectional one-tick relays. prop:drop is operational partial trace, not permanent deletion. Continuum statements stay conditional on C1 through C7, and conj:family remains open. No invariant physical speed is claimed. En04-A, En03-A, VII-J, Landmark I, and the OpenAI catalogue are not premises. This is not a metric, not a Page curve, and not spacetime emergence.
• En05-B constructs one isotropic matched operational continuum limit for a declared finite-experiment class. thm:main makes the Euclidean envelope and the scheduled past converge under one clock. thm:identity is logical identity transport, including untouched references. thm:relay has gap one in every direction. cor:maxspeed equals the prescribed speed c and is not a speed extracted from entanglement. prop:weakC4 does not infer a unique instrument from one terminal law. No uniform degree or block bound is claimed. En05-A, En04-A, VII-J, Landmark I, and the OpenAI catalogue are not premises. This is not Lorentz covariance, not a Page curve, and not spacetime emergence.
• En06-A is a corrected layer account. lem:comparison equates snapshots, channels, and adjoint support. thm:order and thm:metric give the discrete cone. thm:coneconv is a Euclidean envelope for changing word metrics. thm:coarseDOD holds only for one restricted full-tail outcome-law theory and is not an instrument-level limit. thm:withdrawal keeps unrestricted device resynchronization withdrawn. thm:algmicro does not promote commuting channels to algebraic microcausality. The registered En05-B construction is not a premise. En05-A, En04-A, and the OpenAI catalogue are not premises. This is not an invariant physical speed, not a Page curve, and not spacetime emergence.
• En05-C states a tensor-free snapshot comparison for gauge-invariant local algebras. thm:comparison equates equal state restrictions, UCP factorization, and Heisenberg containment without a spatial tensor factor. prop:centers keeps sector probabilities. prop:extensiongap shows a regional restriction need not determine the global device. thm:onelayer holds only for specified internal Kraus devices. thm:refinementnet is an exact finite-mode subdivision, not a relativistic field theory. En05-A, En05-B, En06-A, and the OpenAI catalogue are not premises. This is not Lorentz covariance, not a Page curve, and not spacetime emergence.
• En06-B constructs spacetime transport for finite future-causal instrument networks on one increasing-stencil family. lem:residues keeps residue lanes disjoint, including in one dimension. lem:pacing controls every prefix. thm:identity preserves the complete instrument, including untouched references. thm:T has a complexity-independent coarse coefficient. thm:pairing matches one Bell instrument to a commuting observable net, with CHSH value 2 times the square root of 2. prop:obstruction shows a fixed cardinal stencil still fails. The constant c is an input. En06-A, En05-C, En05-B, En05-A, and the OpenAI catalogue are not premises. This is not a quantum field theory, not a Page curve, and not spacetime emergence.
• En07-A is a framing note for complete residuals, destructive readout, and thermodynamic language. thm:exact equates whole-code recovery from the accessible factor with a constant complete complement. lem:erasure-interface equates readout followed by discard with partial trace, including references. thm:classical bounds a classical record by one minus one over d. prop:no-landauer-from-channel says channel equality does not fix heat, work, or reset cost. cor:dimension is a Hilbert-space count, not an area law. Hawk04-B, En05-C, En06-B, and the OpenAI catalogue are not premises. This is not the gauge-theory designation refused by En05-C. This is not a Landauer bound, not holographic identification, not a Page curve, and not spacetime emergence.
• En07-B states a finite endpoint certificate under destructive Enter. thm:exact equates outgoing recovery with a constant complete complement. thm:approx converts an imported information-disturbance theorem into half-diamond bounds. A nearly constant complete complement is a recovery upper bound. A nearly constant accessible output is a recovery lower bound. Those directions cannot be interchanged. thm:endpoint requires four same-model obligations that are not constructed. En07-A, Hawk04-B, and the OpenAI catalogue are not premises. This is not a gravitational endpoint, not a Page curve, and not spacetime emergence.
• En07-C compares Hawking's 1975 thermal emission with that finite interface. The occupation formula and temperature are external inputs. thm:exact still equates outgoing recovery with a constant complete complement. A nearly constant accessible channel is a recovery lower bound. A nearly constant complete complement is a recovery upper bound. thm:endpoint stays conditional. En07-B, Hawk04-B, and the OpenAI catalogue are not premises. This is not a Bogoliubov calculation, not a Page curve, and not spacetime emergence.
• 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. lem:boundary accounts for the cut. lem:cancellation is the two-family entropy bound. thm:terminal prices an area-law constant only when a partition and information charges are supplied. It does not extract that constant from the gap. thm:recovery equates reference-preserving recovery with the complete complement. lem:constant gives the replacement-channel error one minus d to the minus two. PEPS representability is not tensor production. prop:forty is procedure-dependent and is not a universal sample bound. thm:separation refuses a Page curve, an island, and a radiation history. 265-01 and 265-02 are not verified. The single active successor is quantitative constant extraction. Canonical265.lean is not an area-law formalization. En02-B, En07-C, Hawk04-B, and the OpenAI catalogue are not premises. This is not a Page curve, not an island, and not spacetime emergence.
• Oai265-B version 2 certifies one implemented qubit decoder from three Bell correlations. thm:main gives coverage at least one minus alpha for a half-diamond interval. The transfer allowance stays outside the square root. A supplied report of 140 simulated datasets cannot accept the 0.1 threshold at 40 shots per setting. That report is not an independent rerun and not a laboratory calibration. Oai265-A, En07-C, and Hawk04-B are not premises. This is not decoder optimality, not a Page curve, and not spacetime emergence.
• Oai290-A version 1 types a finite recovery decision. thm:exact equates full-code recovery with a constant complete complement. thm:effect separates one named observable from that criterion. thm:certificate bounds one specified decoder from a Choi-overlap interval and a transfer allowance outside the square root. thm:bounded restates the modular-band witness of OpenAI preprint 290-02 and does not verify it. 290-01 is not imported. thm:assembly allows certified, excluded, and inconclusive outcomes. Four endpoint obligations are not constructed. Family 290, Oai265-B, En07-C, and XIV-J are not premises. This is not bulk reconstruction, not a Page curve, and not spacetime emergence.
• Oai211-A version 1 marks critical finite-variance trees conditioned on size. thm:path controls offspring-bounded ancestral labels. thm:channel compares a path-averaged channel with its spine average in half-diamond distance. thm:serial is a designed weak depolarizing family, not a dynamics inferred from a metric limit. thm:experiment keeps tree, sampling, calibration, and implementation allowances separate. cor:FK keeps the supplied q>4 Fortuin--Kasteleyn limit conditional. prop:root shows that path concentration does not concentrate one root mark. Family 211 is an external record and is not verified. Hausdorff dimension two is not a surface manifold. Oai290-A, En07-C, and the OpenAI catalogue are not premises. This is not a quantum surface, not a Page curve, and not spacetime emergence.
• Oai280-A version 1 records Family 280 and certifies declared finite channels. thm:exact equates exact recovery with a constant complete complement. thm:main is a simultaneous three-correlation certificate. prop:forty keeps forty shots from accepting the 0.1 threshold under this Hoeffding procedure. prop:effect shows that a named observable can survive. thm:extensionseparation says a Q-system is not a gravitational dictionary. Family 280 is an external record and is not verified. A sector tag is not sector identification. Oai211-A, En07-C, and the OpenAI catalogue are not premises. This is not a conformal net derived as spacetime, not a Page curve, and not spacetime emergence.
• Oai280-B version 1 connects one printed five-qubit encoding, one audited access interface, and one complete decoder. 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. thm:main certifies the connected implemented channel. prop:spectatortrap shows that a fixed spectator is not arbitrary-spectator recovery. En02-B and Oai280-A are not premises. This is not a gravitational dictionary, not a Page curve, and not spacetime emergence.
• Oai280-C version 1 certifies one declared decoder on one declared accessible interface for a logical code, a subsystem, or a finite direct-sum algebra. thm:complement restricts the constant-complement criterion to full-code recovery. thm:snapshot is linear determination, not a CPTP decoder. thm:block re-proves the ideal five-qubit access table. thm:programme keeps failure branches inside the tested channel. thm:simultaneous gives simultaneous reference-preserving intervals. prop:forty keeps the forty-shot limitation certificate-specific. Oai280-B, En02-B, and En05-C are not premises. This is not a gravitational dictionary, not a Page curve, and not spacetime emergence.
• Oai282-A version 1 records Family 282 and certifies a finite local-Ward residual for declared improvement data. thm:ward and prop:finitefit are an exact finite defect certificate. prop:coverage says finite vanishing is not a distributional identity without an independently proved coverage condition. prop:free calculates L on a supplied Wick domain and does not reconstruct a new physical scalar. prop:einstein says symmetry, conservation, and zero trace do not imply the Einstein equation. prop:flow separates a local current from a global action on the Minkowski chart. VII-H, Em02-E, En05-C, and the OpenAI catalogue are not premises. This is not a verification of Family 282, not Einstein dynamics, not a Page curve, and not spacetime emergence.
• Oai282-B version 1 constructs the free massless improvement scalar and its local conformal action. prop:physicalL puts L equal to minus Q over 2 in the original Weyl net. thm:localaction implements translations, Lorentz transformations, dilations, and special conformal transformations on the ordered Wick algebra. thm:classification leaves a two-dimensional homogeneous residual family. thm:coverage shows that two probes separate that family. prop:invisible keeps unrestricted conserved tensors outside that coverage. prop:flow and prop:nonintegrable separate the local action from global integration. prop:einstein says the improved tensor does not imply the Einstein equation. Oai282-A, VII-H, and XIV-J are not premises. This is not a verification of Family 282, not a general scale-to-conformal theorem, not Einstein dynamics, not a Page curve, and not spacetime emergence.
• Oai069-A version 1 certifies one finite-monodromy local-system decoder and one independent free-scalar Ward defect. thm:category is a dagger equivalence on a fixed elliptic curve. thm:exact returns the named label and the qubit multiplicity. thm:loss gives sharp all-decoder errors after a coefficient leg is removed and still recovers a named effect. thm:simultaneous gives simultaneous intervals for complete implemented channels. prop:ward is a finite defect for one declared homogeneous class. The torus benchmark is not a specialization of Family 069. Oai280-C, Oai282-B, and VII-H are not premises. This is not a verification of Family 069, not a Page curve, not Einstein dynamics, and not spacetime emergence.
• XVIII-A version 2 states an interface contract and does not evaluate the companion coefficient. thm:witness and cor:smoothwitness keep a pure-trace witness from determining the compact kernel. prop:hbar separates a classical formal coefficient from a positive formal order. thm:ward is an affine quotient, not ambient BRST cohomology. eq:readout is a finite readout convention, not a decoder. XVII-A is not replaced. XVI-H, Oai282-B, and Hawk04-B are not premises. This is not a Page curve, not Einstein dynamics, and not spacetime emergence.
• XVIII-B version 2 evaluates one massive-scalar stress response. thm:spectral gives the spin-two and spin-zero densities. thm:retarded builds a once-subtracted causal kernel. thm:contacts and cor:unique fix the transverse contacts. thm:ward is linear transversality. thm:residual is a fixed-preparation remainder. prop:detector is a vacuum norm, not an instrument. VII-H, Oai282-B, and XVIII-A are not premises. This is not VII-H, not a Page curve, not Einstein dynamics, and not spacetime emergence.
• XIX-A version 1 separates four time-related prescriptions. thm:main keeps the harmonic scalar, the original-rod lapse, the incidence register, and the density ramp distinct. lem:scalar-lapse shows a scalar value does not determine the lapse. The ramp is a named non-clock. Family 271 names 271-04 only. VI is not 271-04. The VI–XVI-D comparison is not decided. Em02-E, VIII-B, and X-A are not premises. This is not spacetime emergence.
• XIX-B version 1 excludes one direct first-coordinate identification. thm:mismatch detects a nonzero residual after the declared sign transport. lem:hbar says a positive formal order does not cancel that residual. prop:switch keeps the scalar-switch identity separate. XVI-D's conditional compatibility is not discharged. VI and XVI-D are not premises. This is not a universal obstruction and not spacetime emergence.
• XIX-C version 1 states a finite incidence interface. lem:matching is uniqueness in one fixed presentation. prop:residual separates equal records from residual sources. prop:two-limits gives two continuum limits of one finite channel. The XIX-B mismatch is not used. VIII-C and En05-A are not premises. This is not a native continuum evolution and not spacetime emergence.
• XIX-D version 1 inventories unclosed quantum inputs. def:slots names five missing slots for the original-rod lapse. prop:repair requires the actual counterterm image. lem:formal separates a classical coefficient from a positive formal order. VI's certificate stays RG-open. XVI-Q Q11 is not a clock. Em02-E and XVIII-A are not premises. This is not a certificate and not spacetime emergence.
• XIX-E version 1 records the release boundary. thm:boundary does not identify the four labels and does not open a successor. prop:placement separates convolution from density multiplication. prop:blind does not erase XVI-H's reported kernel. XIV-I's I2 advance is not withdrawn. XV-B is not opened. XVI-N is not discharged. This is not a universal prohibition and not spacetime emergence.
• XX-A version 1 freezes one original-rod lapse. thm:lapse keeps the rod term and leaves the second spatial rod out of the quadratic lapse. thm:classical-gauge is classical. thm:release leaves the quantum milestone unresolved at Q1. Em02-E is not identified in full. This is not spacetime emergence.
• XX-B version 1 constructs the compact-test free input. thm:NH is the normalized hyperbolic operator. thm:contractions is an algebraic Hadamard class, not a positive state. def:closure limits Q1. Rods are not propagating fields. This is not spacetime emergence.
• XX-C version 1 audits subtraction and tails. thm:nonpositive is one same-class obstruction, not a universal exclusion. thm:tworod keeps an inverse-distance term. prop:repair is unsolved. Q2 is not closed. This is not spacetime emergence.
• XX-D version 1 separates the classical jet, the compact-cutoff symbol, and a conditional native symbol. thm:native does not verify the infrared hypotheses. Native Q3 stays open. This is not spacetime emergence.
• XX-E version 1 proves the coupled classical Ward identity, the cutoff residual, and an escaping-source example. thm:repair is conditional. Native Q4 and Q5 stay unentered. This is not spacetime emergence.
• XX-F version 1 proves the Leibniz defect, the order-three centrality correction, weighted Newton bounds, and conditional repair. def:entry is not discharged. Native Q3 stays open. Native Q4 and Q5 stay unentered. This is not quantum evolution without an external time and not spacetime emergence.
• En08-A version 1 separates scheduler consistency from Lorentz-cone selection. thm:main shows that acyclic dependency, schedule-independent records, operational sensitivity, finite reachability, and confluence do not determine a Lorentz cone. thm:weaker is conditional on homogeneity and strict convexity and cites the Ito–Lourenço classification. A finite ordered sample does not determine the metric. Chronology alone does not. En05-B and En06-B are not this cone. This is not Einstein dynamics and not spacetime emergence.
• En08-B version 1 approximates a prescribed Euclidean null boundary by finite local SWAP protocols. thm:main combines a locality lower bound, constructive routing, exact identity transport, and an O(j) resource ledger. cor:operational-limit is endpoint and arrival-time convergence, not a field algebra. The metric and the speed are inputs. En05-B, En06-B, and En08-A are not premises. This is not Einstein dynamics and not spacetime emergence.
• En09-A version 1 realizes relational time by destructive Enter on a finite clock. thm:main equates the readout with the Page–Wootters conditioning channel, including an untouched reference. The classical code is the label. The clock names are consumed. Sampled covariance and stationarity give the conditional unitary. Born attribution stays conditional on Landmark I. XIX-C, Em02-E, En08-A, and En08-B are not premises. This is not quantum evolution without an external time and not spacetime emergence.
• En10-A version 1 estimates a source weight from a finite qubit–antiqubit Enter instrument. thm:main is the complete destructive record and the calibrated estimator. The measured names are consumed. prop:no-return obstructs record-only recovery. prop:inversion does not certify the antiqubit sign. En09-A, XIX-C, and En08-B are not premises. This is not Galactic identification and not spacetime emergence.
• En10-B version 1 derives a finite acquisition channel and a conditional identification bridge. thm:derived is the generator-to-record instrument. thm:competition requires a positive complete-law margin. thm:main applies only when a physical package is supplied. That package is not constructed. En10-A is not this derived channel. This is not an exclusion of classical gravity and not spacetime emergence.
• XXII-A through XXII-F version 1 are a conditional Lorentz-cone programme. thm:order is a component order. thm:flat says the constant representative is flat. thm:assembly is conditional on a package and a rule that are not constructed. Registered En10-A is not a premise of XXII-F. This is not Einstein dynamics and not spacetime emergence.
• Oai212-A version 1 states explicit quantum-to-first-passage interfaces. thm:exact-otoc is one controlled CNOT identity. thm:transfer is the macroscopic comparison. cor:regularity is conditional on unverified 212-02. prop:cone does not supply homogeneity. This is not Einstein dynamics and not spacetime emergence.
• Oai365-A version 1 states a conditional boundary-to-interior identification. thm:pilot-cone is one enriched Lorentz pilot. thm:scaled is a restricted scaled-ball dictionary. thm:boundary stays conditional. Family 365 is not verified. This is not Einstein dynamics and not spacetime emergence.
• Oai283-A version 1 certifies a finite coherent-oracle circuit. thm:assembly is conditional on a supplied instance. lem:normalization converts full-diamond 1/2 into half-diamond 1/4. 283-01 is not verified. This is not Einstein dynamics and not spacetime emergence.
• Oai272-A version 1 states a conditional secret-bit and PPT-composition audit. thm:bit-gap is the unhalved 1/5 gap. thm:assembly applies only when a finite instance is supplied. 272-01 is not verified. This is not gravity-generated entanglement, not a Page curve, and not spacetime emergence.
• Oai276-A version 1 states a conditional one-use Holevo audit. thm:oneuse is the one-use formula. thm:finite-certificate encloses the frozen channel at gamma 1/2 and nu 1/4. 276-01 is not verified. Partner additivity is not proved. This is not gravity-generated entanglement, not a Page curve, and not spacetime emergence.
• Oai279-A version 1 states a finite exact-output certificate. thm:finite is the 175-gate circuit for every integer from 2 through 15. The output at 12 is (2,2,3). 279-01 is not verified. This is not a Page curve, not gravity-generated entanglement, and not spacetime emergence.
• Oai227-A version 1 states a finite stationary--quench certificate. thm:finite-certificate is the two-spin comparison on [4,5] times [1,2]. For every real coupling the difference is less than 1/65536. 227-01 is not verified. This is not a Page curve, not gravity-generated entanglement, and not spacetime emergence.
• Oai119-A version 1 states a finite Hellinger certificate. thm:finite covers every Boolean function on the two-dimensional cube at correlation 1/2. Equality holds for the four signed coordinates. 119-01 is not verified. This is not a Page curve, not gravity-generated entanglement, and not spacetime emergence.
• Landmark II version 2 keeps the same SEP-finite certificate. On the three-label family the rank is 2, the original minor is 64, and the coefficients are 2/3 and 2/3. cor:affine-fits identifies the whole affine family. A finite fit is not a global contact identity. Complete coverage is three clauses. Action equivalence is not response-space equivalence. Injective evaluation is sufficient and not necessary. Weighting does not preserve the unweighted integration-by-parts quotient. Contact rebasing is not a prescription change. The unweighted certificate is not a weighted class, not a changed gauge prescription, and not an unidentified counterterm space. Companion manuscripts are not premises. The embedded checker is not executed. This is not spacetime emergence. O.1 stays NOT_CLOSED. XV-B is not opened. H2, I3, and J2 stay unresolved. No quantum coefficient is admitted. No compilation is asserted.
• Landmark I version 2 characterizes destructive Enter inside a stated class. thm:main identifies Born probabilities and projective residual rays. That uniqueness is not record-free. lem:path is a first-order interface, not a field instrument. prop:pullback and ex:equal-records separate record compatibility from residual instruments. prop:process does not reverse complete-process equality. thm:stability uses a total global live-qubit budget, which is not a scheduled laboratory peak. prop:classical-recovery shows that a finite classical record is entanglement breaking. The static non-Born family fails operational nullity. Companion records, including En03-A, En02-B, Psy02-B, Hawk01-B, Em03-C, and XIV-I, are not premises. This is not a Frauchiger-Renner no-go, not a horizon construction, and not spacetime emergence. O.1 stays NOT_CLOSED. XV-B is not opened. No quantum coefficient is admitted. No compilation is asserted.
• Connections is a source-based map. A line there is not a verification and not a formal premise unless the later manuscript says it uses the earlier one as input.

Server environment

Set these where the server runs. Do not put them in the browser. See the project README and the placeholder file .env.example.

• LLM_PROVIDER
• LLM_MODEL
• LLM_REASONING_EFFORT
• LLM_BASE_URL
• LLM_API_KEY
• XAI_API_KEY
• LLM_MAX_TOKENS