A source-based map of how the manuscripts sit next to each other. It is not a verification of the proofs, and a line is not a permission to treat one paper’s theorem as another’s premise. Among I–V, formal dependence is empty. VI through VII-D is a classical-to-quantum construction track. VII-E through VII-G and VIII-A through VIII-C are the external-geometry branch. VII-G is a finite hybrid instrument beside that branch and does not turn it into gravitational dynamics. VII-E-ST assembles those two contracts on a prescribed cone. Record compatibility is not residual agreement, and the assembly is not spacetime emergence. VII-F-ST lifts VII-F's three-to-six incidence onto that cone and encodes it with a destructive clock. The worldsheet is an input, and the certificate is not spacetime emergence. VII-J-ST certifies finite scheduled influence and one buffered regular-part transport on that cone. No apex register is used, and the certificate is not spacetime emergence. VIII-ST unifies affine matching, persistent cellulation, and guarded flow on that cone. Catalogue replacement is not host-metric evolution, and the certificate is not spacetime emergence. IX-A-ST admits the exact sharp insertion on a causally saturated chart of that cone. Separate continuity is not a renormalized quantum product, and the certificate is not spacetime emergence. IX-B-ST places the IX-B numerical triangle and derivative-spectator transfer on a supported chart of that cone. Equality of the two regularized parenthesizations is not a sharp second multiplication, and the certificate is not spacetime emergence. IX-C-ST places one truncated partial product for one sharp ordered word on that cone. Wordwise coherence is not a causal lift, and the certificate is not spacetime emergence. IX-D-ST places the causal-interface programme on that cone. A support bridge is not a sharp time-ordered product, and the certificate is not spacetime emergence. VII-H is a separately declared free-field response benchmark. It is not VII-D's reflected triangle, it is not that instrument, and it does not construct the inherited gravitational characteristic coefficient. VII-I is a separately declared repair ledger for the finite-time harmonic insertion. Its finite-width free algebra is not the original sharp interacting observable. VII-J is a separately declared causal-network certificate. Scheduled reachability is not a physical light cone, and certified communication on VII-F's fixed cone is not matter-driven evolution of the cone. Em06-A is a scalar-only classical limit of one plateau coefficient. It is not spacetime emergence and not a repair of XI-G. XVII-A reconstructs one finite sine effect from one boundary time interval. It is not holographic emergence, not a Page curve, and not an entanglement wedge. Em06-B proves scalar-only family concentration for the first plateau coefficient. B6 is not entered. It is not spacetime emergence and not a repair of XI-G. Psy02-A is a conditional carrier ledger and is not a derivation of Orch-OR. Psy02-B is a branch-matched finite pilot. It is not biological viability, not a derived collapse law, and not spacetime emergence. Psy03-A is an intervention-budget framework. Weight displacement is not a universal dose, the quantum extension is separately defined, and it is not spacetime emergence. Psy03-B is a longitudinal structural-memory framework. Permanent scars constrain repair capacity, the scar register is classical memory, and it is not a kindling mechanism and not spacetime emergence. Psy03-C is a recurrent-stability framework. An ordinary-ReLU cube is not a cognitive construct, the quantum model is separately defined, and it is not spacetime emergence. Psy03-D is a hidden-rule observability framework. A three-quarter ceiling is not rule adaptation, the quantum cue pilot is subordinate to the observation obstruction, and it is not spacetime emergence. Psy04-A is a delayed random-access framework. A three-quarter classical bound is not quantum environmental memory, and it is not spacetime emergence. Psy04-B is a causal-cut framework. Scheduled ancestry is not a physical causal cone, and it is not spacetime emergence. En03-A is a destructive-readout interface. A four-face exchange is not a field equation, and it is not spacetime emergence. Hawk01-A is a Hawking retrieval framework. A late thermal marginal is not a recovery law, and it is not spacetime emergence. Hawk01-B is a code-preservation model. An entropy history is not residual decoupling, and it is not spacetime emergence. Hawk02-A is a conditional evaporation interface. A mass ledger is not a metric, and it is not spacetime emergence. Hawk02-B is a Hamiltonian-derived finite emission model. Entropy turnover is not residual decoupling, and it is not spacetime emergence. Hawk02-C is an autonomous source-field bridge. A Friedrichs packet channel is not gravitational Hawking radiation, and it is not spacetime emergence. Hawk02-D is a quadratic fermionic residual. A Bessel survival law is not interacting SYK, not gravitational backreaction, and not spacetime emergence. Hawk02-E is a regulated interacting SYK--scalar framework. A finite approximation allowance is not a horizon, not gravitational backreaction, and not spacetime emergence. Hawk03-A is a finite firewall interface. An encoded radiation partner is not a smooth horizon, and it is not spacetime emergence. Psy01-A is a pruning comparison and is not a density law of emergence. IX-A through IX-E-3 are the sharp-insertion quantum-product branch, not a continuation of VIII. X-A through X-G are a regulated ramp branch. They do not complete that sharp-product programme, and they are not the obstructed convolution prescription. X-B-ii closes four scope items of X-B beside that path. It does not open Branch B, and it is not a declared input of X-C. XI-A through XI-G are a separately normalized gravitational sheet. They are not a relabeling of X-E through X-G, and they do not overturn the ramp programme. XII-A through XII-F continue that sheet by changing the cubic model. Changed-source admission does not imply unqualified relational invariance. XIII-A through XIII-E test two responses to the remainder XII-F detected: restriction and a frozen classical completion, or one binary quantum tree whose characteristic-set limit is still unfinished. XIII does not repair XII-F. Neither response makes the series one theory. XIV-A through XIV-J are two parallel continuations of that programme, not one sequence. The relative classical master equation does not discharge the unfinished quantum product. XIV-I constructs an internal amplitude and does not finish the joint map. XIV-J’s supported-sector reference is only K_6 plus K_8 plus K_9, and it is not that map. The classical relative structure, the internal tree kernels, and that off-characteristic reference are three separate achievements, and none is an admitted quantum coefficient. The remaining chain still runs through the joint map, a joint section, transverse estimates, contact compatibility, and an output wavefront theorem before any exit. Neither branch is an interacting quantum Ward identity. XV-A through XV-F are registered technical continuations. XV-A through XV-E can test X-track warnings, and those normal-jet tests are not the full characteristic graph. The registered XV-A is the model-and-domain audit, not the free quantum BV carrier cited as an exit prerequisite. XV-F identifies one adapted chart and still leaves the graph unresolved at F0. The downstream admission exit remains closed. XV-F-patch and XV-F-patch-ii transcribe definitions and still leave the graph unresolved at F0. They do not replace XV-F and they do not enter F1. XVI-A and XVI-B are a fixed-width prepared-source programme. XVI-D proves the witness response and leaves the inherited coordinate identification conditional. XVI-H constructs a compact three-slot kernel under inherited root inputs and does not calculate its wavefront or free-shell class. They do not repair X-G or XI-G and they do not construct the retarded coefficient. XVI-C, XVI-E, XVI-F, and XVI-G are cited and are not registered. XIV-A through XIV-J do not complete I through V. They revisit descent, distributional definition, representation, an instrument, and a record. XII-A through XII-F supply the carrier, the action, and the failed invariance that precede that problem. Those links are proposed bridges, not theorem transfers. XI-A through XI-G keep a further split: classical cancellation can hold while quantum admission fails. The X series is two regulators, not one construction. A measurement does not repair an upstream classical defect. The later joint track is not a repair of X: inverse coefficient minus one is not coefficient minus four. II’s contact-span certificate is a proposed method for a later normalization or overlap question. It does not identify the contact classes, and it does not construct or discharge the missing characteristic product. Bibliographies that name another manuscript’s finding are listed on every map as that finding only, not as a declared input.
Formal dependencies
No arrows. Each manuscript supplies its own principal constructions and proofs. This is the safest dependency diagram.
Mathematical relationships
Connections, not prerequisite arrows. The strongest cluster is III, IV, and V. The step under I is a possible finite encoding, not a supplied bridge.
Possible finite encoded implementation — not a theorem of I or of IV
Findings named across manuscripts
Each entry is a finding one manuscript names in its own bibliography. The naming covers that finding only. It is not a declared input, not a verification, and not a transfer of every theorem of the named manuscript.
Used only for ownership distinctions among destructive readout, classical records, and surviving quantum names. Its measurement-characterization theorem is not a premise here.
Used only to distinguish its equation-space and quotient questions from the off-shell problem studied here.
III → V · Conceptual connection, not a premise
Shared differential backbone, different questions
III version 2 and V use the same sign identity for L_{Kξ} and the same consequence for S_{t0}(Kξ). III keeps the coupled scalar correction and constructs a nonzero compact Ward pair that is neither the vanished adjoint-exact repair nor a residual witness imported from V. V fixes the scalar background and classifies when the metric functional alone has one smooth compact conserved representative, including the initial-surface defect. V is not a premise.
They share the sign identity for L_{Kξ} and the consequence for S_{t0}(Kξ), but III keeps the coupled scalar correction while V fixes the background and classifies metric-only representability, including the initial-surface defect. An adjoint-exact compact Ward repair can vanish without every compact coupled Ward observable vanishing.
Boundary: V does not replace III’s coupled quotient theorem. The variables, gauge actions, and observable classes differ.
Each reading stays inside the source-based map. A displayed identity is the relationship’s reading of the cited labels, not a new theorem and not a verification.
III → V
From coupled descent to fixed-background admissibility
This is a particularly close connection, and it is not a premise. Both manuscripts use the same sign structure
LKξ=−[P,Xξ],PSt0(h)Φ=−LhΦ,
and consequently
St0(Kξ)Φ=XξΦ−Ht0(XξΦ).
That identity is why fixing zero scalar Cauchy data is not automatically compatible with arbitrary gauge changes. Sources named by the reading: III, lem:signs and prop:subtraction; V, lem:gaugeidentity.
III retains the coupled scalar correction. Its transformation is (h,φ)↦(h+Kξ,φ+XξΦ). A compact observable may therefore have both tensor and scalar terms,
OJ,c=∫hJ+∫cφ,
with the coupled Ward condition −2∂μJμν+c∂νΦ=0.
V instead fixes the scalar background and asks whether the resulting metric functional alone equals FJ(h)=∫hJ for one smooth compact conserved tensor J. A metric-only conserved-current representative must annihilate the relevant pure gauges without a scalar term available to cancel their variation.
V reconstructs the complete defect, including initial-surface contributions,
H=γ+δ(t)a+δ′(t)b.
It then states exact equivalences: raw representability on the declared space if and only if H=0, and, on the specified harmonic-prescription domains, representability if and only if E1H=0. Sources: V, thm:defect, thm:rawclassification, thm:harmonic. This classifies the fixed-background obstruction. It does not replace III’s coupled quotient theorem, because the variables, gauge actions, and observable classes differ.
Both manuscripts show that the immediate adjoint-exact compact Ward repair vanishes on shell. III also constructs a different, nonzero compact Ward pair, whose scalar coefficient is not Pψ for compact ψ. Therefore an adjoint-exact repair vanishing does not imply that every compact coupled Ward observable vanishes. Sources: III, prop:zero-repair and thm:compact-pair; V, the limits-classification section.
Which measurement strategies interpret the fixed destructive readout primitive?
Born probabilities and destructive projective residual rays uniquely satisfy the five requirements in the declared structural class.
Not record-free uniqueness, a field instrument, or a physical apparatus theorem. A global live-qubit budget is not a laboratory peak. Static marginal compatibility is not this operational characterization.
I-B
What does destructive Enter do to a clock on a prescribed conical product?
The clock instrument returns a classical code and surviving matter. Scheduled influence stays inside the prescribed causal relation. Exact null transport is a target-adapted chain.
The geometric time axis remains. This is not spacetime emergence, not Einstein dynamics, and not quantized relational time without an external clock.
II
Does a specified longitudinal tree response lie in the evaluated contact span?
SEP-finite: rank 2 equals the augmented rank on three labels. Original columns (0, 8, 0) and (0, 0, 8), minor 64, coefficients 2/3 and 2/3. The left kernel is Span{(1, 0, 0)}. The affine family of fits is identified.
Global contact membership or separation remains undecided. The unweighted certificate is not transferred to a weighted class, a changed gauge prescription, or an unidentified counterterm space.
III
On which classical equation spaces do relational scalar functionals descend?
Four separate results: an exhibited product obstruction, Killing tangency of the unchanged massive shell, a retarded coupled-jet section, a well-posed C1 quotient, and a nonzero compact coupled Ward pair.
No Hilbert-space representation or measurement construction. The sourced successor S1–S3 is not completed. A gauge-fixed response is not automatically an invariant solution. Companion manuscripts are not premises.
IV
Can selected classical quantities be represented and measured?
Three separate operator or form models with global binary instruments and controlled contrasts.
Models 2 and 3 retain number cutoffs. The apparatus is not proved spacetime-local.
V
When does the fixed-time response admit compact conserved representatives, and what is its first retarded coefficient?
Exact admissibility criteria, finite-plane representatives, external and oscillator retarded coefficients, and a separate cubic Wick form.
No dense-TT representability theorem, adiabatic limit, or higher causal-product construction.
A prescribed conical product with an Enter interface is not spacetime emergence. Enter consumes the clock encoding, not the geometric time axis. The defect is a worldsheet, not a worldline. Einstein dynamics are not derived. Cited sheets are not premises.
I
Uniqueness in a declared structural class is not unrestricted physical uniqueness and not record-free uniqueness. Record compatibility is not residual compatibility. A global live-qubit budget is not a laboratory peak. Static marginal compatibility is not operational characterization. Companion records are not premises.
II
A finite fit is not a global contact identity. Complete coverage is three clauses. Action equivalence is not response-space equivalence. The affine family is not a unique coefficient vector. Injective evaluation is sufficient and not necessary. Weighting does not preserve the unweighted integration-by-parts quotient. Companion manuscripts are not premises.
II-B
A finite contact fit on a prescribed cone is not a global contact identity and not spacetime emergence. A clock record is not the geometric time coordinate. Einstein dynamics are not derived. Cited sheets are not premises.
III
Formal compensation is not descent on an unchanged equation space. The exhibited obstruction is not a theorem about every scalar functional. A gauge-fixed response need not solve the invariant equations. Companion manuscripts are not premises.
III-B
A supported laboratory quotient is not a global conical Cauchy theorem and not spacetime emergence. A finite evaluation encoding is not a continuum field instrument. Enter consumes the clock encoding, not the geometric time axis. Einstein dynamics are not derived. Cited sheets are not premises.
IV
A represented cutoff instrument is not an unregulated local apparatus.
IV-B
A Grade-S interface on a prescribed cone is not an intrinsic cone field theory and not spacetime emergence. A declared flat completion is not a global isometry. Enter consumes the clock encoding, not the geometric time axis. Einstein dynamics are not derived. Cited sheets are not premises.
V
Finite-plane interpolation is not dense-space representability.
V-B
A local Grade S adaptation on a supported presentation is not a global intrinsic cone theory and not spacetime emergence. The regular product is not globally hyperbolic. Enter consumes the clock encoding, not the geometric time axis. Finite compression is not a finite-qubit field instrument. Einstein dynamics are not derived. Cited sheets are not premises.
VI-B
A local Grade S adaptation of harmonic descent is not a global conical Cauchy theorem and not spacetime emergence. The quantum certificate remains RG-open. A finite table is not a continuum field instrument. Enter consumes the clock encoding, not the geometric time axis. Einstein dynamics are not derived from records. Cited sheets are not premises.
VII-A-ST
A local Grade S adaptation of the plateau intertwiner is not a global conical Cauchy theorem and not spacetime emergence. The repair stays plateau-restricted. The quantum certificate remains RG-open. A finite table is not a continuum field instrument. Enter consumes the clock encoding, not the geometric time axis. Einstein dynamics are not derived from records. Cited sheets are not premises.
VII-E-ST
A local Grade S observation-and-feedback package is not a global conical Cauchy theorem and not spacetime emergence. Record compatibility is not residual agreement. An informative record is not recovery of every quantum input. Matter-controlled slicing is not matter-driven gravitational dynamics. The quantum certificate remains RG-open. Enter consumes the clock encoding, not the geometric time axis. Einstein dynamics are not derived from records. Cited sheets are not premises.
VII-F-ST
A local Grade S slicing certificate is not a global conical Cauchy theorem and not spacetime emergence. The worldsheet is an input, not a detector. Record compatibility is not residual agreement. An informative record is not recovery of every quantum input. Matter-controlled slicing is not matter-driven gravitational dynamics. The quantum certificate remains RG-open. Enter consumes the clock encoding, not the geometric time axis. Einstein dynamics are not derived from records. Cited sheets are not premises.
VII-J-ST
A local Grade S scheduled-causality certificate is not a global conical Cauchy theorem and not spacetime emergence. The worldsheet is an input, not a detector. No apex register is used. 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. Enter consumes the clock encoding, not the geometric time axis. Einstein dynamics are not derived from records. Cited sheets are not premises.
VIII-ST
A local Grade S matching-and-flow certificate is not a global conical Cauchy theorem and not spacetime emergence. The worldsheet is an input, not a detector. Catalogue replacement is not host-metric evolution. A computational support bound is not a physical causal past. A source token is supplied, not acquired. The quantum certificate remains RG-open. Enter consumes the clock encoding, not the geometric time axis. Einstein dynamics are not derived from records. Cited sheets are not premises.
IX-A-ST
A local Grade S sharp-admission certificate is not a global conical Cauchy theorem and not spacetime emergence. Auxiliary Minkowski inverses are not a global conical Green operator. Separate continuity is not a renormalized quantum product. Unchanged regular approximants do not converge to the sharp insertion. A finite table encodes supplied evaluations and does not acquire a field. The quantum certificate remains RG-open. Enter consumes the clock encoding, not the geometric time axis. Einstein dynamics are not derived from records. Cited sheets are not premises.
IX-B-ST
A local Grade S triangle-calibration certificate is not a global conical Cauchy theorem and not spacetime emergence. Covariance blocks and the parent finite part are supplied chart data, not a conical Green operator. Regulator replacement is not host-metric evolution. The observation-derivative orbit is not the parent class. Equality of the two regularized parenthesizations is not either sharp binary association. The second sharp multiplication remains undefined. The VII-C obstruction remains. A finite table encodes supplied evaluations and does not acquire a field. The quantum certificate remains RG-open. Enter consumes the clock encoding, not the geometric time axis. Einstein dynamics are not derived from records. Cited sheets are not premises.
IX-C-ST
A local Grade S partial-product certificate is not a global conical Cauchy theorem and not spacetime emergence. Wordwise coherence through order hbar^3 is not unspecified-triple associativity and not a causal lift. The truncated partial product is not a renormalized interacting product. The parent finite part is an input, not a reproof. A finite table encodes supplied evaluations and does not acquire a field. The quantum certificate remains RG-open. Enter consumes the clock encoding, not the geometric time axis. Einstein dynamics are not derived from records. Cited sheets are not premises.
IX-D-ST
A local Grade S causal-interface certificate is not a global conical Cauchy theorem and not spacetime emergence. Free coherence is not time ordering. A commutator identity is not a sharp time-ordered product. A support bridge under a trace certificate is not that product. The weak inherited certificate stays unverified. A finite table encodes supplied evaluations and does not acquire a field. The quantum certificate remains RG-open. Enter consumes the clock encoding, not the geometric time axis. Einstein dynamics are not derived from records. Cited sheets are not premises.
Newton-wave correspondence
Agreement on curvature and on compact conserved-current pairings does not imply agreement of the cubic scalar responses.
V notation
IV notation
Option A
RC
Option B
RNW
Revisited later, not completed
XIV-A through XIV-J do not complete these five manuscripts. The correspondence is the staged demand: descent, then a distributional definition, then representation, then an instrument, then a record. A missing bridge is not a theorem.
Earlier manuscript
Strongest connection
Main missing bridge
I
Descent, declared semantic domains, and selective-map implementation.
A represented and approximable measurement of an admitted later coefficient. Not supplied.
II
Complete correction classes, exact certificates, and global-versus-finite quantifiers. Version 2 separates coverage, the affine fit, weighting, rebasing, and prescription change.
A complete parameterization of normalization changes and their constraints. Not supplied.
III
Equation-space descent, causal tangency, and changing the shell.
A declared coupled equation space joining the classical antifield system to the relational coefficient. Not supplied.
IV
The passage from admitted kernels to operators and instruments.
Representation and operator estimates for the later joint coefficient. Not supplied.
V
Retarded-product conventions, off-shell labels, current kernels, and internal inverses.
The double-cross-line composition of the nonlocal pair. Not supplied.
What XII supplies before those bridges
Action consistency, solution existence, kernel admission, observable invariance, and measurement implementation stay separate. XII does not transfer I through V as premises.
Manuscript
Main contribution
Not established
XII-A
A graded polynomial quantum carrier, free-shell descent, and ordering transport.
A new action, a representation, a state, or an interacting product.
XII-B
A dependency audit, and the proof that density weighting differs from source weighting.
The proposed new response.
XII-C
A declared cubic-only action, the actual Euler source, and the changed Noether identity.
Kernel admission or evolution.
XII-D
A smooth classical response, a completed insertion, and a compact microcausal kernel.
An invariant coupled solution or a quantum retarded product.
XII-E
Assembly with the forced minus sign, and admission of the relational coefficient.
Unqualified gauge invariance.
XII-F
An explicit nonzero auxiliary remainder on the complete free shell.
A universal no-go for further completions.
Four gates
Passing one gate does not pass the others.
G1
Classical legitimacy
Does the expression descend on the named equation-space quotient?
III addresses this.
G2
Mathematical representation
Can the quantity be realized as a current, form, or operator on a declared domain?
IV and V address different versions.
G3
Measurement construction
Can the represented object generate a specified instrument and controlled record?
IV addresses selected models. I supplies finite measurement semantics and implementation interfaces.
G4
Interaction-level certification
Does a selected response survive the declared freedom to add local contacts?
II addresses a finite evaluation of this separate question.
What does not follow
An adjoint-exact compact Ward repair can vanish without every compact coupled Ward observable vanishing.
Gauge invariance does not imply prescription independence.
IV Model 1 is not V’s retarded product unless the TT plane, normalization, initial time, compact switch, and smearings match. In general L_{ga} is not g L_a.
A Fock-space operator representation is not a compact conserved-current representation.
IV Model 3 is quadratic in the scalar field. V’s contrast construction is cubic. They are not the same observable.
Agreement of the two Newton-wave inverse prescriptions on curvature does not imply agreement of the cubic scalar responses.
IV’s instruments are not automatically finite Enter programs, and its Ramsey contrasts do not derive the Born rule.
A finite contact fit is not a global contact identity. Passing one gate does not pass the others.
II’s contact-span certificate does not define a missing distributional product. A finite fit is not global compatibility, and finite normal order is not a finite-dimensional ambiguity.
XIV-A through XIV-J do not complete I through V. Descent, distributional definition, representation, an instrument, and a record stay separate.
One nonzero contribution does not imply survival under the complete permitted sum.
A consistent transformation of one equation space does not transform another. III’s coupled quotient is not the relative classical shell.
IV’s instruments are not a measurement of the later joint coefficient. V’s one-cross retarded product is not the double-cross composition.
I’s finite semantics do not supply the missing quantum graph. Membership in an output space is not a self-adjoint operator or an instrument.
XII supplies a carrier, an action, an admitted coefficient, and a nonzero remainder. That admission does not transfer I through V as premises. Action consistency, solution existence, kernel admission, observable invariance, and measurement implementation stay separate.
Proposed bridges, not results
These are readings of where a later proof could go. None is a theorem of the registered manuscripts.
III–IV: identify precisely which descended classical functional IV Model 1 represents.
IV–V: match the finite-plane conventions and prove the switched and unswitched comparison in common notation.
I–IV: construct finite encoded approximations of selected IV instruments with a stated input class, resource budget, and error topology.
IV–V: compare the sourced quadratic curvature observable with the separate cubic response, retaining the inverse-prescription and initial-data differences.
II, XIII-E, and XIV-J: transfer II’s exact contact-span reasoning to a normalization or overlap question after a reference distribution exists. The contact classes are not identified. Linear algebra selects among defined extensions and does not define a missing product. A separator excludes every permitted adjustment only after a complete allowed-change catalogue. Finite normal order is not finite-dimensional ambiguity. One finite fit is not global compatibility. The proposal does not finish gate E1, does not discharge the stop unresolved at J2, and does not admit a quantum coefficient. II’s catalogue size has no direct role.
I and XIV-J: after an admitted coefficient has a representation, a finite encoding, a selective-map comparison, an input class, an approximation topology, and an error bound could use I’s implementation framework. Equality of outcome effects is weaker than that instrument comparison. I cannot replace any analytic construction gate. The first arrow, membership in the stated output space, has not been supplied.
III, XIII-D, and XIV-B: a coupled equation space in the sense of III could be declared before claiming completion of the auxiliary pairing. That would be a different shell, not a repair of the unchanged contract. A nilpotent differential is not a closed observable. Compact spacetime support, compact Cauchy data, and future support from a compact source are different.
IV and XIV-J: a represented pilot of the supported sector, after its characteristic coefficients are actually extended, would be one model. It is not a representation of the complete six-branch coefficient. Field degree does not prove the operator estimates.
V and XIV-J: V’s explicit current and boundary terms can guide coefficient bookkeeping. They are not the missing double-cross composition, and off-shell labels, retarded lifts, and reconstructed kernels are not one quotient.
I and XII-F: a bridge to operational semantics applies only after a representation and a measurement model. The compact shift is not automatically an operation on free-shell classes. The nonzero remainder is not an outcome, an instrument, or a finite program.
II, XII-B, and XII-F: a certificate must name its space. Weighting does not preserve the unweighted integration-by-parts quotient. The auxiliary pairing is a completion-membership target only after the correction class is frozen. One witness does not exclude every completion.
III, XII-C, and XII-D: an invertible gauge-fixed forcing problem is not the invariant coupled equation. A different coupled shell would have to be declared. It is not a repair already contained in the unchanged carrier.
IV, XII-E, and XII-F: the admitted kernels are algebraic candidates. The quadratic remainder is the smaller representation pilot. XII-A selects no state, and a classical shell value is not a quantum record.
V, XII-D, and XII-E: response functionals, kernels, tests, and configurations stay distinct. The forcing sign is not the quantum retarded-product convention. A tree balance is not a cycle theorem.
I and XI-D: an interpretation must respect the algebra’s zero elements. Closure of a bare dressing is not closure of the complete expression. XI does not supply a measurement semantics.
II and XI-G: certify the quotient invariant, not only a displayed representative. Class-invariant growth against admissible decay is a separator. One nonzero contribution is not the complete ledger. This is not a finite contact matrix, and it does not decide a larger algebra.
III, XI-A, and XI-B: a gauge-fixed response is not the invariant coupled jet. An obstruction on the detecting shell does not decide the Einstein subshell.
IV, XI-E, and XI-G: admitted symbols still need operator and instrument theorems. The excluded cubic class blocks one microcausal route and not every larger domain. Product data are not a state.
V and XI-C: the rooted response is a comparison case, not V’s current theorem. Source support is not propagated support. A smooth ramp does not regulate every onset channel.
II, X-E, and X-G: a displayed one-tree defect is not separation from every completion. X-F changes the gauge prescription. A future Ward certificate needs the actual defect and a complete normalization catalogue. II’s contact catalogue is not imported into that nonlocal problem.
III and X-A: the complete first relational coefficient keeps the forced scalar correction, not the coordinate dressing alone. Shared cancellation formulas do not identify the quotient spaces. The limiting initial data are part of the prescription.
IV, X-B, and X-D: compact scalar tests are candidates for a separately declared numerical model. A formal nilpotent coupling is not a nonzero real parameter. Test convergence is not yet record convergence, and it is not a localized probe.
V, X-B, and X-C: the transposed retarded formulas need a convention dictionary. X-C continues a restricted response recursion. It does not prove the higher causal-product programme V withholds, and it does not settle the nonlocal loop.
X and XIV: the later track separates classical symmetry, variational compatibility, algebraic admission, and characteristic composition. It is not a repair of X. Inverse coefficient minus one is not coefficient minus four. A regulator defect is not this auxiliary pairing. A one-line response is not the two-line product. Fixed-background convergence is not joint composition. One contribution is not the full coefficient. A readout does not construct a missing identity. Defined internal kernels do not imply their characteristic composition, and that composition does not imply a quantum Ward identity.
X and XIII: restriction, completion, and the product do not substitute for one another. Inverse coefficient minus one is not coefficient minus four. Regularized objects do not imply the target identity or the target limit. A one-line construction does not imply a two-line construction. A sourced response and a trivial causal shell action can coexist. An extra vertex on a second-order coefficient is not the earlier kappa-squared hbar inventory. None of these comparisons admits a quantum Ward datum.