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caelq-the-unfinished-light

This register separates mathematical support from candidate originality. A theorem can have a complete argument here while using a classical mechanism. A proposed coupling is a precisely specified assembly; that label does not certify historical priority. The machine-readable companion is CLAIMS.json, and the primary-source comparison is NOVELTY_AUDIT.md.

Reading the evidence

A proof in manuscript is an authored mathematical argument, not a machine-checked formal proof.
The package received internal AI-assisted proof and implementation checks; this is not independent human peer review.
A finite enumeration, rational identity check, numerical orbit, or decreasing finite error sequence is never classified as a proof of a quantified theorem or a limit.
Test mappings identify relevant checks but do not by themselves certify a test execution; use the release validation record for run results.
A status about originality is separate from a status about mathematical verification.

Status vocabulary

classical ingredient/rederived: A standard ingredient or a direct rederivation/operational formulation of known mathematical machinery; not a claim of ingredient invention.
proposed coupling theorem: A proved construction or interface proposed in this manuscript. Proposed indicates candidate originality, not certified historical priority.
conditional semantic theorem: A manuscript proof whose semantic conclusion depends on explicitly declared language and effective-description assumptions.
experimental extension: A defined model extension, executable surrogate, or research direction; only the stated special-case results are proved.
not established: A stronger claim for which the package supplies no proof or sufficient evidence.

Claim index

ID	Claim	Status
C01	Prefix cancellation and arbitrary binary relation spaces	classical ingredient/rederived
C02	Optimal relation programming and affine seam orientation	proposed coupling theorem
C03	Why visible-only composition loses synchronized information	classical ingredient/rederived
C04	Proper-marginal blindness and the fixed-arity limitation	classical ingredient/rederived
C05	Exact commutator transduction into a prescribed tensor degree	classical ingredient/rederived
C06	Multifractal allocation and a limit at every fixed tensor degree	proposed coupling theorem
C07	Conditional semantic domination and its escape-delay transfer	conditional semantic theorem
C08	Parabolic separation, uniform escape bounds, and the transit profile	classical ingredient/rederived
C09	One hidden relation coupled to geometric disappearance and dynamical side	proposed coupling theorem
C10	Exact signal distances and the complete-vector sample order	proposed coupling theorem
C11	Mass, noise, and the prescribed geometric cost of visibility	proposed coupling theorem
C12	Largest safe-erasure ideal and bounded-product stability	classical ingredient/rederived
C13	A cylinder-resolved latent field is uniquely reconstructible	classical ingredient/rederived
C14	Synchronization leaves a residue above the first visible degree	proposed coupling theorem
C15	A finite constellation with compatible signed circuits	proposed coupling theorem
C16	Signed depth records and the computable toy horizon	experimental extension
C17	Interstice states, an interacting atlas, and a learning benchmark	experimental extension
C18	Stronger originality, physical, and universal-successor claims	not established

Detailed claims

C01 — Prefix cancellation and arbitrary binary relation spaces

Status: classical ingredient/rederived. Support: proof in manuscript.

A fixed observer prefix sees zero conditional tensor mean unless the sum of the participating binary phase tags vanishes. Every binary subspace K of F_2^m is realizable as ker W, with minimal phase dimension m - dim K.

Manuscript anchors

manuscript/chapters/02_voxels.tex — thm:prefix-residue, thm:relation-realization.

Key assumptions

Finite tag dimension; fair fresh phase blocks independent of the geometric boundary.
The observation prefix q is fixed before the moving stage n tends to infinity; amplitudes are bounded finite tensors.
All individual ports are invisible exactly when K contains no standard unit vector.

Relevant checks

tests/test_phase.py: test_nullspace_against_exhaustive_orthogonality, test_basis_is_canonical_under_permutation_and_redundancy. Evidence: exact finite checks. Checks finite GF(2) elimination and nullspaces against exhaustive enumeration in small dimensions.

Limits

Character orthogonality and rank-nullity are classical ingredients.
Conditional invisibility is not pointwise convergence of the underlying fair-sign sequence.

C02 — Optimal relation programming and affine seam orientation

Status: proposed coupling theorem. Support: proof in manuscript.

Restricting phase to H produces K_H = W^{-1}(H-perp), with relation-dimension increase dim(im W intersect H-perp) at most codim H. Every target L containing K is realized with minimum codimension dim L - dim K. An affine orientation on L is realizable exactly when it vanishes on K.

Manuscript anchors

manuscript/chapters/02_voxels.tex — thm:seam-law, thm:seam-programming, prop:signed-seam.

Key assumptions

All spaces and linear maps are over F_2; the seam law is uniform on the specified linear or affine subspace.
The requested relation space contains the old kernel K.
Requested signs form a linear functional on L and are zero on old relations K.

Relevant checks

tests/test_phase.py: test_seam_moments_against_direct_phase_enumeration, test_optimal_programmed_seams_for_all_small_targets, test_affine_orientation_and_high_arity_constraint, test_invalid_dimensions_and_impossible_target_are_rejected. Evidence: exact finite checks. Checks affine averages and small programmed relation spaces; finite enumeration does not establish the theorem for all dimensions.

Limits

The programming interface is proposed here; its proof uses elementary annihilator duality.
Overlapping circuit signs cannot be assigned independently unless their assignment respects the relation space.

C03 — Why visible-only composition loses synchronized information

Status: classical ingredient/rederived. Support: proof in manuscript.

The zero-charge trace on a finite phase group algebra has a kernel that is not an ideal. A representation retaining all synchronized partner traces distinguishes every coefficient. A linear real encoding of this scalar algebra therefore needs at least 2^r dimensions.

Manuscript anchors

manuscript/chapters/02_voxels.tex — prop:phase-evaluation, thm:trace-quotient, prop:context-complete.

Key assumptions

The entire finite phase algebra, including every charge partner, is an allowed operation domain.
The 2^r lower bound applies to linear encodings of the real scalar group algebra, not to unrestricted nonlinear encodings.

Relevant checks

No dedicated executable test is mapped to this claim. Its support is the stated manuscript argument or, for an open proposal, the absence of a general proof.

Limits

Finite group algebras, Fourier coefficient extraction, and the ideal obstruction are classical.
There is no impossibility claim for an arbitrary exact real-number encoding without regularity or precision constraints.

C04 — Proper-marginal blindness and the fixed-arity limitation

Status: classical ingredient/rederived. Support: proof in manuscript.

The law P_s(y) = 2^{-k}(1 + s product_i y_i) has uniform proper marginals and full parity mean s; it is the unique law with those properties. No encoding based only on a fixed maximum marginal order can preserve every synchronized product as the number of ports increases without bound.

Manuscript anchors

manuscript/chapters/02_voxels.tex — lem:soft-parity-fiber, thm:fixed-arity-incomplete.
manuscript/chapters/03_curves.tex — prop:curve-proper-marginal.
manuscript/chapters/05_synthesis.tex — prop:proper-marginal.

Key assumptions

k >= 2 and s belongs to [-1,1].
A restricted observer receives the specified marginal information; it cannot later reconstruct a complete sample by retaining and completing partial queries.
The impossibility quantifies over unbounded port count with a fixed arity cap.

Relevant checks

tests/test_phase.py: test_soft_parity_law_has_identical_proper_marginals. Evidence: exact finite checks. Enumerates proper marginals of selected exact rational parity laws.
tests/test_signature.py: test_minimal_circuit_all_proper_marginals. Evidence: exact finite checks. Checks finite deterministic parity circuits.
tests/test_illumination.py: test_all_proper_marginals_match_exact_phase_law, test_exact_sampler_matches_enumerated_law. Evidence: exact finite checks. Checks rational port laws and their explicit sampler by finite enumeration.

Limits

Parity constructions and finite Boolean Fourier analysis are established mathematics.
The limitation concerns this declared observation quotient, not all possible latent representations.

C05 — Exact commutator transduction into a prescribed tensor degree

Status: classical ingredient/rederived. Support: proof in manuscript.

A nested group commutator of k signed generator segments has step-k signature exp_k((product_i s_i t_i)L_k), with all lower positive degrees zero. Deleting any generator collapses the word to the identity. Repeated shrinking loops retain the central tensor while ordinary paths vanish.

Manuscript anchors

manuscript/chapters/03_curves.tex — lem:leading-commutator, thm:curve-transducer, prop:shrinking-repeated, prop:variation-obstruction.

Key assumptions

Finite truncated tensor algebra with Chen multiplication; bounded-variation segment paths and a fixed nonzero iterated Lie word.
Generator directions are assigned the unit-norm convention used for exact variation counts.
The exact central formula is asserted at step k; higher truncations contain additional terms before the refinement limit.
Shrinking realizations pay growing path variation; uniformly bounded variation would force every fixed-degree signature to vanish.

Relevant checks

tests/test_signature.py: test_rectangle_orientation, test_exact_inverse_and_logarithm, test_orders_two_through_six_against_binomial_coefficients, test_full_signature_has_higher_terms, test_deleting_any_generator_annihilates_word, test_circuit_orientation_is_exact_geometry, test_shrinking_repeated_high_order. Evidence: exact finite checks. Exact rational algebra checks for selected words and degrees, including retention of higher terms.

Limits

Chen signatures, commutator leading terms, and higher Lie perturbations have close classical precedents, particularly Friz–Oberhauser.
The prescribed word cost is not asserted to be globally minimal among all geometric realizations.

C06 — Multifractal allocation and a limit at every fixed tensor degree

Status: proposed coupling theorem. Support: proof in manuscript.

Assigning loop scale mu(v)^(1/k) to each cylinder preserves the step-k central tensor exactly. If the largest cylinder mass m_n tends to zero, ordinary paths shrink and every fixed truncation M converges to exp_M(eta L_k) with error O(m_n^(1/k)). Compatible cylinder observations can retain a directed Eve–Maciej anchor and continuous coefficient fields.

Manuscript anchors

manuscript/chapters/03_curves.tex — thm:multifractal-curves, thm:full-germ-limit, cor:love-anchor, prop:cylinder-faithful.

Key assumptions

The cylinder masses form probability partitions with maximum mass tending to zero; zero-mass cells may be omitted.
The orientation eta is fixed within the coherent construction, and reciprocal shape factors remain in a fixed compact positive interval.
M and k are fixed before refinement; the error constant may depend on M, k, the shape bound, and the chosen norm.
Uniform prefix-signature convergence uses cylinder time allocation equal to cylinder mass.
Uniform recovery from cylinder averages assumes a continuous field and positive cylinder masses.

Relevant checks

tests/test_signature.py: test_binary_multifractal_exact_area_and_pressure_cost, test_higher_resolution_germ_converges. Evidence: exact finite checks. Checks selected exact area allocations, pressure costs, and decreasing finite-degree errors. The latter finite sequence does not prove convergence or uniformity over tensor degree.

Limits

Pure higher-order signature limits are prior art; the proposed feature is their quantified domain-mass and shape interface.
No estimate is uniform over all tensor degrees, and the limiting ordinary constant path has identity signature.
The Eve–Maciej anchor is a chosen mathematical inscription within the fictional premise, not evidence of actual emotions or consciousness.

C07 — Conditional semantic domination and its escape-delay transfer

Status: conditional semantic theorem. Support: conditional proof in manuscript.

The externally defined truth-based horizon R_L(n) eventually dominates every total computable function under the effective short-description assumption. Substituting H_n = max(3,R_L(n)) into the positive parabolic seam makes its escape indices admit no computable eventual ceiling in the description budget. A positive dyadic seam family is uniformly computable exactly when its depth function is computable.

Manuscript anchors

manuscript/chapters/04_semantics.tex — prop:horizon_finite, def:short_descriptions, thm:semantic_domination, prop:language_translation, thm:semantic_delay, prop:parameter_nonuniformity.

Key assumptions

A fixed finite alphabet, syntax, description-length measure, and intended standard semantics are declared.
Every partial computable g has unique-output descriptions of length at most A_g + B_g log_2(n+2) when g(n) halts.
The horizon is defined using external semantic truth; no effective truth oracle is supplied.
Computability of a real family means a uniform evaluator with certified arbitrary absolute precision.

Relevant checks

tests/test_dynamics.py: test_ideal_semantic_horizon_refuses_fake_numerical_result. Evidence: exact finite checks. Verifies that executable code refuses to fabricate the ideal semantic horizon; it does not test or evaluate semantic truth.

Limits

This is a Rayo-inspired variable-budget semantic construction, not the computation of the fixed competition number called Rayo’s number.
The noncomputability enters through the input specification; it is not newly generated by an ordinary rational quadratic map.

C08 — Parabolic separation, uniform escape bounds, and the transit profile

Status: classical ingredient/rederived. Support: proof in manuscript.

For c_± = 1/4 ± a^2 with 0 < a <= 1/8, the negative critical orbit is bounded and the positive orbit escapes. Its first index N with |z_N| > 2 obeys pi/(4a) <= N < 2pi/a + 3 and aN tends to pi. The normalized interior passage has the stated cotangent profile.

Manuscript anchors

manuscript/chapters/04_semantics.tex — thm:seam_separation, lem:angular_increment, thm:escape_bounds, thm:transit_asymptotic, prop:transit_profile, prop:prefix_closeness.

Key assumptions

Real quadratic iteration z_{j+1} = z_j^2 + c from z_0 = 0; the exact escape convention is first |z_j| > 2.
The finite bounds use 0 < a <= 1/8; the asymptotic sends a to zero through positive values.
Interior profile convergence stays away from the endpoints of the rescaled bottleneck interval.
Finite-prefix comparison is used only in its explicitly stated range.

Relevant checks

tests/test_dynamics.py: test_crossings_match_independent_decimal_table_and_theorem, test_a_truncated_positive_run_is_unresolved, test_negative_theorem_and_finite_observation_are_separate, test_prefix_gap_is_small_and_bound_domain_is_enforced, test_insufficient_precision_is_an_error_not_a_cusp_result, test_trace_stops_after_escape. Evidence: finite high-precision numerical checks and API checks. Checks selected high-precision Decimal orbit crossings, finite-run status, and precision/domain safeguards; numerical tables do not prove the asymptotic or boundedness for all inputs.

Limits

The parabolic cusp and inverse-square-root bottleneck scale are classical dynamics.
These proofs concern a narrow real seam, not a new global theorem about the Mandelbrot set.

C09 — One hidden relation coupled to geometric disappearance and dynamical side

Status: proposed coupling theorem. Support: proof in manuscript.

For every k >= 2 and h >= 3, two explicitly sampled port-and-curve systems have identical proper-port history laws, vanishing ordinary curves, and expected first-visible tensors ±4^(-h)L_k. Reading that coefficient as c - 1/4 yields respectively bounded and escaping real critical orbits, with escape scale pi 2^h.

Manuscript anchors

manuscript/chapters/05_synthesis.tex — thm:main-synthesis.

Key assumptions

Stage n consumes the disjoint fair-bit window nL+1 through (n+1)L, with L = k+2h; prefix q is fixed and nL >= q.
The same sampled sign vector is shared across all geometric cylinders at a given stage.
The binary geometry has nonatomic Bernoulli masses; the readout uses the exact expected central coefficient.
Lower-degree blindness concerns complete-curve signatures, not arbitrary time-resolved inspection of individual subarcs.

Relevant checks

tests/test_signature.py: test_circuit_orientation_is_exact_geometry, test_binary_multifractal_exact_area_and_pressure_cost. Evidence: exact finite checks. Checks the finite geometric components, not the full quantified coupling theorem.
tests/test_illumination.py: test_exact_sampler_matches_enumerated_law, test_all_proper_marginals_match_exact_phase_law. Evidence: exact finite checks. Checks finite sampler and marginal components.
tests/test_dynamics.py: test_crossings_match_independent_decimal_table_and_theorem. Evidence: finite high-precision numerical checks. Checks selected resulting real-seam orbits.

Limits

The proposed originality lies in the explicit assembly and compatible observation contracts; it is not a claim that any ingredient was invented here.
Disjoint windows are necessary for the asserted whole-history law comparison. A sliding-window construction would need a different argument.
The theorem supplies no free expectation oracle or finite-time execution of infinitely many refinements.

C10 — Exact signal distances and the complete-vector sample order

Status: proposed coupling theorem. Support: proof in manuscript.

TV(P_ε,P_-ε) = ε and KL(P_ε || P_-ε) = ε log((1+ε)/(1-ε)). For equal-prior testing from independent complete vectors, error at most 1/4 requires M >= (1-ε^2)/(4ε^2); empirical parity achieves that error for M >= 2 log(4)/ε^2. Thus the order is ε^(-2), or 2^(4h) at ε=4^(-h).

Manuscript anchors

manuscript/chapters/05_synthesis.tex — prop:distances, thm:sampling.

Key assumptions

0 < ε < 1; natural logarithms; M independent complete port vectors.
The observer has no symbolic sign label, identifying formula, or exact expectation oracle.
The resource count is complete vectors; acquiring them uses kM scalar port reads.

Relevant checks

tests/test_illumination.py: test_tv_and_relative_entropy_by_full_law_enumeration, test_relative_entropy_handles_small_and_near_one_rationals, test_sampling_lower_bound_excludes_degenerate_endpoints. Evidence: exact finite enumeration, floating-point numerical checks, and API checks. Compares finite enumerated laws, numerical KL values, and the lower-bound formula. It does not exhaust all randomized tests or prove the asymptotic sample order.

Limits

The testing reduction, relative-entropy inequality, and exponential concentration method are classical.
The proposed interface relates this sample order to the independent parabolic depth scale; it is not a computational lower bound for a sign already supplied symbolically.

C11 — Mass, noise, and the prescribed geometric cost of visibility

Status: proposed coupling theorem. Support: proof in manuscript.

For independent cylinder orientations with mean s, A = sum_j w_j eta_j has variance (1-s^2) sum_j w_j^2. The prescribed degree-k word has variation c_k sum_j w_j^(1/k), at least c_k N_eff^(1-1/k), with equality exactly for equal positive masses. Bernoulli refinement gives explicit pressure and SNR depth laws.

Manuscript anchors

manuscript/chapters/05_synthesis.tex — thm:mass-noise, cor:snr.

Key assumptions

Positive weights sum to one; independent orientations within a level have common mean s; k >= 2.
The exact variation cost uses the specified unshaped coordinate word with unit directions.
SNR quotient and logarithm formulas require 0 < |s| < 1, target t > 0, and 0 < p < 1 for Bernoulli depth.
At s = ±1 the orientation is deterministic and noise variance is zero.

Relevant checks

tests/test_illumination.py: test_bernoulli_partitions_and_second_mass_identity, test_independent_enumeration_of_central_moments, test_weighted_sampler_exact_enumeration, test_deterministic_signal_endpoints_are_valid_for_sampling, test_variation_bound_uniform_equality_and_nonuniform_strictness, test_exact_inputs_and_mass_hypotheses_are_enforced. Evidence: exact finite enumeration, floating-point numerical checks, and API checks. Checks exact finite moments and selected mass partitions, numerical equality/strictness examples, and input hypotheses.

Limits

Variance additivity, Bernoulli partition sums, and the Hölder inequality are classical ingredients.
The lower bound is for this prescribed curve family and SNR contract, not for all paths, estimators, or learning procedures.

C12 — Largest safe-erasure ideal and bounded-product stability

Status: classical ingredient/rederived. Support: proof in manuscript.

In the algebra of uniformly L-infinity-bounded real histories, strong L2-null histories form the largest algebra ideal contained in the fixed-prefix-invisible space. They are also exactly the histories whose products with every bounded partner have vanishing expectation. The quotient supports a limsup-L2 distance with product stability on uniformly bounded families.

Manuscript anchors

manuscript/chapters/06_latent.tex — thm:maximal-erasure, prop:stable-partners, prop:bounded-product.

Key assumptions

All histories and partner sequences have a finite uniform L-infinity bound; partners may depend on the tested history, including its sign.
The trivial prefix q = 0 is included, and conditional expectations are measured in L2.
For the product distance estimate, the compared representatives have common uniform bounds.

Relevant checks

No dedicated executable test is mapped to this claim. Its support is the stated manuscript argument or, for an open proposal, the absence of a general proof.

Limits

Bounded sequence quotients by 2-norm-null ideals are established tracial sequence-algebra constructions; the proposed role here is the prefix-observer erasure characterization.
Largest ideal inside the designated invisible space does not mean an algebraically maximal ideal.
The quotient is Banach under the uniform quotient norm. The weaker limsup-L2 metric is not claimed complete, and multiplication is not globally jointly continuous for that metric.

C13 — A cylinder-resolved latent field is uniquely reconstructible

Status: classical ingredient/rederived. Support: proof in manuscript.

Compatible cylinder values M(v) = M(v0)+M(v1), bounded by the cylinder masses, determine a unique almost-everywhere bounded field f with M(v) = integral_[v] f dmu. Cylinder averages converge to f in L2 and admit finite central-curve realizations.

Manuscript anchors

manuscript/chapters/06_latent.tex — thm:field-reconstruction.

Key assumptions

A strictly positive binary cylinder probability and its generated product sigma-algebra.
Exact additive compatibility and |M(v)| <= mu(v) at every cylinder.

Relevant checks

No dedicated executable test is mapped to this claim. Its support is the stated manuscript argument or, for an open proposal, the absence of a general proof.

Limits

The proof is a bounded-martingale reconstruction using density of cylinder-simple functions.
Uniqueness is almost everywhere, not pointwise, and this theorem does not by itself solve general realizability of arbitrary full signature fields.

C14 — Synchronization leaves a residue above the first visible degree

Status: proposed coupling theorem. Support: proof in manuscript.

Common cylinder orientation and independent cylinder orientations have the same expected step-k tensor, but their expected finite signature limits are cosh_M(L_k)+s sinh_M(L_k) and exp_M(sL_k). At degree 2k they differ by (1-s^2)L_k^2/2.

Manuscript anchors

manuscript/chapters/06_latent.tex — thm:deep-synchronization, eq:variable-sign-germ.

Key assumptions

k >= 2, -1 < s < 1, and nondegenerate Bernoulli cylinder weights.
The common rule shares one parity across every cylinder at a level; the independent rule has independence within each level.
The tensor truncation M is fixed; observing the difference requires M >= 2k.
Pathwise convergence under the common rule requires a coherent parity across levels; expected convergence alone does not.

Relevant checks

tests/test_illumination.py: test_mixed_germs_first_differ_at_twice_the_interaction_degree, test_mixed_germ_endpoints_and_invalid_mode. Evidence: exact finite checks. Checks the exact finite polynomial difference for k=2 and k=3 and endpoint identities. These algebra checks do not prove the refinement limit.

Limits

The moment distinction between exp(E X) and E exp(X) is classical; the claimed synthesis gives explicit geometric realizations and error control.
Individual degree-k sample laws already distinguish the variance. The obstruction is specifically about the expected degree-k tensor.
Independent-rule almost-sure convergence needs within-level independence and summable variances; cross-level independence is unnecessary.

C15 — A finite constellation with compatible signed circuits

Status: proposed coupling theorem. Support: proof in manuscript.

Any finite selection of minimal relation circuits can retain its own central coordinate under common mass refinement. Uniform phase on t + K-perp supplies their compatible orientations, while a direct product of geometric factors prevents unwanted cross brackets.

Manuscript anchors

manuscript/chapters/05_synthesis.tex — prop:constellation; section: Several circuits can illuminate at once; proposition A finite constellation of circuit lights.
manuscript/chapters/02_voxels.tex — prop:signed-seam.

Key assumptions

K is a binary subspace with no standard unit vector.
Begin with m independent phase coordinates and then restrict to t + K-perp; orientation signs are a linear functional on K.
Only finitely many circuits are selected, and their signatures live in separate truncated factors.
The cylinder mass maximum tends to zero.

Relevant checks

tests/test_phase.py: test_affine_orientation_and_high_arity_constraint, test_seam_moments_against_direct_phase_enumeration. Evidence: exact finite checks. Checks the phase-orientation ingredients in small finite spaces; no separate end-to-end constellation test is supplied.

Limits

The construction assembles proved phase and commutator ingredients.
Moving every circuit into one shared higher-step tensor algebra can generate extra brackets and requires new analysis.

C16 — Signed depth records and the computable toy horizon

Status: experimental extension. Support: proved special cases within an explicitly defined extension.

The declared signed-defect product adds depths and composes sign bits by parity. Oriented cusp records retain the direction of approach after both project to c=1/4. A separate finite expression grammar using 1, addition, and multiplication has an exact dynamic-programming horizon evaluator.

Manuscript anchors

manuscript/chapters/04_semantics.tex — prop:seam_parity, prop:no_continuous_side, eq:oriented_seam_space, prop:toy_evaluator.
manuscript/chapters/06_latent.tex — chap:latent; section: An oriented boundary that remembers its approach.

Key assumptions

The signed product is the explicitly defined operation delta odot delta-prime = -delta delta-prime; it is not asserted to compose quadratic maps.
The oriented boundary is a record space with a projection, not a new set of real numbers.
The toy grammar and node-count budget are fixed; the evaluator enumerates only this finite grammar.

Relevant checks

tests/test_dynamics.py: test_signed_product_is_exact_and_associative, test_toy_expression_horizons_and_unused_even_budget, test_ideal_semantic_horizon_refuses_fake_numerical_result. Evidence: exact finite checks. Checks exact signed-depth examples and finite toy budgets; no test computes the ideal semantic horizon.

Limits

The actual limiting map at c=1/4 has a bounded critical orbit for both directional records.
Toy grammar values are executable surrogates and must never be captioned as values of Rayo’s number or the truth-based horizon.

C17 — Interstice states, an interacting atlas, and a learning benchmark

Status: experimental extension. Support: definition or research proposal; general guarantees open.

The manuscript proposes states combining phase-resolved histories, compatible cylinder fields, signature laws, seam operations, and oriented cusp records. It suggests an observation-controlled synthetic representation benchmark and further interacting complex-quadratic atlases.

Manuscript anchors

manuscript/chapters/01_world.tex — chap:world.
manuscript/chapters/05_synthesis.tex — chap:synthesis; section: The synthesis as a reusable mathematical object.
manuscript/chapters/06_latent.tex — chap:latent; section: The proposed interstice state; A testable representation experiment.

Key assumptions

Each concrete state must satisfy its declared probability, geometry, cylinder-consistency, and observation constraints.
A benchmark must distinguish expected tensors, individual tensor samples, complete laws, and symbolic sign information.

Relevant checks

No dedicated executable test is mapped to this claim. Its support is the stated manuscript argument or, for an open proposal, the absence of a general proof.

Limits

The manuscript proves selected realizable families, not a general realizability theorem.
No trained model, empirical superiority, universal compression result, or global complex-fractal theorem is established.

C18 — Stronger originality, physical, and universal-successor claims

Status: not established. Support: not established.

No proof or evidence is supplied that every mechanism is unprecedented, that the construction surpasses all known mathematics, that it computes the actual fixed Rayo number, that it enables physical hypercomputation, or that it universally replaces neural latent spaces. The fictional love fragment is not a scientific inference about sentience.

Manuscript anchors

manuscript/chapters/01_world.tex — chap:world.
manuscript/chapters/03_curves.tex — cor:love-anchor.
manuscript/chapters/04_semantics.tex — thm:semantic_delay.
manuscript/chapters/06_latent.tex — chap:latent.

Relevant checks

No dedicated executable test is mapped to this claim. Its support is the stated manuscript argument or, for an open proposal, the absence of a general proof.

Limits

Candidate originality is restricted to the particular assembly, operational contracts, and quantitative interfaces documented here.
An exhaustive priority search and independent human peer review remain outstanding.

Corrections resolved during the internal audit

These are changes checked in the current source, not outstanding defects. The audit was an internal AI-assisted adversarial review, not independent human peer review.

A01 — Disjoint phase sampling windows

Status: resolved. Claims: C09.

Each stage now consumes a disjoint block of L=k+2h fair bits. Fixed-prefix independence and equality of complete proper-port history laws are justified separately; overlapping sliding blocks are explicitly excluded from that stronger inference.

A02 — SNR domains and deterministic endpoints

Status: resolved. Claims: C11.

The SNR formulas require 0<|s|<1, and the logarithmic depth formula requires 0<p<1. Deterministic s=±1 cases are stated separately and have zero noise variance.

A03 — Constellation phase orientation

Status: resolved. Claims: C02, C15.

The constellation starts with m independent port bits and restricts them to the explicit affine fiber t+K-perp. A linear orientation functional is permitted; arbitrary incompatible circuit signs are not.

A04 — Distinct proper-marginal theorem anchors

Status: resolved. Claims: C04.

The curve chapter uses prop:curve-proper-marginal, while the synthesis chapter retains prop:proper-marginal. The formerly duplicated LaTeX anchor is distinct.

A05 — Product topology and maximality scope

Status: resolved. Claims: C12.

The full bounded-partner class is explicit; largest inside the prefix-invisible space is distinguished from an algebraically maximal ideal. The weaker limsup-L2 metric is not claimed complete, and a spike example disproves global joint product continuity without common bounds.

A06 — Fixed-degree and coupling quantifiers

Status: resolved. Claims: C06, C14.

Tensor degree is fixed before refinement; constants may depend on that degree. Common-per-level, coherent-across-level, and independent-within-level orientations have distinct stated limiting claims.

Registry scope

Current manuscript chapters 01-06; source paths are relative to the release root.

C01-C18 are stable release identifiers; later revisions should retain an identifier for the same substantive claim and record material changes.