On Boundaries of Evidence

Boundary-State Calculus for Typed Observation, Admissible Transfer, and Falsifiable Persistence

J. Tree · Independent researcher

Latest released version: v1.4.0 · 31 July 2026.

Repository state: immutable version 1.4.0 release plus explicitly marked post-release presentation and application notes, research milestones, and formal projects on main.

Release status: v1.4.0 is a foundational preprint with mathematical framework, audit artifacts, and explicit claim boundaries; not peer reviewed.

Canonical repository: https://github.com/jkolantree/BSC

Version record: https://github.com/jkolantree/BSC/releases/tag/v1.4.0

Zenodo concept DOI (all deposited versions): https://doi.org/10.5281/zenodo.21541160

Scientific claims often fail in the crossing between two otherwise valid descriptions. Boundary-State Calculus (BSC) treats that crossing as a typed, inspectable, and falsifiable object.

BSC audits one claimed transfer: what moves, what is lost, what still satisfies the target equations, what physically implements the move, and what evidence licenses the resulting claim.

The unit of evaluation is not the universe. It is one claimed transfer.

Start here

Time	Read	Purpose
2 minutes	This page	Understand the claim and its limits
2-minute v1.5 brief	BSC Core v1.5 executive summary	See the new mathematical center, exact evidence, and residual limits
Current core milestone	BSC Core v1.5	Inspect product readiness, cyclic caps, operational identifiability, exact experiment design, the first non-Q26 Lean slice, and every authority ceiling
10 minutes	Technical synopsis	See the formal object, status boundaries, and fixture set
Field-specific	Reader map	Go directly to the sections nearest your expertise
Full review	Complete paper	Inspect definitions, proofs, fixtures, applications, and references
Framework module	Normalized scale profiles	Inspect the reusable finite-family, rate, singularity, zero-transfer, and decision mathematics
Framework module	Simulation evidence profiles	Inspect intended-use records, statistical evidence, compatibility reserves, and coupled-surrogate propagation
Framework module	Operational channel core	Inspect fixed-interface mixed classical/quantum propagation, no-resurrection, driven and strong-coupling energy boundaries, energy-port gluing, typed efficiencies, Bernoulli encoding, semantic alignment, and the 1/137 boundary
Framework module	Electromagnetic evidence bridge	Inspect gauge descent, sources and flux, boundary power, calibrated scattering, inverse scope, coupling normalization, metrology, RG flow, and aperiodic geometry-to-field descent
Framework module	Lorentz auxiliary-state passivity	Inspect the post-v1.4.0 scalar storage theorem, explicit coefficient-modulation pump, coupled energy balance, and exact F13 certificate boundary
Framework module	Exact rational derived-holonomy certificates	Inspect the post-v1.4.0 exact-Q homotopy/left-null certificate and its evidence boundary
Mathematical-physics application	Electrostatic critical-point transfer	Inspect quantitative critical-point transfer, positive-source compactness, the four-charge at-least-nine construction, and the bounded five-charge reconstruction
Source-admission crosswalk	ASTRA dual-rent audit	Inspect corrected physical-change and diagnostic-gain semantics, exact countermodels, static reservoir degeneracy, source identities, and preserved verification failures
Finite combinatorics theorem	Q26 grid-annihilator proof	Inspect the direct Lean theorem giving an explicit 14-queen dominator and proving that every dominator has at least 14 queens, and the separate root-CNF status that remains UNKNOWN
Finite combinatorics campaign	Q26 queen domination	Inspect three independent encodings, theorem-derived search reductions, the checked 14-queen witness, and the separate root-CNF certificate track that remains UNKNOWN
Finite combinatorics reduction	Q26 symmetry-parity shells	Reproduce the exhaustive 156-shell structural over-cover and its 142-shell Weakley-Lemma-6 tightening without treating shells as placements or UNSAT cases
Application crosswalk	Four July 2026 experiments	Compare hybrid photons, a driven plasmonic time crystal, Hiroshima alloy evidence, and a microwave probabilistic-bit processor without conflating their physics
Number-theory application	Collatz recursive sufficiency	Inspect the exact induction defect, replacement RS sieves, conditional finite certificate, and blocked universal claims
Number-theory calculus	Collatz affine certificates	Inspect merge kernels, exact affine descent, valuation screens, a scoped one-turn binary-cylinder obstruction, and one proved recursive subprogression
Status audit	Claim-status ledger	Separate mathematical verdict from support and other readiness coordinates
Source audit	Revision memorandum	See every material repair and unresolved source conflict
Release audit	v1.0.0 audit report	See what survived, what failed, and what v1.0.1 repaired

The proposal

The paper proposes a typed transfer record:

$$\mathfrak M_{\ell\to m} = \left( T_{\ell m}, T_{\ell m}^{\sharp}, K_{\ell m}, R_{\ell m}, \Theta_{\ell m}, \delta_{\ell m}, C_{\ell m}, \mathsf{Cert}_{\ell m} \right).$$

It keeps together:

• state transport;
• reverse-direction observable transport;
• observation post-processing or statistical simulation;
• target-equation residual;
• naturality or commuting-square defect;
• directed Blackwell–Le Cam deficiency;
• physical carrier, controller, instrument, reference frame, clock, and boundary conditions; and
• assumptions, tolerances, sources, proofs or execution artifacts, hashes, unresolved obligations, and status.

The originality claim is deliberately narrow: BSC proposes a joint contract among established mathematical primitives and supplies composition and demotion semantics for that contract. It does not claim that each primitive is new, or that no equivalent formalism exists.

What this is not

BSC is not presented as:

• a fundamental ontology or unified field theory;
• proof of holography, quantum gravity, consciousness, QCD, quark charge, or hadron dynamics;
• a proof of the Riemann Hypothesis, an independent physical origin for it, or a demonstrated end-to-end quantum advantage;
• a proof of the Collatz conjecture or an official verification-frontier announcement;
• a universal law of persistence;
• a claim that every boundary determines an interior;
• a single total error score;
• a machine-checked formalization of the immutable paper or complete eight-field record; or
• a complete reference implementation.

The paper's strongest present territory is the grammar governing when boundary data, representation change, topology, learned operators, scale transfer, recurrence, or duality earns the right to support a target claim.

Available now

• A reviewer-facing preprint and editable LaTeX/BibTeX source.
• A post-v1.4.0 BSC Core v1.5 research milestone with human-readable proofs for product readiness, cyclic cap closure, operational identifiability, target-relative pair cover, and approximate oscillation; a separate pinned Lean-checked theorem slice; exact F14/F15 fixtures; proposed causal and AI-evidence profiles; and a machine-readable selected-claim package. It is not a new immutable release.
• Standalone framework modules for certified finite scale families, normalization collapse, logarithmic-rate decomposition and stability, singular-set and slice visibility, analytic zero transfer, and exact-decision bounds; and for claim-relative simulation evidence, statistical coverage, factored identity, compatibility-bounded deployment, and coupled-surrogate propagation; and for fixed compatible preparation-to-report channels, implemented-reachable-set error propagation, data processing, residual-localized energy-port gluing, denominator-typed efficiency, probabilistic encoding, and relation alignment; and an electromagnetic completion separating gauge, local Maxwell laws, constitutive response, boundary ports, calibrated reports, inverse authority, coupling normalization, and metrology.
• A post-v1.4.0 exact rational derived-holonomy certificate that returns either a chain homotopy or a normalized left-null obstruction over $\mathbb Q$.
• A post-v1.4.0 ASTRA source-admission crosswalk that gives dual rent a common prior and typed physical/report outcomes, proves two finite independence countermodels and a sole-sink static degeneracy, and preserves the supplied verifier and numerical contradictions as non-promotions.
• A post-v1.4.0 scalar Lorentz auxiliary-state theorem with exact rational symbolic and finite-ledger checks for storage, damping, boundary power, and coefficient-modulation pump accounting.
• A two-page technical synopsis and field-specific reader map.
• A symbol and notation ledger, claim-status ledger, and revision memorandum.
• Eleven exact mathematical fixtures in immutable v1.4.0; immutable v1.3.0 and v1.2.0 contain ten, immutable v1.1.0 contains nine, and immutable v1.0.1 contains eight. Post-release main additionally contains F12 through F15.
• Three executable fixtures, F8, F10, and F11, in immutable v1.4.0, plus the post-release F12 exact-Q, F13 Lorentz-passivity, F14 intervention-design, and F15 cyclic-readiness certificates, with deterministic CPython receipts or source-bound reports.
• Fail-closed checkers for retained receipts and, where shipped, parsed JSON Schemas, with exact recomputation or explicitly labeled cross-checks and negative regression tests.
• Reproduction instructions, release metadata, licenses, source-availability statement, and file-integrity manifest.
• A complete-set manifest gate that rejects missing, extra, duplicate, unsafe, or hash-mismatched release paths.

Fixtures F1–F7 and F9 have exact mathematical derivations but no separate execution receipts. F9 checks only the finite engineered zeta–coherence identity; it does not execute the application-level analytic transfer and is not an NMR-data replay. F10 executes only its declared exact finite recurrence; it is not empirical or physical validation of a surrogate model. F11 executes exact row replay and complete candidate enumeration, but its finite-prefix conclusion remains conditional on the external $2^{71}$ base that BSC did not replay. F12 is an independent exact-Q reconstruction; the absent historical script remains NOT_REPLAYED. F13 independently checks one scalar auxiliary-state identity and four finite energy ledgers; it is not a continuous Maxwell execution or physical material calibration. The immutable v1.4.0 paper includes no proof-assistant artifact; separate post-release Lean projects check the Q26 theorem and the bounded BSC Core v1.5 theorem slice without converting the paper as a whole into a formalization.

How to evaluate the contribution

The most useful first responses are:

1. an existing formalism that already provides an equivalent joint record and semantics;
2. one ill-typed map or missing hypothesis;
3. a counterexample to a composition law or fixture;
4. a case in which the added record changes no scientific decision; or
5. a nearby valid transfer that the calculus incorrectly blocks.

If established work already supplies the same obligations and demotion semantics—or if the record never distinguishes an invalid transfer from a nearby valid one—the additional structure is unnecessary.

Use the repository issue forms for prior art, type or proof errors, fixture failures, or scope corrections.

Normalized-scale framework and zeta–DQPT instance

Version 1.1.0 adds a reusable normalized-scale profile to the core calculus and applies it to Wei et al.'s engineered correspondence between finite quantum observables, the Riemann zeta function, and dynamical quantum phase transitions (DOI 10.1038/s41467-026-74935-8). The general layer separates a carrier $A_N$, nonzero normalizer $Z_N$, normalized observable $L_N$, logarithmic size gauge, ideal parameter-space rate, physical parameter slice, and estimator law. It proves normalization collapse, additive rate signatures, normalization covariance, lower-margin rate stability, singular-set and slice-visibility theorems, contour-certified zero transfer, multiplicity-sensitive local root transfer, and deterministic and stochastic exact-decision bounds. It does not manufacture an infinite-system state or a physical phase transition from a finite family.

The zeta instance proves the declared finite alternating-sum identity, an explicit local-uniform tail bound, the fixed $s$ decay-exponent split between zeros and nonzeros, the corresponding pointwise free-energy values and exact rate-singularity set for $N=2^d$, the exact fixed $\beta$ real-time singularity slice, a sharp local finite-root drift, and a bounded zero-count transfer conditional on a certified whole-contour separation. Confining every rate singularity to the critical line is an exact re-encoding of RH, not a proof of it. The release records the five-qubit NMR result as one source-reported study and blocks promotion from finite agreement to exact zero certification, a thermodynamic singularity, the universal Riemann Hypothesis, a comparator-independent quantum advantage, a unique Kelvin temperature, or an independent physical-origin claim.

No raw-data replay, fitting re-execution, hardware run, or complexity benchmark has been performed in this repository. The inspected Nature Communications source was an unedited article-in-press version, so the citation state is also recorded rather than silently treated as final typeset text.

Simulation-evidence framework

Version 1.2.0 adds a claim-relative simulation-evidence profile without changing the eight-field BSC morphism. It separates statistical simulation, computational simulation, and surrogate deployment; records intended use, typed source estimands and target BSC losses, hard gates, estimators, a joint observation law, sampling or oracle models, joint coverage, optimization gaps, proxy-transfer theorems, and factored evidence identity; and proves compatibility-bounded deployment after monotone, unit-respecting propagation:

$$\ell^{\mathrm{dep}}_{c,j} \le \ell^0_{c,j}+\rho_{c,j}, \qquad U^0_{c,j}+\rho_{c,j}\le\tau_{c,j}.$$

Frozen-state estimator uncertainty already enclosed by $U^0_{c,j}$ is not counted again in $\rho_{c,j}$; uncertainty in estimating the deployment change is represented exactly once. Quantities with different units are combined only through a declared propagation map. An implemented statistical channel gives an upper bound on directed deficiency; it does not establish the optimum or a lower bound. A zero declared failure probability is only a probability-one statement unless the bounds hold pointwise.

The finite-horizon specialization shows why standalone surrogate accuracy does not determine coupled-host accuracy. Executable Fixture F10 uses the same exact interface error $1/100$ in two stable hosts for ten steps. Host A ($a=1/2$) remains within tolerance with exact maximum error $1023/51200$; Host B ($a=9/10$) first violates the $1/20$ tolerance at step 7 and ends at $6513215599/100000000000$. This is a deterministic code-verification result for that recurrence and loss coordinate, not full BSC admissibility, physical validation, or a general surrogate guarantee. The V&V disciplines and finite-horizon coupling mechanism are prior art; BSC's narrower contribution is their typed integration, transfer authority, and local demotion semantics.

Operational-channel framework

Version 1.3.0 adds a restricted preparation-to-report layer:

$$\theta \longrightarrow \mathsf{Prep} \longrightarrow \mathsf{Drive} \longrightarrow \mathsf{Measure} \longrightarrow \mathsf{Report} \longrightarrow \mathsf{Decision}.$$

Classical interfaces use total variation, quantum interfaces use trace distance, and POVMs form a declared quantum-to-classical boundary. For fixed compatible ideal and implemented stages, local defects must cover the implemented reachable set. If those defects are $\varepsilon_k$ and the ideal-stage contractions are $\eta_k$, then

$$E_m \le \sum_{k=0}^{m} \varepsilon_k \prod_{j=k+1}^{m}\eta_j.$$

This propagates state or report-law discrepancy only. It does not compose the full BSC morphism and does not resolve BSC-QOP-03.

The same module proves:

• downstream Markov, CPTP, measurement, and report channels cannot resurrect lost distinguishability; a complete postselection instrument is contractive, but normalizing on success can amplify distance;
• a uniform forward-report defect $B$ gives two-sided containment of actual and ideal compatible parameter sets after enlarging the radius by $B$;
• identical spectral-intensity laws can belong to orthogonal photon states, so unit marginal overlap does not certify quantum identity;
• a driven open quantum system satisfies $\dot E=\mathrm{Tr}(\rho\dot H)+\mathrm{Tr}(H\mathcal D_t(\rho))$ under its declared split and finite-dimensional or separately justified domain assumptions;
• finite additive energy-port diagrams satisfy $R_G=\sum_vr_v+\sum_eg_e$, so interface storage must be explicit and a globally closed residual cannot certify locally defective seams;
• count yields, energy efficiencies, and conditioned efficiencies remain differently typed, and stage ratios telescope only across the identical intermediate quantity and evidence identity;
• conditionally iid scalar Bernoulli repetitions have sufficient count $K=\sum_iY_i$ and at most $\log_2(N+1)$ bits of input information;
• 256 scalar Bernoulli labels cannot be recovered with zero error for any finite $N$ under that model;
• under $P_{\phi(i),i}=1$, one same-entity relation alignment requires $S=PCP^{\mathsf T}$, not independent row and column permutations; and
• generic channel form cannot derive the electromagnetic fine-structure constant. The approximate 1/137 value needs a typed QED and metrological bridge.

The first application crosswalk binds four primary publications: hybrid atom–quantum-dot two-photon interference, a driven plasmonic photonic time crystal, a Hiroshima blast-forged multicomponent alloy, and an integrated microwave probabilistic-bit processor. The commonality is evidentiary form, not a claim that these systems share one microscopic law. No hardware, spectroscopy, crystallography, classifier, or raw-data analysis was replayed by BSC.

ASTRA dual-rent source-admission crosswalk

The post-v1.4.0 ASTRA crosswalk treats the supplied v0.3 package as a source family, not as independent validation. It freezes six outer hashes, independently checks the package inventory, and separates physical future $W$ from terminal report $Y$. A common candidate prior is required before comparing $R_{\mathrm{dyn}}=\sum_kp(k)d_{\mathrm{phys}}(\sigma_1^k,\sigma_0^k)$ and $R_{\mathrm{epi}}=I_{P_1}(K;Y)-I_{P_0}(K;Y)$.

Two exact fair-bit examples show that diagnostic access can increase without physical change and physical change can occur without diagnostic gain. The crosswalk also derives the model-local sole-sink identity $T_s=(\mathbf1^Tb)/\lambda$. Existing BSC-CHN-02 remains decisive: a common passive downstream channel cannot create information, and conditioned gains must retain the complete instrument and success probability.

The note allocates no new claim or fixture. It withholds the package's SPPT frequency result because the narrative and canonical JSON disagree, treats the package verifier as source asserted rather than fail closed, and leaves the Keller, prime-difference, experimental, quantum, archaeological, and origin lanes unpromoted. The strongest exact Keller candidate is deferred until after the existing electromagnetic fixture sequence.

Electromagnetic evidence bridge

The electromagnetic bridge instantiates the operational report envelope as

$$\mathsf{EMC} = (M,g,P,[\mathcal A],\mathcal F,\mathcal H,\mathcal J, \mathcal C,\mathcal B,\mathcal M,\mathcal R,\mathsf{Cert}_{\mathrm{EM}}).$$

It proves gauge descent and the curvature/holonomy distinction; source compatibility and topological-flux boundaries; Poynting balance with explicit boundary, pump, material, and loss accounting; passive scattering only in a declared calibrated power metric; a magnitude-only phase/delay no-go; and field-normalization and charge-flux invariants. Maxwell boundary inversion remains theorem-, coefficient-class-, gauge-, frequency-, and data-local. Static curved-space fluxes instantiate the same energy-port theorem through metric volume and boundary forms; moving boundaries, time-dependent metrics, and non-Killing relativistic currents require their additional transport or bulk terms.

The bridge sharpens rather than reverses the 1/137 boundary. Revised-SI definitions move uncertainty into $\mu_0$ through $\mu_0=\alpha\mkern3mu 2h/(ce^2)$; they do not derive $\alpha$. Likewise, $\mu\mkern3mu dg/d\mu=\beta(g)$ transports a supplied coupling between scales but does not determine its boundary value. The exact counterexample $\beta\equiv0$ admits every constant coupling.

A separate arithmetic screen records the genuine relation $\mathrm{ord}_{137}(2)=68$, so $1/137$ has a 68-bit repetend. It also shows that $2^{31}-1$, $2^{32}-1$, and $65\mkern3mu 537$ are not divisible by 137 and that the regular 137-gon is not straightedge-and-compass constructible. Those binary and Fermat-number facts do not identify the measured $\alpha$.

The Einstein-monotile crosswalk adds BSC-EM-11. The Hat is an aperiodic union of eight kites from the periodic deltoidal-trihexagonal carrier grid, but a tiling theorem is not yet a material or Maxwell model. Translation aperiodicity transfers to a coefficient field only under a declared faithful materialization. A selector can instead erase the tiling or retain only its periodic carrier: peer-reviewed Hat point diffraction is a concrete case in which an aperiodic real-space tiling has a periodic reciprocal-space report. The 2026 centroid-selected SiN experiment supplies single-study evidence along one specific finite geometry-to-fabricated-sample-to-diffraction chain; it does not establish a universal band gap, nonreciprocity, or a route to $1/137$.

Electrostatic critical-point transfer

The post-v1.4.0 electrostatic application allocates BSC-ECP-01 through BSC-ECP-05. It records quantitative $C^2$ transfer for isolated Morse points, the normalization-sign index rule, and the extra exterior-gradient and no-escape evidence needed before a local roster can become an exact compact or global count. Its positive-source completion adds uniform source exclusion before compact regular zeros are called finite; genericity remains existential.

For fixed $c>4/9$ and sufficiently small positive $\varepsilon$, the triangle-plus-apex construction retains six Morse-Bott split points and three remote points. A subsequent generic strength perturbation gives four pairwise-unequal positive charges with a finite Morse set containing at least nine points. This is not exactly nine, not a four-charge maximum, novelty, or priority claim, and not a stable-trap result.

The same module independently reconstructs the five-charge theorem as an exact 21-point limit-polynomial roster plus three persistent remote points, and states the derivative-controlled pair-insertion gate. It is NOT_REPLAYED: there is no historical script or receipt, no interval certificate at $\varepsilon=1/6$, no exact finite-parameter total, no explicit generic perturbation or robustness radius, and no transfer from point charges to finite-size distributions.

Collatz recursive-sufficiency application

Version 1.4.0 audits the first nontrivial layer of Ansari's 2025 recursive-sufficiency induction. Exact residue expansion gives

$$F_1\setminus F_2 =(36\mathbb N_0+27)\cup(36\mathbb N_0+31).$$

The $31$-class has an explicit merge to a smaller integer; the $36k+27$ class remains unresolved. The release proves an unconditional parity-prefix RS family with exponentially vanishing density, a safety-net ternary-spine replacement, and a sharper $2^{71}$-conditioned $W_{173}$ sieve with exact density.

Executable Fixture F11 replays all 52,686 retained first-descent rows and exhaustively tests all 1,388,888,889 compatible candidates in the ten-billion-wide interval. Strong induction gives a conditional extension through $2^{71}+10^{10}$. BSC did not replay the external base campaign; the result is not an official computational record, a repair of the original $F_n$ induction, or a proof of the Collatz conjecture.

The post-v1.4.0 affine-certificate calculus adds a separately reviewed merge-kernel characterization, the exact uniform affine descent criterion, typed log-slope and valuation screens, a narrow no-go theorem for finite binary-cylinder proofs that assign one fixed one-turn path to each leaf, and an exact certificate for $8748\mathbb N_0+6219$. The full $36k+27$ class remains unresolved. Proposed depth-28/30/32 catalogs are not promoted because the catalogs, manifest, miners, and independent replay program were not supplied to the repository.

Current status boundary

Object	Verdict	Math support	Empirical	Computational	Transfer
Repaired partial stochastic composite	True	Proved under stated support and completion hypotheses	N/A	Symbolic, unexecuted	Bounded
Normalized-scale profile theorems	True	Normalization collapse, additive rates, covariance, singular support, slice visibility, and analytic zero transfer proved	N/A	Unexecuted	Certified
Simulation-evidence profile	True	Typed source-to-loss propagation, joint coverage obligations, factored identity, compatibility-bounded deployment, and coupled-surrogate propagation proved	N/A	Unexecuted	Bounded
Operational fixed-interface channel core	True	Implemented-reachable-set product-sum propagation and classical/quantum no-resurrection proved	N/A	Unexecuted	Bounded
Driven energy, scalar Bernoulli, and semantic-alignment consequences	True	Exact symbolic proofs under declared finite-dimensional, iid, and same-entity hypotheses	N/A	Unexecuted	Bounded
Electromagnetic evidence bridge	True under its declared local hypotheses	Gauge/source, Poynting, passive-scattering, phase, normalization, flux-product, revised-SI, RG boundary-value, and aperiodic materialization-descent results proved; inverse and spectral claims remain theorem local	One experimental study; not replayed	Unexecuted	Bounded
ASTRA dual-rent source-admission crosswalk	Citation-only terminology with exact finite reconstructions	Common-prior dual-rent typing, two independence countermodels, and sole-sink static degeneracy; no new BSC claim identifier	Source package only; experiments not replayed	27 bundled tests rerun in an unpinned environment; verifier defects and SPPT contradiction preserved	Local only
Electrostatic critical-point transfer	True under its declared point-source, scale, compactness, and derivative-control hypotheses	Quantitative local transfer, source-exclusion completion, a four-charge at-least-nine theorem, and an independently reconstructed five-charge at-least-24 theorem	N/A	Exact symbolic regressions; historical computations not replayed and no finite-parameter interval certificate	Bounded
Channel form determines $\alpha^{-1}\approx137$	False	The abstract envelope axioms contain no equation fixing a coupling; no operationally equivalent pair is asserted	N/A	Unexecuted	Blocked
Exact finite-label observation decoding	True	Measurable-partition criterion and total-variation lower bound proved	N/A	Unexecuted	Certified
Generic decorated-cospan theorem	True	Proved under the assumed lax-monoidal functor	N/A	Unexecuted	Bounded
Canonical BSC-specific decoration functor	Open	Conditional schema only	N/A	Unexecuted	Blocked
Persistent-object principle	Open	Conjectural organizing principle	Untested	Unexecuted	Local only
Fixtures F1–F7	True	Exact mathematical derivations	N/A	Unexecuted	Fixture-local
Fixture F8	True fixture result	Proved counterexample	N/A	One exact receipt	Fixture-local
Fixture F9: zeta–DQPT scope audit	True fixture result	Finite identity proved; application-level scaling and contour theorems are not fixture executions	N/A	Unexecuted	Fixture-local
Fixture F10: coupled-surrogate host dependence	True fixture result	Equal standalone error yields different exact host-relative tolerance disposition under two stable recurrences	N/A	One exact receipt	Fixture-local
Fixture F11: Collatz recursive-sufficiency repair	True implication; conditional support	Exact induction defect, replacement sieve arithmetic, exhaustive interval enumeration, and first-descent replay	N/A	One exact receipt; external base not replayed	Fixture-local
Fixture F12: exact-Q derived holonomy	True fixture result	Exact chain-homotopy pass or normalized left-null obstruction under BSC-DHC-01	N/A	One independent-reconstruction receipt; historical script not replayed	Fixture-local
Fixture F13: Lorentz auxiliary-state passivity	True fixture result	Exact symbolic storage and coupled-balance cancellation plus four rational energy ledgers under BSC-EM-12	N/A	One independent-reconstruction receipt; not a PDE or historical replay	Fixture-local
Fixture F14: finite intervention identifiability	True fixture result	Exact finite target-relative set cover, all minimum-cost ties, and rational target oscillations	N/A	One source-bound exact report with two internal criterion checks; no causal or empirical validation	Fixture-local
Fixture F15: cyclic readiness	True fixture result	Exact simultaneous cap closure and exhaustive greatest-feasible cross-check for the declared three-node graph	N/A	One source-bound receipt and shared-model exhaustive cross-check; not an independent implementation	Fixture-local
Collatz affine-certificate calculus	True within its declared path classes	Merge-kernel, affine-descent, valuation-screen, one-turn ghost-cylinder, and one-subprogression results proved; arithmetic-bar completeness remains open	N/A	Exact symbolic regressions; no catalog execution	Bounded
Finite-resolution observation decides exact zero	False	Query fails operational descent when zero and nonzero amplitudes are confusable	N/A	Unexecuted	Blocked
Finite evidence entails limiting DQPT exclusivity or RH	False	Limit, zero-census, and universal quantifier are not discharged	Single study	Unexecuted	Blocked
End-to-end quantum advantage	Open	Conditional resource comparison only	Untested	Unexecuted	Blocked
Independent physical origin or unique Kelvin temperature	Not established	No causal/ontological or energy-unit/calibration bridge	N/A	Unexecuted	Blocked
Generic BSC physical validation	Open	No general bridge	Untested	Unexecuted	Blocked

The complete axis-by-axis record is in the claim-status ledger.

Verify the retained executable fixtures

From the repository root:

python3 fixtures/F08_sqrt_square_sign/check_fixture.py
python3 fixtures/F10_coupled_surrogate/check_fixture.py
python3 fixtures/F11_collatz_recursive_sieve/check_fixture.py
python3 fixtures/F12_derived_holonomy_q/check_fixture.py
python3 fixtures/F13_lorentz_auxiliary_passivity/check_fixture.py
python3 fixtures/F14_intervention_identifiability/check_fixture.py
python3 fixtures/F15_cyclic_readiness/check_fixture.py

No checker overwrites its retained receipt. F8 and F10 parse their shipped schemas, independently recompute their declared mathematics, run their generators in temporary locations, and require byte-identical output. F11's routine gate replays every retained row and identity; its publication-only --full-scan mode repeats the complete candidate enumeration. Negative tests retain the two F8 mutants that the v1.0.0 checker incorrectly accepted, add stale-host, altered-horizon, false-tolerance-disposition, decimal-substitution, and overwrite controls for F10, and reject changed certificate bytes, false completeness, nested schema errors, self-hash-policy changes, and overwrite attempts for F11. F12 rejects malformed complexes, non-chain maps, noncanonical rationals, arbitrary fields, tampered pass/fail witnesses, input substitution, evidence promotion, namespace collisions, and nondeterministic bytes. F13 rejects nonpositive storage parameters, negative damping promoted as passive, classification errors, missing or sign-flipped pump terms, Maxwell and port-sign errors, noncanonical JSON, identity changes, sample-to-theorem promotion, namespace collisions, and receipt overwrite.

For the full local verification sequence:

make verify

See REPRODUCING.md for the pinned environment and build commands.

Repository map

paper/        immutable-release manuscript PDF and editable source
framework/    reusable mathematics and post-release evidence profiles
applications/ source-bound domain crosswalks
synopsis/     released synopsis plus current reader and executive maps
ledgers/      claim status, notation, and the selected v1.5 claim package
fixtures/     mathematical fixtures plus executable F8, F10, F11, and post-release F12–F15 evidence
formal/       separate pinned Lean projects for Q26 and the bounded BSC core
research/     prior-art and recent-research maps for BSC Core v1.5
revision/     explicit definition repairs and unresolved obligations
provenance/   supplied-corpus identity records
tools/        complete-set manifest and release verification
tests/        positive and negative release-gate regressions

Citation, disclosure, and licensing

Machine-readable citation metadata is in CITATION.cff. Version 1.4.0 is published in the immutable GitHub release record. The concept DOI 10.5281/zenodo.21541160 identifies all deposited versions and resolves to the latest Zenodo deposit. The v1.4.0 version DOI is assigned after the immutable tagged bytes are built and is recorded on the GitHub release page. The immutable v1.3.0 version DOI is 10.5281/zenodo.21713285. The immutable v1.2.0 version DOI is 10.5281/zenodo.21711341. The immutable v1.1.0 version DOI is 10.5281/zenodo.21710743. The immutable v1.0.1 DOI is 10.5281/zenodo.21541561, and the immutable v1.0.0 DOI remains 10.5281/zenodo.21541161.

Material generative assistance and its limits are recorded in DISCLOSURE.md. Automated or model-assisted checks are not independent peer review.

Paper and documentation are licensed under CC BY 4.0. Code and machine-readable fixture tooling are licensed under the MIT License. The F11 tabular certificate is licensed as factual data under CC BY 4.0. The supplied internal source corpus is not redistributed by this repository. The license map also records the historical clarification for commits preceding the explicit dual-license notice.

Contact

Use this repository's Issues. A citation, counterexample, type correction, or one-sentence scope correction is a complete and valuable contribution.