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 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status: v1.4.0 is a foundational preprint with mathematical framework, audit artifacts, and explicit claim boundaries; not peer reviewed.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.
| Time | Read | Purpose |
|---|---|---|
| 2 minutes | This page | Understand the claim and its limits |
| 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 | 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 |
| 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 paper proposes a typed transfer record:
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.
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; 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.
- A reviewer-facing preprint and editable LaTeX/BibTeX source.
- 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 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
mainadditionally contains F12. - Three executable fixtures, F8, F10, and F11, in immutable v1.4.0, plus the post-release F12 exact-Q certificate, with deterministic CPython receipts.
- Fail-closed checkers for those receipts and their parsed JSON Schemas, with independent semantic recomputation 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 NOT_REPLAYED. No proof-assistant
artifact is included.
The most useful first responses are:
- an existing formalism that already provides an equivalent joint record and semantics;
- one ill-typed map or missing hypothesis;
- a counterexample to a composition law or fixture;
- a case in which the added record changes no scientific decision; or
- 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.
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
The zeta instance proves the declared finite alternating-sum identity, an
explicit local-uniform tail bound, the fixed
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.
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:
Frozen-state estimator uncertainty already enclosed by
The finite-horizon specialization shows why standalone surrogate accuracy
does not determine coupled-host accuracy. Executable Fixture F10 uses the same
exact interface error
Version 1.3.0 adds a restricted preparation-to-report layer:
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
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.
The electromagnetic bridge instantiates the operational report envelope as
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
A separate arithmetic screen records the genuine relation
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
The post-v1.4.0
electrostatic application
allocates BSC-ECP-01 through BSC-ECP-05. It records quantitative
For fixed
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
Version 1.4.0 audits the first nontrivial layer of Ansari's 2025 recursive-sufficiency induction. Exact residue expansion gives
The
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
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
| 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 |
| 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 |
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 |
| 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.
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.pyNo 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.
For the full local verification sequence:
make verifySee REPRODUCING.md for the pinned environment and build commands.
paper/ manuscript PDF and editable source
framework/ reusable scale, simulation, channel, electromagnetic, and exact-Q certificate mathematics
applications/ source-bound domain crosswalks
synopsis/ two-page synopsis, source, and reader map
ledgers/ claim status and notation
fixtures/ mathematical fixtures plus executable F8, F10, F11, and post-release F12 receipts
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
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.
Use this repository's Issues. A citation, counterexample, type correction, or one-sentence scope correction is a complete and valuable contribution.