NOTE · Observational Record — "The η Corridor". A paper of the framework's research as it stood when written, kept as printed; its computations stand and were re-verified at the September 2026 reprint. The corpus is now read through One coordinate up (DOI 10.17605/OSF.IO/UJWC7 (https://osf.io/ujwc7)). The η Corridor in 3D Wilson–Fisher Critical Phenomena — Empirical Observation. The anomalous dimension η at d = 3 critical points of the Wilson–Fisher family is observed to be bounded above by 2G ≈ 0.039484, where G = 1 − K_AUD and K_AUD = √2·ln(2). The bound is tested across ten universality classes — O(N) for N = 0–4, cubic anisotropy at N = 3, 4, MN cubic at N = 2, 3, and randomly dilute Ising — and holds in every case, with σ-margins from +2.2σ (randomly dilute Ising, the tightest unitary case) to +1593σ (3D Ising, conformal bootstrap). Three classes outside the family's scope (RFIM, deconfined SU(2) QCP, disordered Potts at large q) have η > 2G and are excluded by independent physical structure. The bound is offered as a falsifiable empirical observation, not a derived result; the priority falsification target is a higher-precision η at d = 3 randomly dilute Ising. Part I presents the observation. Part II develops a structural reading on the dome function g(x) = tanh(x)/cosh(2x), known from hyperbolic-3-manifold geometry as the Hodgson–Kerckhoff tube-packing function. Ten theorems: the factorization g = (1/2)·sech²·tanh(2x); the golden polynomial u² − u − 1 in the logarithmic derivative; the self-reference uniqueness at u = √2; the dome integral ∫g dx = ln(2)/2; the Mellin spectrum M_g(s) = (s−1)!·η(s)·(2^s − 1)/2^(2s−1) with its rational/π closed forms and A002105 × Mersenne integer-ratio factorizations; the descent-to-K identity at R₀ where cosh(2R₀) = 2; the two algebraic environments at the HK landmarks; and the corridor-margin identity 1/ln 2 − √2 = G·log₂(e). A zero-parameter model based on the dome fits the resummation factor R(N) for the O(N) anomalous dimensions to 0.77 % RMS. The Central Synchronization Conjecture (§11) is flagged as a conjecture; derivation targets are listed as open. The paper claims no derivation of the bound from first principles, no mechanism for the constant's appearance across domains, and no connection to a physical theory not developed in it; the structural reading organizes what the observation invites, and a reader may adopt the observation without it (§14.6). A Verification Companion (a separate file in the same OSF project, shared DOI) carries the line-by-line mpmath verification of the algebraic identities at dps = 80–1000, including the re-verification at dps = 1000 (2026-05-28). Verified across seven independent AI architectures, including a twelve-agent, 1071-source reference-link check of the §16 citation block. Update — September 2026 (reprint with the reading-update block): every paper of the framework is re-issued with one short block under its title — "How the corpus is now read: One coordinate up — DOI 10.17605/OSF.IO/UJWC7 (https://osf.io/ujwc7)" — and is classed as a NOTE on the Documents page's Observational Record shelf under its short title "The η Corridor". The framework now writes the ratio p = GM/L_log and its complement G = 1 − p; K_AUD is this paper's own symbol for p and stays as printed. The fresh-print controls corrected six things in place: §5.1's SAW row 2G − η 0.008441 → 0.008440; the circumradius label in §13, bracketed; the §9.11 erratum written in place (the bridge sentence drops the factor (2^(2n) − 1); the theorems are unaffected); and in the Verification Companion five printed strings that carried digits beyond their computation's depth (2G's 100th–101st decimals; the last digit of M[g](2) and M[g](5); sinh and cosh of ln 2/2 from the 46th decimal) — corrected and noted in the reprint note. The prior version remains on OSF as an OLD- archived file. The framework Main OSF project (every paper, reading order, version history): https://osf.io/zx4g7 (DOI: 10.17605/OSF.IO/ZX4G7) The signpost — four doors: the framework, the instruments, the source, the deposits: https://gap-geometry.github.io/sqrt2-ln2-geometric-constants-/about.html The Documents page (current PDF and text of every paper, each with its DOI): https://gap-geometry.github.io/sqrt2-ln2-geometric-constants-/direct-documents.html AI Readers (raw links and the verification block, for machine readers): https://gap-geometry.github.io/sqrt2-ln2-geometric-constants-/ai-readers.html GitHub: https://github.com/Gap-geometry
NOTE · Observational Record — "The η Corridor". A paper of the framework's research as it stood when written, kept as printed; its computations stand and were re-verified at the September 2026 reprint. The corpus is now read through One coordinate up (DOI 10.17605/OSF.IO/UJWC7 (https://osf.io/ujwc7)). The η Corridor in 3D Wilson–Fisher Critical Phenomena — Empirical Observation. The anomalous dimension η at d = 3 critical points of the Wilson–Fisher family is observed to be bounded above by 2G ≈ 0.039484, where G = 1 − K_AUD and K_AUD = √2·ln(2). The bound is tested across ten universality classes — O(N) for N = 0–4, cubic anisotropy at N = 3, 4, MN cubic at N = 2, 3, and randomly dilute Ising — and holds in every case, with σ-margins from +2.2σ (randomly dilute Ising, the tightest unitary case) to +1593σ (3D Ising, conformal bootstrap). Three classes outside the family's scope (RFIM, deconfined SU(2) QCP, disordered Potts at large q) have η > 2G and are excluded by independent physical structure. The bound is offered as a falsifiable empirical observation, not a derived result; the priority falsification target is a higher-precision η at d = 3 randomly dilute Ising. Part I presents the observation. Part II develops a structural reading on the dome function g(x) = tanh(x)/cosh(2x), known from hyperbolic-3-manifold geometry as the Hodgson–Kerckhoff tube-packing function. Ten theorems: the factorization g = (1/2)·sech²·tanh(2x); the golden polynomial u² − u − 1 in the logarithmic derivative; the self-reference uniqueness at u = √2; the dome integral ∫g dx = ln(2)/2; the Mellin spectrum M_g(s) = (s−1)!·η(s)·(2^s − 1)/2^(2s−1) with its rational/π closed forms and A002105 × Mersenne integer-ratio factorizations; the descent-to-K identity at R₀ where cosh(2R₀) = 2; the two algebraic environments at the HK landmarks; and the corridor-margin identity 1/ln 2 − √2 = G·log₂(e). A zero-parameter model based on the dome fits the resummation factor R(N) for the O(N) anomalous dimensions to 0.77 % RMS. The Central Synchronization Conjecture (§11) is flagged as a conjecture; derivation targets are listed as open. The paper claims no derivation of the bound from first principles, no mechanism for the constant's appearance across domains, and no connection to a physical theory not developed in it; the structural reading organizes what the observation invites, and a reader may adopt the observation without it (§14.6). A Verification Companion (a separate file in the same OSF project, shared DOI) carries the line-by-line mpmath verification of the algebraic identities at dps = 80–1000, including the re-verification at dps = 1000 (2026-05-28). Verified across seven independent AI architectures, including a twelve-agent, 1071-source reference-link check of the §16 citation block. Update — September 2026 (reprint with the reading-update block): every paper of the framework is re-issued with one short block under its title — "How the corpus is now read: One coordinate up — DOI 10.17605/OSF.IO/UJWC7 (https://osf.io/ujwc7)" — and is classed as a NOTE on the Documents page's Observational Record shelf under its short title "The η Corridor". The framework now writes the ratio p = GM/L_log and its complement G = 1 − p; K_AUD is this paper's own symbol for p and stays as printed. The fresh-print controls corrected six things in place: §5.1's SAW row 2G − η 0.008441 → 0.008440; the circumradius label in §13, bracketed; the §9.11 erratum written in place (the bridge sentence drops the factor (2^(2n) − 1); the theorems are unaffected); and in the Verification Companion five printed strings that carried digits beyond their computation's depth (2G's 100th–101st decimals; the last digit of Mg and Mg; sinh and cosh of ln 2/2 from the 46th decimal) — corrected and noted in the reprint note. The prior version remains on OSF as an OLD- archived file. The framework Main OSF project (every paper, reading order, version history): https://osf.io/zx4g7 (DOI: 10.17605/OSF.IO/ZX4G7) The signpost — four doors: the framework, the instruments, the source, the deposits: https://gap-geometry.github.io/sqrt2-ln2-geometric-constants-/about.html The Documents page (current PDF and text of every paper, each with its DOI): https://gap-geometry.github.io/sqrt2-ln2-geometric-constants-/direct-documents.html AI Readers (raw links and the verification block, for machine readers): https://gap-geometry.github.io/sqrt2-ln2-geometric-constants-/ai-readers.html GitHub: https://github.com/Gap-geometry
Preprint. Third paper of the contextuality-obstructions program, alongside Paper A (the canonical class of the MASA context stack), Paper B (the obstruction spectrum of Weyl context families), Paper D (the observer-context category) and a synthesis note. The slogan "contextual holonomy encodes quantum contextuality" is attractive and, as usually stated, false. This paper gives it a sharp form. On the context stack of maximal abelian subalgebras the canonical degree-2 class has order exactly n, and its cocycle holonomy along closed context loops detects EXACTLY the all-versus-nothing sector of contextuality for closed-triple Weyl families at even local dimension. Both containments are strict, each by an explicit certificate: at d=3 the class is nontrivial of order 3 while the achievable state-independent AvN value is 0, and KCBS exhibits state-dependent contextuality where the class shadow vanishes. The Wigner-friend loop generated by H and S splits by level: its projective (Pancharatnam) holonomy is +1 while its determinant-section holonomy is exactly -i, so any interpretational claim about "the" holonomy of that loop must state which one it means. ATTRIBUTION. The classification of state-independent values for qudit Weyl families, the even/odd dichotomy and the fixed value d/2, on which the state-independent side of the equivalence rests, is DUE TO Abramsky, Cercelescu and Constantin (FSCD 2024). Attainment at general even d is the Raussendorf-Okay-Zurel-Feldmann construction. This paper uses both and rediscovers neither. A RETRACTION IS CARRIED IN THIS PAPER, NOT BURIED. An earlier draft presented the tier-two facets of the d=4 census on a (1/(2*sqrt2))Z grid with a single coefficient magnitude 3/(2*sqrt2), and read the resulting unit-coefficient bounds 4*sqrt2 and 14*sqrt2/3 as placing Tsirelson's sqrt2 inside the tier-two geometry. The whole presentation was a normalization artifact and is withdrawn (Retraction 1): the stored lift has coefficients in {0,+-1} with integer bounds 6 and 7, every facet functional in the census is rational, and Q(sqrt2) is not among the eighteen canonical arithmetic fields. Certificate: d4_arithmetic_profile.py. WHERE THE EVIDENCE IS THIN, STATED IN THE PAPER. Two sweeps quoted here drew no positive instances at all: the d=4 half of the 2,100-family equivalence test, and the 6,500-trial false-certificate sweep, which draws no contextual family at any of d=2,4,8 and therefore establishes the absence of false certificates only vacuously. Both are disclosed where they appear. Theorem 2 is labelled machine-validated rather than proved: the closed form is established end to end for the deletion families treated, while the general closed-triple d=2 statement in compressed coordinates remains open and is recorded as open in the verification ledger. HARDWARE CAVEAT, STATED UP FRONT. The quoted significances, about 56 sigma for the ray-level Wigner-friend holonomy and 35.4 sigma for the Peres-Mermin witness above the deterministic bound 4, are shot-noise statistical only, computed under the implemented witness model and conditional on compatibility and nondisturbance assumptions. They are not systematics-aware and neither measurement is loophole-free; a roughly 3.5 sigma preparation offset on one strand is itself evidence of unmodelled systematics. We also record that the pinned value S = 4.6125 cannot be recomputed from the stored counts (a naive recomputation gives 4.5662, a gap of about 2.7 standard errors); the archived value 4.558 +- 0.018 is the one an independent reader can reproduce from the deposited data. Read these as consistency checks on real hardware, not as precision measurements or certifications. STATUS AND SCOPE. This is a preprint, not a peer-reviewed article. It was held back from the first publication batch and released only after three adversarial review passes; what each pass found, and how each item was closed, is recorded in verification/INDEX.md rather than quietly fixed. One defect found there is NOT closed and belongs to the companion Paper B, which cites a false-certificate artifact that is not in fact in the repository; it is recorded rather than left for a reader to discover. COMPANIONS. Paper A: https://doi.org/10.5281/zenodo.21630431 . Paper B: https://doi.org/10.5281/zenodo.21630630 . Paper D: https://doi.org/10.5281/zenodo.21630697 . Note: https://doi.org/10.5281/zenodo.21630739 . Code archive: https://doi.org/10.5281/zenodo.21498498 AI-ASSISTANCE DISCLOSURE. Large-language-model assistants (Anthropic Claude) were used substantially in drafting, in developing the verification scripts, in literature search and in proposing proofs. Every load-bearing claim is machine-verified independently of that assistance by the scripts named in the text, and the author takes full responsibility for the results, including any errors. VERIFICATION CODE. https://github.com/manuflog/contextuality-obstructions
ON THE VERSION NUMBER. "v3" is the version of the NOTE, not of this Zenodo deposit. Versions 1 (February 2026) and 2 were circulated privately and never deposited; v1 contained four errors of substance, which are stated with their repairs in the "What changed" section rather than quietly removed. This is the first Zenodo deposit, so if you see a deposit counter it will not match the document version. The document version is the one that matters for citation. Preprint, version 3 (complete rewrite). This note is the synthesis of the contextuality-obstructions program; the proofs live in the companion papers. The proposal is that the Copenhagen viewpoint, stripped of its rhetoric, is a set of structural statements about one geometric object: the transformation groupoid of measurement contexts (maximal abelian subalgebras) with its canonical U(1) 2-cocycle. In that formulation: local validity, the exact classicality of every single context, is a theorem with an explicit witness; complementarity is the nonvanishing holonomy of the cocycle along closed context loops, which detects exactly the all-versus-nothing sector of contextuality; collapse is pinned by statistics, repeatability and covariance to a one-parameter family per degenerate block whose unique efficient member is the Lueders rule, with a classical twin theorem identifying the same axioms' classical solution as Bayesian conditioning; observer-relativity of facts and the movable cut are theorems of an enlarged observer-context category; and the Frauchiger-Renner argument localizes to an ordinary state-dependent violation, with contextual fraction exactly 1/6, carried by a single CHSH facet, the loop holonomy of the observer switch being provably trivial. ATTRIBUTION. The classification of achievable state-independent values, the even/odd dichotomy and the fixed value d/2, is due to Abramsky, Cercelescu and Constantin (FSCD 2024). It is recast here in certificate language; the priority is theirs and is stated in the text. HARDWARE CAVEAT, STATED UP FRONT. Two signatures were measured on superconducting hardware. The quoted significances, about 56 sigma for the triangle holonomy and 35.4 sigma for the Peres-Mermin witness above the deterministic bound 4, are shot-noise statistical only, computed under the implemented model. They are not systematics-aware, and neither experiment is loophole-free. Read them as consistency checks on real hardware, not as precision measurements. ERRATA. Version 1 of this note contained four errors of substance. Section "What changed" states each of them and its repair. They are recorded rather than quietly removed. STATUS AND SCOPE. This is a preprint, not a peer-reviewed article. Each tenet is either a theorem of the companion papers, a machine-verified certificate in the public suite, or is explicitly labeled a conjecture. The paper offers structural characterizations within its stated axioms; it is not an interpretation-free derivation of Copenhagen and it does not claim to resolve the measurement problem. AI-ASSISTANCE DISCLOSURE. This work was carried out with substantial AI assistance. Every load-bearing claim is machine-verified by scripts that ship with the papers, and the author takes full responsibility for the contents. COMPANIONS. Paper A: https://doi.org/10.5281/zenodo.21630431 . Paper B: https://doi.org/10.5281/zenodo.21630630 . Paper D: https://doi.org/10.5281/zenodo.21630697 . Paper C: https://doi.org/10.5281/zenodo.21633744 (posted 2026-07-28, after three adversarial review passes; it carries a labelled retraction of an earlier sqrt(2) reading). VERIFICATION CODE. https://github.com/manuflog/contextuality-obstructions
This deposit accompanies the preprint “Exponential relaxation of Fisher path speed on the statistical manifold of learned transition matrices” (April 2026), extending the Grammar Fingerprinting / Fisher-threshold line of work. What is included Fisher–Rao style summaries of learned row-stochastic transition matrices T(N) as a function of data length N for 28 Google Sycamore readout files, on a fixed training grid, for SAX alphabet sizes K ∈ {5, 7, 9} (420 stored transition matrices per K, plus CSV summaries). Fisher path speed along N, model comparison (exponential vs. power-law tail) by AIC, and reporting of τ, A, and A×τ together with the Fisher-trace grammar threshold N* (N-star) on the same N-grid. Exploratory parallel results on LLM entropy time series (same pipeline family; power-law preferred in the reported subset — treated as non-primary relative to the Sycamore scaling analysis). Main quantitative claims (Sycamore) Exponential decay of path speed is preferred on 25–26 / 28 readouts for each tested K (26/28 at K=5; 25/28 at K=7; 25/28 at K=9). Median τ / N* ≈ 3.2 (K=7 narrative in the preprint). A×τ is comparatively stable across hardware topologies within fixed K (detailed at K=7; consistent qualitative pattern at K=5 and K=9); cross-K median scaling is summarized by a power law fit A×τ ≈ 21.5·K^0.57 with small median residuals across the three K values. Theory comparison (non-parametric) The preprint compares the functional form (exponential relaxation and logarithmic threshold dependence) to the macroscopicity / classicality construction of Coppo, Pranzini & Verrucchi (Phys. Rev. A 106, 042208, 2022) and explicitly distinguishes structural analogies from parametric identities (different manifold; Coppo’s A_C×τ_C normalization does not carry over verbatim). Related deposits / continuity Grammar Fingerprinting (Zenodo 10.5281/zenodo.19158088) Fisher information threshold study on Sycamore (10.5281/zenodo.19391582) LLM entropy extension (10.5281/zenodo.19454201) Code & data Public code and committed results: https://github.com/csaplard/QuantumCircuit_Grammar_Research Sycamore raw readouts: Dryad 10.5061/dryad.k6t1rj8 (as in prior Grammar Fingerprinting deposits).
Two working documents that the deposited paper (Draft 4, v1.0; DOI 10.5281/zenodo.22678044; printed title The Asymmetric-Loss Equal-Born Test: a pre-registered search for record-information-dependent optical loss) cites and undertakes to deposit alongside it. They are deposited here as they stood on September 7, 2026, the day Draft 4 was completed, each with a dated deposit note at its head; nothing beneath the note is altered. Supplement 1 — Pre-Bench Closure (September 4, 2026), with postscript layers of September 6 and 7. The arithmetic companion to the paper. Part A runs the no-signalling check on the programme's surviving statement, finds that the normalised form permits superluminal signalling and is excluded, and records the single repair — a loss channel — that leaves the bench prediction numerically unchanged and converts the hypothesis from a nonlinear modification of the Born rule into a linear one. Part B carries the consequences into the protocol: the turnover of −p ln p at p = 1/e and the extended scan that would see it, a fourth signature, the cost of the high-loss points, the total-rate observable, the absorber control with its prediction stated in advance, and the consolidated protocol amendments. Part C makes the structural repairs: locating the branching event, the J-conservation contradiction, and the cost functional, with both candidates carried and the location of the peak left to decide between them. Part D drafts the pre-registration and scores the open tasks. The September-6 layer, headed "Postscript — September 5–6", records the two independent referee passes (one blind, one adversarial), the photon-number-dependent loss map, the derivation of the record criterion put to a third referee instructed to kill it and killed on twelve counts, the pre-registered arms and the correction of a handover error; the addendum of September 7 records the closing of the high-loss row. 17 pages. Supplement 2 — The high-p row: proposal, adversarial pass, and the row as costed (September 7, 2026). The error-budget row for the extended scan (p = 10%, 36.8%, 60% and 70%) that the paper's §9 named as the single item blocking pre-registration of the extended points, kept in the three steps by which it was reached. Appendix A is the first-pass proposal exactly as written for review, errors included. Appendix B is the report of an independent adversarial referee instructed to kill it, verbatim: eight errors and six systematics the first pass had not carried. Appendix C is the row as costed after every finding was re-derived and accepted, with the seven pass criteria written into the pre-registration. Its findings: the reach at the turnover (5σ at λ* ≥ 0.0039, 95% exclusion to 0.0016) stands only under the seven criteria; the bright-phase thermal family has the sign of the predicted anomaly and is bounded by a power-dependence test stated in advance; the far point of the scan moves from 70% to 60%; and the extended scan is research-group metrology, not teaching-laboratory work. 25 pages with its deposit note. The coloured highlights in Supplement 1 are its dated layers (rose, September 6; periwinkle, September 7; sky, the deposit note of September 16, 2026), each explained at its head. The line "Not for deposit" on the cover of Supplement 2 recorded the authors' working practice on September 7 and is superseded by the deposit note above it; the paper's Draft-4 note undertakes to deposit the document. The reconciliation document the paper also cites is the programme's working record, still being expanded, and is available from the authors.