Living Document Archive

The rework. The page is now the claims register and nothing else: the object — one classical function, p(L) = L/(2 sinh(L/2)); the chord identity at r = 2; the gap as the complement 1 − √2·ln 2, the shortfall of the argument against its chord in one metric — then the Summary of Claims (kind · scope · status; no numbered levels), the published record on two shelves with no paper numbers and a read now line for each paper, what connects, the corrections log, the history. Readings taken through the Binary Tower live with the instrument. The neutral forms √2·ln(2) and 1 − √2·ln(2) are printed alone, the corpus symbols named once. The complement 1 − √2·ln 2 — the paper on the object itself, its place on the line, the cells and the saddle — stands on the Foundational shelf; the synthesis, One coordinate up, reads the thirteen papers on that line, and the read now column is drawn from it. Pre-update snapshot preserved below.

Two-paper publication day — and the Lock Atlas goes live. K_AUD = √2 · ln(2): The Crossing Zone Hinge — Three Thresholds and the Identity 1/(2 ln 2) − 1/√2 = G_AUD/(2 ln 2) published (DOI 10.17605/OSF.IO/F7PCX) — three exactly-positioned thresholds in the Binary Tower’s [35, 37] interval, bound by exact identities, after a seven-round review chain across five AI architectures. Gap Scaling Across Domains: The 400/11 Formula updated to v1.0.4 (error-bound wording erratum, three fixes, no mathematical content changed; source filenames neutralized to Gap_Scaling_Formula.txt/.pdf; DOI unchanged). The Lock Atlas — the framework’s identities as a living map, 87 released locks with a reader/map two-arrival design — went live the same morning. The Living Document now lists The Crossing Zone Hinge with live links, OSF code, and Published date; The 400/11 Formula’s row carries the v1.0.4 update note. Pre-update snapshot (v1.5 state, 10 July) preserved below.

New paper added: 1, 7, 124, 4318, … — Integer Mellin Moments of the Dome tanh(x)/cosh(2x) (DOI 10.17605/OSF.IO/WVD3G) — the standalone number-theory paper on the dome's even-moment integer sequence. Integrality proved for all n; the full 3×3×3 weight-family cube classified (unique integer triple, double-swept); the sequence verified absent from OEIS prior to publication (novelty check archived in the paper folder). First framework paper whose title is its own sequence. The Living Document now lists Integer Mellin Moments of the Dome with live links, OSF code, and Published date. Pre-update snapshot (v1.4 state) preserved below.

Two-paper publication day. Saturation Constants of the Exact-Approximation Method added to the framework following OSF publication on 2026-06-02 (DOI 10.17605/OSF.IO/6QZRB) and same-day GitHub repo upload — the first framework paper to carry its own DOI on page 1 of the .txt and .pdf, establishing the new standard for future papers. The η Corridor in 3D Wilson–Fisher Critical Phenomena — Empirical Observation and its Verification Companion published the same day under a single shared OSF project (DOI 10.17605/OSF.IO/PD73B) — the framework’s first multi-file deposit, with main paper and Companion sharing one DOI and cited together. Both papers carry their own DOI on page 1. The Living Document now lists both with the live links, OSF codes, and Published date 2026-06-02. Pre-update snapshot (v1.3 state) preserved below.

Cross-paper link architecture overhaul. Five of the early papers had paper-to-paper file URLs (which would break under any future filename change) replaced with a durable three-anchor block: OSF main project, About page, and Direct Documents download index. Paper-specific DOIs preserved (DOIs are stable). Per-paper Update entries added/extended on the Living Document. OSF deep-link IDs refreshed across all hub HTMLs after each push. No mathematical content changed in any paper. Same-day pre-link-cleanup state archived as the v1.2 snapshot below.

Evidence-level unification. The Living Document now uses the three-level evidence classification from the Methodology page: Level 1 — Exact [Theorem], Level 2 — Empirical [Observation], Level 3 — Conjectural [Conjecture]. The existing Verified / Conjectural / Open status badges are retained as secondary labels that map onto the primary levels. A new “Level” column is added to the Summary of Claims table. The Verification Protocol section now references all three levels by name.

Three-threshold refinement of the 35–37 zone. The earlier single “Landauer crossing” framing is replaced with three distinct thresholds: the Landauer crossing at n·G = ln 2 (n ≈ 35.11), the geometric-damping threshold at n·G = 1/√2 (n ≈ 35.82), and the Shannon bound at n·G = 1/(2 ln 2) (n ≈ 36.54). The identity 1/(2 ln 2) − 1/√2 = G/(2 ln 2) is retitled as the “√2-to-Shannon gap identity”. All OSF files refreshed to match.