Documents
Direct access to all published Gap Geometry documents. Plain text, PDF, and archival links for each.
Foundational
Two shelves. Foundational holds the first paper
— the identification of the ceiling and the gap. The observational record holds the
campaigns that followed and the exact computes they produced, each paper standing as printed,
corrections carried as dated notices. No shelf implies rank: observations are how this framework
found everything it found. The text, PDF and raw links point at the September 2026 reprints in the repository’s papers/ folder; an OSF file link still grey belongs to a paper whose re-upload is waiting on OSF’s queue. The DOI and the OSF project link are each paper’s stable addresses.
The Coherence Ceiling and the Geometric Singularity of Binary
The first identification — §4’s 0.7071 − 0.6931 is the defect; the founding computation.
Published: 2026-01-21 · Last update: 2026-09-16 (the September 2026 reprint; before it 2026-05-05) · OSF: 5vz2r
The complement 1 − √2·ln 2
The paper on the object itself — one classical function, the chord identity at r = 2, the gap as its shortfall in one metric; the map of the line.
Published: 2026-09-15
The Observational Record
The Hodgson–Kerckhoff Closed Form and the Framework
The closed form identified in the published literature — 1/S = √2·ln 2, four lines.
Published: 2026-04-03 · Last update: 2026-09-16 (the September 2026 reprint; before it 2026-04-13) · OSF: jbrhq
Geometric Constants from H4 — Mathematical Framework v2.0.2
The constructions; §3.4’s restraint — no origin privileged — aged best.
Published: 2026-01-24 · Last update: 2026-09-16 (the September 2026 reprint; before it 2026-05-05 (v2.0.2 — §1.1 attribution clarification crediting Gemini for KAUD closed-form identification, gap articulation, and naming; §6.3/§7.1/§8.3 typography correction)) · OSF: sjbe9
Complete Framework v3.3.1
The framework assembled; corrected itself twice, and the corrections were right.
Published: 2026-01-25 · Last update: 2026-09-16 (the September 2026 reprint; before it 2026-05-05 (v3.3.1 — typography correction in §6.3 φ-scaling ratio test; top banner UPDATE NOTICE added)) · OSF: qh5s2
Saturation Constants of the Exact-Approximation Method
Contains eq. (3.4): p(L) derived for arbitrary L — the framework’s own derivation of the object.
Published: 2026-06-02 · OSF: 6qzrb
1, 7, 124, 4318, … — Integer Mellin Moments of the Dome tanh(x)/cosh(2x)
The dome’s integers, proved for all n — the paper that taught us to build visuals and ask better questions.
Published: 2026-06-12 · OSF: wvd3g
KAUD = √2 · ln(2): The Crossing Zone Hinge — Three Thresholds and the Identity 1/(2 ln 2) − 1/√2 = GAUD/(2 ln 2)
The tower used exactly — solutions never rounded; the corpus standard.
Published: 2026-07-15 · OSF: f7pcx
Gap Scaling Across Domains: The 400/11 Formula
Where the control test was invented; its interpretive erratum carried openly.
Published: 2026-02-04 · Last update: 2026-09-16 (the September 2026 reprint; before it 2026-07-15 (v1.0.4 — error-bound wording erratum, three fixes; filenames neutralized)) · OSF: c4gk5
The Boundary Information Invariant of Quadratic Systems
The boundary campaign; precision now stated at the data’s own resolution.
Published: 2026-03-18 · Last update: 2026-09-16 (the September 2026 reprint; before it 2026-04-13) · OSF: e72h8
Cross-Domain Signatures of √2 × ln(2)
The widest scan — and the second Hodgson–Kerckhoff appearance was found here.
Published: 2026-03-26 · Last update: 2026-09-16 (the September 2026 reprint; before it 2026-05-05) · OSF: ra3uq
The 50 Hinge
The count campaign; §12’s pre-registered falsifiers fired, and the correction leads.
Published: 2026-04-03 · Last update: 2026-09-16 (the September 2026 reprint; before it 2026-04-13) · OSF: fbd9a
Binary Scaling of ρ
Every value correct; the prime-hierarchy reading withdrawn; ord11(2) = 10 stands.
Published: 2026-04-03 · Last update: 2026-09-16 (the September 2026 reprint; before it 2026-04-13) · OSF: wtu4j
The η Corridor in 3D Wilson–Fisher Critical Phenomena — Empirical Observation
The corridor observation, strengthened twice — and §11.1: the seed of the identification, written in June.
Published: 2026-06-02 · OSF: pd73b
Verification Companion: mpmath verification of the dome identities
DOI: 10.17605/OSF.IO/PD73B (shared with The η Corridor above — single OSF project)
Published: 2026-06-02 · OSF: pd73b
One coordinate up — the thirteen papers read on the line through r = 2 (note)
The synthesis — the thirteen papers above, one line each, in the identified coordinate; the reading-update notice on every paper points here.
Published: 2026-09-15
Standalone
A Closed Form for the Hodgson–Kerckhoff Tube-Packing Coefficient
The identity alone, nothing attached — the citable form.
DOI: 10.17605/OSF.IO/2EXPN — Separate repository: GitHub
Published: 2026-04-03 · Last update: 2026-05-04 (§3 ellipse-area correction; §3.1 added — second appearance of √2·ln(2) in HK 2007 c(R)) · OSF: 2expn