The η Corridor in 3D Wilson-Fisher Critical Phenomena Empirical Observation

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