The E8 lattice and the geometry of biopolymers: verified conjecture with causal mechanism

Abstract

The E8–Biopolymer conjecture is presented in its restricted-scope formulation: the E8 lattice, which in the TTOE framework generates the Standard Model chain E8 → E6 → SO(10) → SU(5) → G_SM, also constrains the geometry of topologically stable biopolymeric structures. For the alpha-helix, E8 generates a discrete set of six allowed helical axes (Samoylovich–Talis, peer-reviewed), and the topological stability of minimal surfaces (catenoid bifurcation, h/a = 2x* = 2.39936, with x* = 1.19968 the root of coth(x) = x) selects the 40/11 axis at the shared ratio a/d = 2.5125, giving d(Cα–Cα) = 3.77 Å (0.8% vs observed). For the genetic code, h(E6) = 12 is the only Coxeter number of the chain whose proper divisors are exactly the observed degeneracies {1,2,3,4,6} — reported as an arithmetic consistency with an explicit numerology flag (a box/wobble-informed null model shows ~60% of null codes respect the set). Six geometric predictions are verified (errors 0–3.6%), plus a beta-sheet twist prediction at 8.4%; the 30/11 axis is confirmed as the internal coiled-coil channel; two of the six E8 axes (40/7, 60/7) are not realized in proteins (H-bonds too long); and three honest no-gos are reported in full (telomeres refuted, topological M-loop refuted, B-factor prediction not replicated — including the autopsy of the v1 false positive). Version 3 — correction notice. The headline change: a/d = 2.5125 is FITTED — it is exactly the value that puts the 40/11 axis on the catenoid target, and each of the six axes admits its own such value — so the "derived, not fitted" claim of earlier versions is withdrawn and the alpha-helix mechanism is reclassified Conditional (uniqueness holds only with a/d held fixed across axes). Also corrected: 2.39936 is not the root of coth(x) = x (that root is 1.19968; 2.39936 = 2x* refers to the neck radius, and the classical ring-radius limit is h/R = 1.32549); h/r = 2.399 with difference 0.00004 (three inconsistent values harmonized); the 12/5 coincidence error is 0.027%; the abstract's error range no longer mixes the six verified predictions (0–3.6%) with the separate beta-sheet twist (8.4%); the NCBI count is harmonized (26 variants / 27 tables); and the claim that the degeneracy multiset is "derived from the E8 chain" is retracted (A5 orbit sizes cannot produce degeneracies 2, 3, 4).