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, with a derived causal mechanism for the alpha-helix and an arithmetic consistency for the genetic code. For the alpha-helix: E8 generates a discrete set of six allowed helical axes (Samoylovich-Talis), and the topological stability of minimal surfaces (catenoid bifurcation, h/r ≈ 2.4) uniquely selects the 40/11 axis. Numerical verification: h/r = 2.3994 exactly, with d(Cα-Cα) = 3.77 Å (0.8% vs observed 3.8 Å). For the genetic code: h(E6) = 12 is the only Coxeter number in the chain E8 → E6 → SO(10) → SU(5) → G_SM whose proper divisors are exactly {1,2,3,4,6}, the observed degeneracies. This is an arithmetic consistency: the degeneracy values arise from box/wobble mechanics, and the coincidence div(12) = {1,2,3,4,6} lacks residual statistical support (flag: numerology, ANA_BIO_048-049). Six geometric predictions are verified (errors 0-8.4%), forward predictions are confirmed (0 violations in 12 biological helices, 30/11 axis as internal coiled-coil channel, 14/27 NCBI codes satisfy {1,2,3,4,6}), it is reported that 2 of the 6 E8 axes are not realized (40/7 and 60/7: H-bonds too long for protein helices), and three honest no-gos are reported (telomeres, topological M-loop, B-factor vs 40/11 not replicated). The recurring pattern is: E8 generates discrete options + a non-adjustable external constraint selects a single point.