ABC Conjecture: Unproven Status and Non-Fibonacci-Wieferich Prime Link — E8 Intelligence Research

FINDING: The ABC conjecture remains unproven; verification efforts (LANA project, Faltings' skepticism) and a derived implication for non-Fibonacci-Wieferich primes are the active mathematical content. | MATH: ABC conjecture (Masser–Oesterlé–Szpiro): For any ε > 0, there exists C(ε) such that for coprime positive integers a + b = c, c < C(ε) · rad(abc)^(1+ε), where rad(n) = ∏_{p|n} p. Equivalent to Szpiro's conjecture: for elliptic curves, discriminant ≪ conductor^(6+ε). The arXiv result (1511.01210) proves: ABC ⇒ infinitely many primes p with F_p (Fibonacci) not ≡ 1 mod p² (non-Fibonacci-Wieferich). | CONNECTION: The radical rad(abc) is a product of distinct primes — a lattice-free, multiplicative structure. No direct geometric ratio (0.618, 1.618) appears. However, the Szpiro form links to elliptic curves — tori (genus-1) with complex multiplication — whose j-invariants and period lattices carry hexagonal (A₂ root system) symmetry in the CM case. The ABC conjecture's quality q(a,b,c) Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com