ABC Conjecture Verification Links to Non-Fibonacci-Wieferich Primes — E8 Intelligence Research

Abstract

FINDING: ABC conjecture remains unverified; Mochizuki's proof disputed; LANA project attempts formal verification; new heuristic links ABC to non-Fibonacci-Wieferich primes. | MATH: ABC conjecture: For any ε > 0, there exist only finitely many coprime triples (a, b, c) with a + b = c such that c > rad(abc)^(1+ε), where rad(n) = product of distinct primes dividing n. Wall's conjecture: primes p where F_{p - (p/5)} ≡ 0 mod p^2 (Wieferich-like for Fibonacci). Heuristic: number of non-Fibonacci-Wieferich primes below X ~ c * log log X. | CONNECTION: No direct geometric ratio or crystallographic symmetry found. The heuristic's logarithmic form echoes natural scaling laws but not golden ratio or base-60. | DEPTH: 6 — The ABC conjecture is a deep structural statement about prime factorization and addition, with implications for Diophantine geometry (e.g., Fermat's Last Theorem, Mordell's conjecture). However, the proof remains unaccepted, and the heuristic is speculative. No new constants or Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com