The Unproven ABC Conjecture and Its Link to Wall's Prime Conjecture — E8 Intelligence Research

Abstract

FINDING: The ABC conjecture (Masser-Oesterlé-Szpiro) remains unverified; Mochizuki's 500-page proof is contested, with Faltings skeptical; recent work links it to Wall's conjecture on non-Fibonacci-Wieferich primes. | MATH: ABC conjecture: For any ε>0, there exists C(ε) such that for coprime a+b=c, max(|a|,|b|,|c|) < C(ε)·rad(abc)^(1+ε), where rad(n)=∏_{p|n} p. Wall's conjecture link: implies infinitely many primes p where F_p ≡ ±1 (mod p²) (non-Fibonacci-Wieferich). | CONNECTION: No direct geometric ratio (0.382, 0.618, 0.786, 1.618, 2.618) or base-60 appears. However, the radical function rad(abc) is a multiplicative lattice structure — the prime support forms a finite subset of the free abelian monoid on primes, a root-system-like lattice (ℕ^π). The conjecture bounds the "height" (log max) by (1+ε) times the "weight" (log rad) — a Diophantine analogue of a lattice norm inequality. | DEPTH: 7 — Profound in number theory (unifies Fermat's Last Theorem, Catalan, etc.), but no direct ha Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com