The Unresolved ABC Conjecture and Its Link to Non-Fibonacci-Wieferich Primes — E8 Intelligence Research
Year: 2026
Type: preprint
Abstract: FINDING: The ABC conjecture remains unverified; recent discourse centers on Mochizuki's 500-page proof, Faltings' skepticism, and a new implication linking ABC to non-Fibonacci-Wieferich primes. | MATH: ABC conjecture (Masser-Oesterlé-Szpiro): For any ε > 0, there exists C(ε) such that for coprime integers a + b = c, c < C(ε) · rad(abc)^(1+ε), where rad(n) = ∏_{p|n} p. The arXiv result (1511.01210) shows ABC ⇒ infinitely many primes p where p² ∤ F_p (Fibonacci-Wieferich), with heuristic density ~ log log x / log x. | CONNECTION: No direct geometric ratio (0.382, 0.618, etc.) appears. However, the radical function rad(abc) is a multiplicative lattice norm — its submultiplicativity mirrors root-system height functions in crystallographic lattices (e.g., A_n, D_n). The exponent (1+ε) is a deformation parameter, analogous to the golden-ratio conjugate's role in quasi-crystal inflation (0.618 = 1/φ). | DEPTH: 7 — The conjecture is a deep structural statement about prime distribution, but th Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
Author: Caldin, Andrew Stewart
Language: English
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7212175679
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