Modular Arithmetic Limits in the Erdős–Straus Conjecture — E8 Intelligence Research

FINDING: Erdős–Straus conjecture (4/n = 1/x + 1/y + 1/z) remains unproven; modular arithmetic mod 3 is a standard tool for classifying residue classes of n, but the search results provide no new classification or proof — only introductory videos and a modular forms paper unrelated to the conjecture. | MATH: Conjecture: ∀n≥1, ∃x,y,z∈ℕ⁺: 4/n = 1/x + 1/y + 1/z. Standard mod 3 reduction: if n ≡ 2 (mod 3), then one denominator must be divisible by 3; if n ≡ 1 (mod 3), a different parity/mod 3 split is needed. No new equations, constants, or ratios extracted from the given sources. | CONNECTION: None found. The Erdős–Straus conjecture has no known direct link to golden ratio, base-60, or crystallographic symmetries. The modular forms paper (arXiv:2512.02348) concerns Tamagawa numbers — unrelated to this conjecture. | DEPTH: 2 — The conjecture is deep (unproven for 75+ years), but the provided findings contain no new mathematical insight, only pedagogical material and an irrelevant paper. The Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com