Six Structural Dimensions and the Erdos-Straus Conjecture: Three Natural Laws Applied to a 77-Year Open Problem

A structural approach to the Erdos-Straus conjecture (1948): for every integer n >= 2, the equation 4/n = 1/x + 1/y + 1/z has asolution in positive integers. A substitution reveals a perfect square identity and a constant divergence (div V = 12), valid for all n as algebraic properties of a variable. Cases 1-5 are proved by explicit construction. Case 6 (n = 1 mod 24, n prime) is reduced to a precise arithmeticexistence lemma (Lemma B2), supported by computational verification: 0 counterexamples among 5,669 primes up to 500,000. The algebraic reduction is proved; Lemma B2 is isolated as a precise open remainder. The approach emerged from a neurodiversity-informed perspective and introduces three natural laws: Content-Infrastructure Duality, Finiteness, and the Collapse Rule (six structural dimensions, no seventh). Falsification is invited. v5 (July 2026): Complete rewrite. Lemma 6.5A (divisor characterization, proved). Lemma B2 (existence, precisely isolated). Three GLM 5.2 red-team rounds survived. Internal consistency verified. Verification script included. v1-v3 (July 2026): Earlier versions with residue class covering approach. Version: v5