Exact Adaptive-Divisor Experiments for the Erdos-Straus Conjecture

Abstract

The Erdos-Straus conjecture asks whether 4/n is a sum of three positive unit fractions for every n >= 2. We present an exact, independently verified computational study of an adaptive-divisor form of the prime case. For a survivor prime p we search for positive integers m,d satisfying d | m^2 and 4m-1 | p+4d, together with a paired offset condition. The released atlas covers p <= 1,000,000, six surviving residue classes modulo 840, A <= 255, and m <= 1,024. It contains 2,370 survivor primes; every one has a bounded adaptive-divisor certificate and a bounded offset certificate. We report exact first-witness frontiers, immutable SHA-256 manifests, independent re-enumeration, and replayable falsifications of tempting universal rules. The divisor bridge and reflection identities are classified as prior-art coordinate forms. The computation does not prove the conjecture: the surviving universal obligation is a pointwise divisor-allocation theorem for every survivor prime. This is an experimental preprint, submitted to Experimental Mathematics; it does not claim a proof of the Erdos-Straus conjecture.