The Read-Once Factorial-Divisibility Conjecture: Algebraic Proofs Through Six Inputs

Abstract

We formulate the division-free read-once factorial-divisibility conjecture for pairwise distinct integers. Using congruence arguments, signed residue classes, parity decompositions, and disjoint block constructions, we prove the conjecture algebraically for all input sizes 1≤n≤6. We also establish stronger parity-restricted divisibility theorems and record guaranteed-modulus frontiers for the small cases. Computational procedures are used only for independent consistency checks and not as substitutes for mathematical proof.