RM-ABC Conjecture ver4

Abstract

Building upon the complementary foundations of Modulus Expansion and Anomalar Elliptic Geometry, this paper introduces and proves the RM-ABC Conjecture, an independent arithmetic formulation distinct from the classical Masser-Oesterle conjecture. By expressing the radical and residual quotient through closed-form algebraic filters and mapping them onto anomalar phase spaces, the paper establishes an explicit, triple-dependent upper bound driven by residual symmetry. The unified synthesis demonstrates how discrete prime distributions are fundamentally constrained by phase-theoretic scale transitions.