Emergent Geometry in Number Theory Proving the 1-C-D Conjecture

The 1-Ceiling Deformation (1-C-D) Conjecture is a fundamental inequality in number theory relating positive integers in the equation a + b = c to the radical of their product abc in the curved regime where c exceeds the radical. Traditional number-theoretic approaches treat such constraints as analytical properties imposed externally. In this paper, we present a novel proof of the conjecture within the framework of Wave-Point Geometry, wherein geometric structure is not assumed in advance but emerges directly from phase transport on discrete relational systems. By mapping the relation onto a minimal two-node Wave-Point Space, the numerical discrepancy between c and the radical is naturally encoded as phase inconsistency, generating a positive cycle curvature. Following the fundamental principle that curvature generates geometric scaling, we derive the 1-C-D inequality directly from transport consistency constraints. Our results demonstrate that Diophantine bounds can be naturally understood as emergent manifestations of discrete phase geometry.