Version 4.0. We reformulate the twin prime conjecture as a problem of vertical alignment in a two-dimensional modular lattice. The Relay Coverage Theorem is established as an independent second-order conservation law. The framework is extended to Goldbach's conjecture via a mirror involution, establishing structural homology. We identify the Alignment Gap Axiom---a higher-order proposition independent of ZFC---that precisely separates the twin prime conjecture from the Goldbach conjecture within the relay coverage framework.
Shengxing He (Sun,) studied this question.