Box Theory: A Structural Reduction of the Twin Prime Conjecture

Box Theory is an axiomatic framework for studying infinite periodic constructions, realization rules, and tail-level process constraints. This first public release presents two routes to the Twin Prime Conjecture inside the theory: a Canonical Branch and a Thinning Branch. The Canonical Branch isolates the prime-power obstruction and makes explicit the imported pressure required to remove it. The Thinning Branch neutralizes prime powers internally and reduces the remaining obstacle to a process-level tail constraint, formalized as Axiom 3 under trace separation. The principal result of v1.0 is therefore a structural reduction: within Box Theory, the Twin Prime Conjecture follows for the standard integer model provided the integers satisfy Axiom 3 under trace separation. This release includes the production manuscript (PDF) and source files.