The Dense Divisor Local Tower and Face-Residue Cancellation: A Downstream Companion to the AM-TRD Non-Local Theorem

This companion preprint develops the application-specific local analysis associated with the dense divisor model underlying the AM-TRD non-local theorem. The paper is deliberately separated from the autonomous AM-TRD result and has a different epistemic status. Whereas the non-local sector is supplied by the AM-TRD theorem, the present work studies the remaining dense-divisor local tower and isolates the downstream obstruction identified as Face-Residue Cancellation. Working with the local expansion of the dense divisor model, the manuscript analyzes the arithmetic residue structure generated after canonical local-conductor extraction and develops the corresponding tower decomposition and cancellation mechanisms. The purpose of the paper is not to reprove the AM-TRD theorem, nor to claim that the local range is automatically negligible. Instead, it makes the residual local problem explicit and separates the terms that require genuine application-specific cancellation from those already controlled by the non-local theorem. Nothing in this companion, either alone or together with AM-TRD, is claimed to prove binary Goldbach unless the remaining Face-Residue Cancellation step and all associated local terms are independently closed.