External Validation of a Positive-Closure Proof Architecture: A Multi-Tranche Survey

Transferability paper. This manuscript establishes that the positive-closure architecture is exportable to ordinary mathematics outside the flagship Infinity Compression modules; it is not the program map and not the venue for theorem-level leverage in algebra, topology, or arithmetic---those roles belong to the companion general-method papers cited below. The Infinity Compression ({}) formalization develops a layered positive-closure proof architecture: collapse to a bare certificate, a typed forgetful map, fiber structure over that certificate, and, where appropriate, canonical witnesses or sections. A natural methodological concern is that this architecture may be endogenous to the flagship NEMS-style case rather than a reusable proof pattern. This paper presents a consolidated machi