Closure, Realization, and Reflective Residue: A Machine-Checked Synthesis of NEMS, Infinity Compression, and APS with Bridge Theorems and the Non-Erasure Principle

Three research lines developed in parallel now admit a common structural formalization: they have been unified in a machine-checked Lean 4 development at the abstract architecture level, with zero proof placeholders. The NEMS (No External Model Selection) program proves that load-bearing determinacy cannot be outsourced: if a framework is non-categorical under closure, some internal adjudicator is structurally forced. Infinity Compression proves that canonical bare certification does not exhaust enriched realization: positive non-injective comparison generates residual fibers, section data, and obstruction laws as theorems. The APS (Anchored Pointer System) program proves indexed composition laws for recursive structure. This paper reports the machine-checked synthesis: a common abstract architecture that simultaneously discharges obligations from all three programs, together with bridge theorems and the Non-Erasure Principle.