From NEMS to MFRR: { A Machine-Checked Bridge Between Semantic Closure and Reflexive Reality}

We construct a formal, machine-checked bridge between the NEMS (No External Model Selection) classification framework and the MFRR (Mathematical Foundations of Reflexive Reality) program. We show that MFRR's Perfect Self-Containment (PSC) condition, combined with record-divergent choice points, forces the existence of an internal adjudication principle (Transputation / PT) as a theorem of the NEMS classification spine. Within the explicit premise bundle and the formalized NEMS/ASR interface, the central forcing result is machine-checked and leaves no unlisted formal escape route. This paper upgrades the forcing theorem to a machine-checked theorem conditional on the stated bridge from PSC and record-divergent choice to the NEMS interface. Under diagonal capability—formalized via an Arithmetic Self-Reference (ASR) structure that bridges record-truth to the halting problem—record-truth is provably not computably decidable, constraining any selector to be non-total-effective. The diagonal barrier is proved via reduction to Mathlib's machine-checked halting undecidability theorem, yielding a library with zero custom axioms. All results compile in Lean 4 (v4.28.0, Mathlib 4.28.0, 8051 jobs, zero sorry). This bridge upgrades MFRR's central claim—that a closed universe must contain a lawful, non-algorithmic internal adjudicator—from a physical argument to a fully machine-checked theorem with no escape hatches. The formalization makes every assumption explicit and auditable, and provides a reusable template for evaluating any candidate theory of everything against the NEMS sieve. This overview presents the core NEMS theorem engine and selected applications; stronger domain-specific derivation and ontological synthesis claims belong to separate release surfaces with their own premise bundles and formal artifacts. Trust boundary. Machine-checked results are conditional on the explicit NEMS/ASR interface and PSC bundle used in the formalization; companion narrative for physical premise import is Paper 9. Pinned artifact: nems-lean . See and .