No-Emulation and Self-Necessitating Adjudication: Paper 15 (C1) of the NEMS Suite

We prove that in any diagonal-capable physical framework—one expressive enough to host the halting problem in its record fragment—no total computable function can emulate the internal adjudication operator (Transputation, ) on all inputs. Formally, we define a choice-point interface identifying states where must actively select among multiple valid continuations, and an adjudication function specifying the valid-selection contract. We then prove the No-Emulation Theorem: any claimed computable emulator for would yield a total computable decider for record-truth on the diagonal fragment, contradicting the diagonal barrier established in Papers 11–12. No total computable function can emulate the internal adjudicator on all inputs; the universe's "chooser" cannot be simulated by a single algorithm. As a corollary, active internal selection (Transputation) is self-necessitating: it cannot be replaced by any static algorithm. This establishes the first theorem in Phase 2 of the NEMS program, bridging the diagonal barrier to the necessity of observer-like adjudication infrastructure (Papers 16–17). The core results are machine-checked in Lean 4 with zero custom axioms, building on the existing nems-lean artifact. 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. No-emulation is conditional on diagonal capability and the diagonal barrier chain (Papers 11–12, artifact nems-lean). Observer-necessity rhetoric here is infrastructural (adjudication interface), not biology. See.