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, \PT) on all inputs. Formally, we define a choice-point interface identifying states where \PT 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 \PT would yield a total computable decider for record-truth \RT 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 .