Transputation versus Computation: { Internal Adjudication Beyond Total-Effective Rule Application in Closed Physical Theories}

We distinguish computation—effective rule application reducible to Turing computation—from transputation—a law-governed internal adjudication required in perfectly self-contained (PSC) theories when observational records do not uniquely determine realizations. We formalize the distinction using the NEMS (No External Model Selection) framework: in record-non-categorical settings, PSC forces an internal selector (adjudicator) selecting canonical representatives of observational world-types. Under diagonal capability, formalized by an Arithmetic Self-Reference (ASR) structure, record-truth on the ASR fragment is not computably decidable, and therefore no internal adjudicator can be total-effective on that fragment. These forcing and diagonal results are kernel-verified in Lean 4 with zero custom axioms, reducing the diagonal barrier to Mathlib's halting undecidability theorem. We then present MFRR's mechanistic proposal for transputation: coherence-driven minimization of a dissonance functional (DSAC/PR-0 style dynamics), which implements internal adjudication as a physical relaxation process rather than a total algorithmic decider. We conclude with a taxonomy of where computation suffices, where transputation is forced, and how transputation may be instantiated in realistic physical systems with stable macroscopic records and universal computation. Trust boundary. Forcing/diagonal lemmas cited as machine-checked route through Paper 8 and nems-lean ; MFRR mechanistic content (DSAC/PR-0) is illustrative physics narrative unless separately formalized. See .