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

Programme status: This record belongs to an active research programme. It is not a finished or final theory. The framework is currently undergoing a systematic audit, together with corrections and improvements prompted by reader feedback. Several significant issues have been identified, and some claims, derivations and interpretations in the current version may be revised, qualified or withdrawn in future versions. Revised versions will be released when this work is complete. Status as of October 2026.

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 .