A Formal Theory of Transputation Closure, Internal Adjudication, and Non-Algorithmic Continuation Selection

In closed, record-bearing, non-categorical, diagonal-capable frameworks, ordinary total-effective algorithmic computation is insufficient to underwrite continuation-selection. This paper defines transputation rigorously as the internal adjudicative layer forced under such conditions. We establish that transputation defines a distinct adjudicative computational class, grounded in a structurally forced internal role: in the diagonal-capable regime, continuation-selection cannot be reduced to ordinary total-effective algorithmic rule application on the relevant self-referential fragment. The formal result establishes the necessity of an internal adjudicative layer of the specified type; 'transputation' names that formally characterized role, not an unearned extra mechanism. We situate it within the theory of computation. Under explicit closure (PSC) and record-divergent choice, an internal adjudicator is required; in diagonal-capable settings, no total-effective decider can replace it on the relevant self-referential fragment. A companion paper (Paper 77) presents DSAC as a candidate realization family. All flagship theorems are machine-checked (transputation-lean). 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. DSAC realization claims are Paper 77; this paper is the abstract forcing layer in transputation-lean . See .