Irreducible Agency (Non-Algorithmic Adjudication as a Physical Requirement) Paper 22 (T5) of the NEMS Suite

We formalize the theorem that in a Perfectly Self-Contained (PSC) universe with computers, the internal adjudicator network cannot operate via a total computable function. By merging the Diagonal Barrier (Papers 11–16) with Adjudicator Necessity (Paper 17) and Execution Necessity (Paper 19), we prove that a "dead" algorithmic law cannot reach a determinate state. The "law of physics" at the choice-resolution layer is strictly non-algorithmic. This establishes irreducible adjudication at the choice-resolution layer: internal record determinacy in a diagonal-capable PSC universe requires a non-total-effective adjudication mechanism. Observer-like subsystems are interpreted as the physical implementation of this mechanism within a record-stabilizing network. All definitions and conditional theorems are formalized and machine-checked in Lean 4. Trust boundary. Claims are conditional on the adjudicator-network and diagonal-barrier premises imported from earlier suite papers; the "non-algorithmic" layer is a precise non-total-effectivity statement in the formalized sense, not a blanket philosophy of mind. Cross-suite checks are in nems-lean . See .