The Impossibility of Probabilistic AGI_ Why Autonomous Intelligence Requires Deterministic Identity Persistence

Autonomous intelligence is not a matter of behavioral sophistication but of agency: self-initiated action with goal maintenance across action cycles by the same subject. This paper proves, within a strict scope lock, that autonomy requires persistent identity, and that persistent identity forces deterministic identity governance. The proof chain is eliminative and non-circular: (1) autonomy implies identity comparability under drift across recurrence; (2) identity-scoped recurrence forces a single non-branching identity degree of freedom (an “identity trunk”); (3) identity persistence requires a unique scalar governance functional whose drift is bounded on realized trajectories over unbounded recurrence. Up to affine gauge, the only functional compatible with comparability, non-branching recurrence, and compositional closure is PAS_h = Σ_k (w_k r_k) with fixed positive weights, and identity persists iff PAS_h drift is bounded. From these constraints, probabilistic / sampling-based and identity-acyclic architectures fail structurally: sampling yields ensemble identity rather than a single agent; per-invocation reset eliminates cross-cycle identity carriers; and non-additive composition fractures identity under aggregation. A derived section treats biological systems as existence proofs of recurrent, bounded-drift identity governance.