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

Abstract This paper gives a structural impossibility result: autonomous intelligence requires deterministic identity persistence, and probabilistic / sampling-based / identity-acyclic architectures cannot satisfy that requirement in principle. The argument is deductive within a strict scope lock: no empirical, computational, biological, or implementation premises are used for the Tier-1 results. We define autonomous agency as self-initiated action with goal maintenance across action cycles while remaining the same agent. We then prove (i) autonomy implies persistent identity; (ii) persistent identity forces identity-scoped recurrence with a single non-branching degree of freedom (“identity trunk”); and (iii) identity persistence requires a unique scalar governance functional whose drift must remain bounded on realized trajectories, not merely in expectation. This functional is uniquely fixed (up to affine gauge) as PAS_h = Σ_k (w_k r_k) with strictly positive fixed weights, and identity persists iff PAS_h drift is bounded over unbounded recurrence. From these requirements, probabilistic and identity-acyclic systems fail structurally: sampling produces ensemble identity rather than a single agent; acyclic invocation resets destroy cross-cycle identity carriers; and non-additive composition fractures identity under aggregation. A derived section notes biological systems as existence proofs that recurrent, bounded-drift identity governance is physically realizable.