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

Supersession Note — May 2026 This CODES-era work is an exploratory predecessor and is no longer the canonical statement of the author’s program. It has been superseded by the identity-persistence stack: https://zenodo.org/records/20127331. Claims in this record concerning replacement of probability, unrestricted universality, ontology, physics, intelligence, biology, governance, or reality should be read as developmental framing, not as the current formal claim. The current claim is restricted to identity persistence under transformation within explicit admissibility constraints. 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.