The Drift Lemma and the Limits of Self-Measurement in Bounded Systems

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 It has been superseded by the identity-persistence stack: https://zenodo.org/records/20127331.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 Any system capable of discovery, judgment, or alignment operates under structural and energetic constraints. This paper proves a general limit: a bounded system governed by a scalar coherence invariant cannot internally verify its own drift or alignment state with certainty. The apparatus required for measurement is itself subject to the same governing constraints, rendering self-certification non-convergent. Alignment can be inferred only through external phase-lock and coherence persistence, not introspection. This result is not skeptical but structural. It establishes external reference as a lawful necessity rather than an epistemic weakness, completing the closure of alignment-based accounts of discovery, agency, and stability.