The Computational Limits of AI Provenance: From Atomic Indistinguishability to Logical Undecidability

Provenance detection aims to determine whether digital artefacts—texts, images, or other media—are human- or machine-generated. This paper argues that provenance attribution faces structural limits that are logical rather than empirical. We present a four-layer impossibility hierarchy:

• Representational Layer: Digital artefacts, modelled as bitstrings, are individuated extensionally and do not intrinsically encode their causal origin.
• Computational Layer: We prove that perfect provenance detection is undecidable by reducing a general origin-membership problem to the Halting Problem.
• Adversarial Layer: Using recursion-theoretic diagonalization, we construct a generator that defeats any computable detector.
• Epistemic Layer: We analyse inference under extensional indistinguishability, arguing that artefact-based evidence is logically underdetermined in a universal generation environment.

These results demonstrate that provenance uncertainty is irreducible at the computational level for any detector that operates solely on digital artefacts. The paper reframes the AI detection problem from one of engineering optimization to one of computability theory and digital ontology.