Elimination of Probabilistic Ontology Under Deterministic Causation

Abstract This paper records a structural result: under the CODES / SO2 axioms, probability cannot be ontological. If evolution from the full state is deterministic—i.e., a function—then genuine stochastic branching from identical states is logically excluded. Probability survives only as a measurement, compression, or ignorance language over a deterministic, PAS_h–ordered substrate. This elimination is not an additional hypothesis or interpretive stance; it is a direct corollary of deterministic causation plus the choice of full state space.