Semantic Identity Drift in Decision Systems under Formal Certification

Abstract

Modern decision systems may satisfy formal correctness criteria while nonetheless undergoing a gradual transformation of their internal semantic identity. This paper isolates and formalizes this phenomenon as semantic identity drift. We distinguish between two orthogonal aspects: (i) epistemic certifiability, expressed by the binary predicate Z_cert(L, M), and (ii) semantic drift, described by the time-dependent operator D(t) : L → L_t acting on problem structures. For a given pair (L, M), it may hold that Z_cert(L, M) = 1, indicating the existence of valid witnesses within the model system. Independently, the semantic structure L may undergo nontrivial transformation under D(t), which is not addressed by output correctness or by certification predicates. We argue that formal correctness, optimization objectives, and telemetry are insufficient to constrain semantic identity drift, because drift operates at the level of internal meaning evolution rather than observable behavior. Accordingly, semantic stability is not entailed by epistemic success conditions. The paper therefore establishes a strict separation between operator-based drift analysis and predicate-based certification, and motivates audit methodologies that explicitly address semantic identity preservation over time.