Quantum Identity: La Profilée and the Structural Conditions of Persistence in Quantum Systems

Classical theories of identity presuppose state distinguishability over time. Quantum mechanics appears to challenge this. The present paper establishes that LP’s structural persistence condition IR = R / (F · I · C) ≤ 1 is compatible with and illuminated by quantum mechanics. LP requires distinguishability of states, not constituents — satisfied in quantum mechanics at the system level. Superposition is a regime of structural indeterminacy (IR > 1 at the outcome level). Measurement is IR-reduction through environmental coupling. v3 strengthens Section 4a: the proof chain LP identity preservation → state-space isometry → Wigner symmetry → unitarity replaces the weaker injective-CPTP argument of v2. Identity is not merely compatible with unitary evolution — it structurally requires it.