Formal proof demonstrates that distinct instantiations of systems show zero behavioral identity, highlighting implications for classical and quantum uniqueness.
Formal proof of the Law of Identity Divergence: for any two distinct instantiations of an open stochastic system with independent private perturbations, persistent behavioral identity has probability zero. This result complements quantum uniqueness (Sych & Leuchs, 2015) by establishing that classical open systems also cannot maintain identical behavior. Includes Lean 4 mechanized proof and empirical validation via NCD-based distinguishability scoring.
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Mohamed Feras Elghandour (2026) studied this question.
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