What question did this study set out to answer?

The objective is to prove that two distinct instances of a stochastic system cannot maintain identical behavior.

February 14, 2026Open Access

The Inevitability of Uniqueness

Key Points

The objective is to prove that two distinct instances of a stochastic system cannot maintain identical behavior.
Develop formal proof of the Law of Identity Divergence.
Utilize Lean 4 for mechanized proof verification.
Empirically validate findings using NCD-based distinguishability scoring.
Establish that distinct instantiations have a probability of zero for maintaining behavioral identity.
Complement theoretical insights with empirical validation of results.

Abstract

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.

The Inevitability of Uniqueness

Key Points

Abstract

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