Randomness as Perceived Non-Uniqueness: A Structural Interpretation of Indeterminacy in Non-Lipschitz Systems

This paper proposes that perceived randomness in complex systems is not ontological indeterminacy, but an epistemic projection of trajectory multiplicity () in non-Lipschitz regimes. We demonstrate that when uniqueness conditions fail, the observer's inability to resolve multiple admissible solutions induces a perception of stochasticity. Utilizing the Theorem of Axiomatic Necessity (TNA) framework, we formalize this phenomenon through the interaction of internal dynamics (N₀), admissibility boundaries (_), and irreducible selectors (N₁). The analysis extends the TNA model to Fokker-Planck probability flows and quantum wavefunction collapse, arguing that "collapse" is the structural requirement for uniqueness in systems that cannot close themselves. This interpretation provides a unified lens for understanding indeterminacy in generative AI, dynamical systems, and quantum measurement.