Identity Continuity: Behavioural Invariants, Supervisory Closure, and the Geometry of Admissible Execution

July 1, 2026Open Access

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Key Points

The aim is to establish a theory of identity continuity based on behavioural invariants and their stability under transformations.
Developed a unified axiomatic theory focusing on perturbation-stable behavioural invariants.
Defined a mathematical structure involving behavioural primitives and supervisory cycle.
Illustrated concepts with a 20-bus microgrid model exhibiting admissibility and identity continuity.
Identity continuity is formalised through the quotient of behavioural states preserved under transitions.
Supervisory closure is identified as a law governing admissible composition in transformations.
Operational and categorical realizations validate the theoretical framework.

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Unified theory demonstrates identity continuity in computational systems, suggesting constraints on transformations.

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Thomas Filsecker (2026) studied this question.

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