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arXiv · 2604.03844

The Cross-Domain State Preservation Functor: A Mechanized Theory of Regulatory State Synchronization in Isabelle/HOL

Jinwook Kim
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Abstract

A regulatory action on a tokenized asset, such as a freeze, a seizure, or a confiscation, must take effect on every domain holding it, or on none. We mechanize cross-domain state preservation in Isabelle/HOL as a functor: state machines are objects, structure-preserving synchronization maps are morphisms, and identity, composition and associativity hold as theorems. Four results follow. Safety: a regulatory transition is reflected across all connected domains, with roundtrip preservation, N-domain consistency, per-asset isolation and preserved terminal states, so regulatory finality survives. Liveness: deterministic conflict resolution and starvation freedom under f < n/3 Byzantine nodes, a cardinality-bounded dishonest tag rather than a message-level adversary, and a fair-leader assumption, with n >= 3f+1 shown to make that fairness assumption inhabitable. Convergence: from an arbitrary unlocked configuration, with no initial consistency assumed, synchronization reaches a valid state in boundedly many steps, along a recovery path that neither manufactures nor erases confiscations. Hierarchy: a tower of synchronization-degree functors linked by natural transformations closed under composition, a layer that, to our knowledge, Lochbihler and Maric's ADS_Functor does not develop, with a one-directional degree monotonicity. We couple the functor to that authenticated data structure, instantiated on a recursive Canton transaction-tree model with a declared consensus-scope limit. Eighteen interpretations, an external-domain instance and deletion-sensitive witnesses keep the theorems off the empty class. The model is atomic and its refinement to code is unproven. Ten theory files build without sorry or oops, released as a versioned Isabelle session.

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Jinwook Kim. 2026-04-04. The Cross-Domain State Preservation Functor: A Mechanized Theory of Regulatory State Synchronization in Isabelle/HOL. https://arxiv.org/abs/2604.03844

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