A necessary and sufficient structural criterion for nondegenerate finite-depth Algebraic Phase Theory consists of nondegenerate phase duality, compatible admissible dynamics, and finite or terminating defect propagation.
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Algebraic phases satisfying APT axioms are reconstructible up to intrinsic equivalence from filtered representation categories plus boundary structure, with additional results on rigidity, finite generation, and boundary detectability.
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A Structural Criterion for the Applicability of Algebraic Phase Theory
A necessary and sufficient structural criterion for nondegenerate finite-depth Algebraic Phase Theory consists of nondegenerate phase duality, compatible admissible dynamics, and finite or terminating defect propagation.
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Duality, Reconstruction, and Structural Toolkit Theorems in Algebraic Phase Theory
Algebraic phases satisfying APT axioms are reconstructible up to intrinsic equivalence from filtered representation categories plus boundary structure, with additional results on rigidity, finite generation, and boundary detectability.