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.
Gildea,Algebraic phase theory ii: The frobenius–heisenberg phase and boundary rigidity, 2026, Available at
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Introduces boundary calculus and rigidity islands to stratify deformation behavior by boundary depth and failure type in algebraic phase structures.
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 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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Introduces boundary calculus and rigidity islands to stratify deformation behavior by boundary depth and failure type in algebraic phase structures.
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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.