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.
Weil,Sur certains groupes d’op´ erateurs unitaires, Acta Math.111(1964), 143–211 (French)
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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.