The excitation-detector principle is equivalent to perfectness of the quadratic form on the excitation module, which is necessary and conjectured sufficient for the compactified 2D theory to be modular.
Throughout, by a ring R, we continue to mean an associative, commutative and unital ring
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Excitation-detector principle and the algebraic theory of planon-only abelian fracton orders
The excitation-detector principle is equivalent to perfectness of the quadratic form on the excitation module, which is necessary and conjectured sufficient for the compactified 2D theory to be modular.