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.
Recall that if ( S, b) is a p-theory of fusion order n, then S is a finitely generated R-module where R = Zn[t±]
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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.