bras.
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Two challenges prevent a straightforward approach.
First, the extended Hilbert space, a Yetter–Drinfeld module whose maximal trivial submodule is the code space, relies on an involutive antipode—a condition equivalent to the underlying Hopf algebra being semisimple.
Second, topological invariance is proven using projectors assembled from (co)integrals.
Since we do not have these tools at our disposal, we follow a new approach, inspired by homological considerations.
We introduce involutive