A tag does not test the S-matrix

The entries of $\mathcal{L},S,\mu ,N,\mathcal{B}$ do not enter (eq:fidelityinterval)–(eq:errorinterval). Their role is to organize declared experimental labels. No estimate in this section validates those categorical data, representation membership, sector transport, or a conformal-net calibration.

A failure to distinguish two labels is also not evidence that their sectors are equal: identical experimental channels produce identical validation laws even for different tags.