Stage 2: sector data are not a complete information account

For a genuinely supplied completely rational net, the standard global-dimension formula is

where $d_{\lambda }$ are statistical dimensions KLM. If $S$ is in the usual unitary modular normalization with positive vacuum column and $d_{\lambda }=S_{\lambda 0}/S_{00}$, then

This is an algebraic consistency calculation. It does not provide a radiation channel or a horizon area.

In a rigid unitary fusion category, simple dimensions are at least one: the tensor unit occurs in $\lambda \otimes \overline{\lambda }$, and positivity of dimensions gives ${d_{\lambda }}^2\ge 1$. Thus the number of simple labels is at most the global dimension. That count is not a Hilbert-space capacity bound for an unspecified memory.