What geometric cut counters can now mean

Suppose an identified link has the following operational service: after legal activation, it transmits one classical bit once in its prepared orientation and is then deleted. A latent link activates at most once. An initially active link also has at most one unspent service. No such link transfers a qubit or supplies entanglement.

Let ${\sigma }_{A\mid B}$ count crossing latent and active identifiers, as in En02-A. The number of one-bit services across the cut is at most its initial value: activation converts one unspent latent service into one active service; transmission consumes it; no update adds an identifier.