Resource ledger

Let

where $p$ is the number of internal matter qubits and $n_{\mathrm{m}}$ the number of original names whose current and history locations are represented. Here $2B+12n_{\mathrm{m}}$ counts the current metadata and retained history after the reversible event; clean work is not transported.

For a route with $n$ hops, a sufficient reserve is:

Using the clock before the metadata circuit, and the pointer after clock consumption, gives the sufficient quantum peak

The metadata registers are basis-coded when decoded as classical geometry; their quantum-carrier implementation does not make the cone a quantum variable. A purely classical implementation can reduce the charged quantum storage but is not needed for this bound.

All blanks at unused sites are counted. Spectator and external-reference holdings are separate. No claim of optimal storage, physical energy cost, Landauer saturation, or thermal reversibility is made.