Three independent ledgers

The ledgers have different defining data:

1. Complete energy. Supply the Hamiltonians and complete dynamics. Conservation means $U^{†}{H}_{\mathrm{tot}}U=H_{\mathrm{tot}}$, or, for an energy-intertwining isometry, $H_{\mathrm{out}}V=V{H}_{\mathrm{in}}$. Unitarity alone does not imply either statement.

2. Physical erasure/reset cost. Supply the memory, input class, reservoirs, work storage, controls, initial correlations, heat/work conventions, and resource-restoration conditions.

3. Residual leakage. Compute the dimensionless complete-channel diagnostic ${\delta }_{\mathrm{full}}$. It is not an energy, stress tensor, area, or bit count.

This separation is central to En07-A/B/C CheungEn07A,CheungEn07B,CheungEn07C.