Neither a heat ledger nor a spacetime metric follows

Equation (eq:drop-record) is a channel equality. It does not assign measurement work, heat, reset cost, an energy budget, or environmental leakage. A thermodynamic implementation requires its own apparatus and resource specification.

Likewise, the code $k$, calibrated scalar $t_k$, and program schedule are not a metric tensor or a matter-defined relational lapse. Em02-E's classical lapse construction uses its own background and relational-map hypotheses CheungEm02E. No comparison map identifying that lapse with the present clock code has been constructed.

Thus the analog in Table tab:analogs is useful precisely because it does not promote a finite interface correspondence into an identity with gravitational spacetime.