The object certified here

The certified object consists of finite registers, a gate list, initial states, a measured output, and an arithmetic decoder of that output. Its proof uses Boolean identities and elementary arithmetic.

It specifies no spacetime metric, gravitational mediator, horizon, radiation algebra, evaporation dynamics, generalized entropy, or island extremization. The prime output is a classical list, not a metric or a time-indexed radiation-entropy history.

The same finite circuit can be regarded solely as an abstract reversible Boolean network. Consequently its exact factorization identity does not determine any of those additional physical objects.