Three corrections to the proposed statement

First, a fresh clock means a new admissible live input name, not a statistical independence hypothesis. Correlated clock supplies are allowed when their joint preparation and storage are declared.

Second, an error theorem must distinguish:

The latter does not imply the former.

Third, no-enlargement is a resource-qualified assertion. Finiteness alone does not prove that a protocol fits a previously fixed capacity or time window. The certificate must pass those checks before a host-level realization is released.