Audit 4: selection of the quench entrance

The source's entrance-selection condition is stronger than merely requiring a zero-coordinate product-topology boundary. It includes local positive-time density bounds, the edge semigroup relation, and a sequential high-mode escape condition inherited from the uniform initial states OAI227Entrance (thm:entrance-selection).

The verification questions are:

1. Do all extracted Gaussian subsequences satisfy the stated escape condition?

2. Does uniqueness hold in the exact density class used?

3. Is the selected family measurable in the edge environment?

4. Are the trace tails controlled when the density and semigroup limits are inserted into the infinite sum?

A possible semigroup entrance is not enough; it must be the entrance selected by the finite uniform starts.

No conclusion at $\beta \ne 1$ is substituted for this selection.