Derived capture budget

The three terms have different comparisons: preparation, mode selection including the nonvacuum background, and vacuum loss. There is no additional overlapping “window” or “background” term.

For this Gaussian input, the actual memory marginal is geometric with mean

This follows directly from (eq:captureann), independence of the memory preparation, and gauge-invariant quasifreeness. It is an apparatus-model prediction, not a replacement for the target value ${\nu }_h$.