An available-source budget scan holds one fixed survival-and-phase source (80 retained shots, 50 of them coherent) and checks two different accepted-readout requests against two different upstream budgets: 50 accepted readouts against the coherent budget passes exactly at capacity, while 80 accepted readouts against the larger retained budget also passes, even though 30 of those 80 retained shots were actually dephased and never carried a visible phase signal exactly for the stated toy audit rule. Choosing the coherent budget as the cap is the physically honest choice; real coherence audits that check against the wrong upstream budget can silently accept readouts that do not correspond to genuine coherent signal.
The same source shots accept very different readout requests depending only on which upstream budget the audit checks against. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.
highlighted = computed this step
The coherent shots are the physically honest cap
The same survival and phase source gives 50 coherent shots out of 80 retained shots. Requesting exactly the coherent count as accepted readouts is checked against that coherent budget.
Naccepted=50≤Ncoherent=50
The same shots, checked against two different budgets
Nothing about the survival or phase source changes between these two rows. Only the budget the accepted-readout request is checked against changes, and that alone changes how many readouts the audit will accept.
Retained is a real count, but not all of it is coherent
The retained-sourced row accepts 80 readouts, but only 50 of the 80 retained shots were actually coherent. The extra accepted readouts this row allows are counted against dephased shots that never carried a visible phase signal.