Coherence Boundary Depth Scans

survival-phase-chain-boundary-scan

Retained survival counts feed phase visibility before a visible-count gate. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

Survival retained shots feed visibility

Each row first closes retained plus lost shots, then uses retained shots as the phase budget input.

Nvisible≥20N_{\text{visible}}\ge20
Survival to visibilityThe retained count feeds the phase-visible budget.retained=80coherent=60visible=30margin=10

Three chained rows show the visible-count boundary

The middle row lands exactly on the visible-count floor; the last row falls below it.

NretNcohNvism806030106040200401010−10\begin{array}{c|c|c|c}N_{\text{ret}}&N_{\text{coh}}&N_{\text{vis}}&m\\80&60&30&10\\60&40&20&0\\40&10&10&-10\\\end{array}
Boundary chain rowThe retained count feeds the phase-visible budget.retained=60coherent=40visible=20margin=0

The final chain fails the visible-count floor

The source budgets still close, but the computed visible count leaves a negative margin.

m=−10failm=-10\quad \text{fail}
Below visible floorThe retained count feeds the phase-visible budget.retained=40coherent=10visible=10margin=-10