Three rows fail at three different pipeline stages, showing that clearing an earlier stage guarantees nothing about a later one. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

A pipeline can fail at its very first stage

Chapter six's chain scan always let survival pass and looked for the failure later. Here the first row fails immediately: only 3/10 of prepared shots survive, well under the one-half survival floor, so the pipeline never reaches the phase or window stage.

fsurvival=310<12f_{\text{survival}}=\frac{3}{10}<\frac{1}{2}
Fails at survivalThe retained fraction alone already misses the floor.3/10retained7/10lostsurvival budget

Three rows fail at three different pipeline stages

Each row passes every stage before the one listed, then fails exactly there. Passing an earlier stage is not a guarantee for any later one.

rowpassesfails at1nonesurvival2survivalphase3survival, phasewindow\begin{array}{c|c|c}\text{row}&\text{passes}&\text{fails at}\\1&\text{none}&\text{survival}\\2&\text{survival}&\text{phase}\\3&\text{survival, phase}&\text{window}\\\end{array}
Fails at phaseSurvival passes; the visible count then misses its floor.3/8coherent5/8dephasedvisible fringe

The third row fails only at the last stage checked

The third row's survival fraction and visible count both clear their floors. Only the coherence window fails: the three declared stages take 12 time units against a window of 10.

Telapsed=12>10=TwindowT_{\text{elapsed}}=12>10=T_{\text{window}}
Fails at windowSurvival and phase both cleared; only the window check fails.4/5coherent1/5dephasedvisible fringe