A pipeline failure-point scan runs the same three-stage chain (survival, phase visibility, coherence window) three times, engineering each row to fail at a different single stage: row one fails immediately at survival (3/10 retained, under the one-half floor), row two clears survival but fails at phase (a visible count of 15 under a floor of 20), and row three clears both survival and phase but fails only at the coherence window (12 elapsed time units against a window of 10) exactly for the stated toy pipeline rule. Clearing an earlier stage is never a guarantee about a later one; real multi-stage measurement pipelines can fail at any stage independently.
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=103<21
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.
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.