DRAFT 2026-05-15Work in progress. Math is load-bearing, copy is being iterated.
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Yield Collapse

The probability your pipeline ships a clean job is the product of every per-gate accept rate. Multiplication is brutal. Tune the sliders and watch the math.

Companion to The Knowledge-Work Assembly Line. The bottleneck is not your model. It is the verification gate at every station.

Start with a scenario

POC-quality gates in a production pipeline. Yield is collapsing.

10

Each station = one WorkUnit with its own gate predicate.

80%

Probability a station clears given upstream cleared.

What the math says

For a pipeline of N stations where each station emits an artifact to the next,

P(ship) = Πi=1..N P(gatei clears | gatei-1 cleared)

The conditional is what makes the math brutal in practice. Errors do not reset between stations. A contaminated upstream feeds a station that updates on the contamination. The cross-terms compound.

Two operational consequences fall out immediately. First: model selection is rarely the bottleneck. Going from one frontier model to another might lift a station from 88% to 93%. Compounded over ten stations, that is the difference between 28% and 48% end-to-end. Real, not life-changing. Second: raising per-gate accept does not necessarily mean a better model at that station. Often it means a better gate predicate: a sharper definition of what counts as acceptable output, instrumented well enough that the station can tell.

See also