firstPassProgramComplete
plain-language theorem explainer
The first-pass empirical program attached to Option A meets its completion gate: readiness holds, the program has exactly five entries, the program and its action, deliverable and pipeline lists are all duplicate-free, and the schedule selects exactly the high-or-immediate combinations. Researchers assembling the empirical validation certificate in the Recognition Science framework cite this result. The proof is a direct term that packages the seven supporting lemmas into the required conjunction.
Claim. The first-pass empirical program satisfies readiness, has exactly five tests, is duplicate-free, produces duplicate-free action, deliverable and pipeline lists, and includes in its schedule a combination if and only if that combination is high or immediate: $ready$ and $length=5$ and $no$ $duplicates$ and $schedule$ $equivalence$ $to$ $high$-$or$-$immediate$.
background
The module constructs a single certificate for the first-pass empirical program attached to Option A. The earlier modules prove the pieces separately: queue, schedule, actions, deliverables, pipelines, and readiness. This file proves that the assembled first-pass program is complete and collision-free at the metadata layer. The completion property is the conjunction of readiness, program length five, duplicate-freeness of the program and the three derived lists, and the schedule membership condition that a combination belongs to the schedule if and only if it is high or immediate.
proof idea
The proof is a term-mode construction that directly supplies the seven conjuncts required by the definition of the completion property. It invokes the readiness theorem, the length theorem for the program, the nodup theorem for the program, the nodup theorem for actions, the nodup theorem for deliverables, the nodup theorem for pipelines, and the schedule membership equivalence theorem.
why it matters
This theorem supplies the completeness component required by the empirical program certificate. It is referenced by the definition of the empirical program certificate, which collects the injectivity, length, nodup, ready and complete properties into a single record. Within the Recognition Science framework it closes the metadata verification layer for the first-pass empirical program of Option A.
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