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def definition def or abbrev high

FirstPassProgramComplete

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The first-pass program completeness gate requires that the initial schedule is ready for execution, the program list has exactly five entries and is free of duplicates, and the derived lists of actions, deliverables, and pipelines are also duplicate-free, with the schedule matching exactly the high or immediate priority combinations. Researchers working on the empirical validation layer of the Recognition Science framework cite this gate when assembling the Option A certificate. It is defined directly as the conjunction of these component ready

claimThe first-pass empirical program is complete if the schedule is ready, the program has length $5$, the program is duplicate-free, the actions are duplicate-free, the deliverables are duplicate-free, the pipelines are duplicate-free, and a combination belongs to the schedule if and only if it has high or immediate priority.

background

The module provides a single certificate for the first-pass empirical program attached to Option A. Upstream, the first-pass program is obtained by mapping each scheduled combination to its program specification. Actions are derived by mapping to analysis actions, deliverables to deliverable records, and pipelines to pipeline specifications. Readiness holds precisely when every combination in the schedule is empirically ready. The local setting is a metadata-level check that the assembled program has no collisions in its output classes and that all rows are prepared.

proof idea

The definition is assembled as a direct conjunction of the readiness predicate, the length equality to five, the noduplicate properties for the program and its three derived lists, and the schedule membership equivalence for high or immediate priorities. It serves as a one-line wrapper collecting the results of the separate lemmas on schedule length, uniqueness, and priority filtering.

why it matters in Recognition Science

This definition supplies the completeness component for the EmpiricalProgramCert structure, which bundles the injectivity of the program specification map with the first-pass length, noduplicate, ready, and complete properties. It closes the first-pass empirical program assembly in the Recognition Science foundation, ensuring the initial execution order is metadata-complete before higher-level validation. It touches the empirical readiness check within the Option A program.

scope and limits

formal statement (Lean)

  95def FirstPassProgramComplete : Prop :=

proof body

Definition body.

  96  FirstPassReady ∧
  97    firstPassProgram.length = 5 ∧
  98    firstPassProgram.Nodup ∧
  99    firstPassActions.Nodup ∧
 100    firstPassDeliverables.Nodup ∧
 101    firstPassPipelines.Nodup ∧
 102    (∀ c : CombinationID, c ∈ firstPassSchedule ↔ isHighOrImmediate c)
 103

used by (2)

From the project-wide theorem graph. These declarations reference this one in their body.

depends on (8)

Lean names referenced from this declaration's body.