pith. sign in
theorem

firstPassProgram_exact_top_priority

proved
show as:
module
IndisputableMonolith.Foundation.OptionAEmpiricalProgram
domain
Foundation
line
67 · github
papers citing
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plain-language theorem explainer

The equivalence asserts that any CombinationID belongs to the first-pass schedule precisely when its empirical priority is high or immediate. Researchers certifying the Option A empirical program cite this when confirming the initial test sequence is complete. The proof is a one-line wrapper that invokes the upstream schedule membership theorem.

Claim. For any combination identifier $c$, $c$ belongs to the first-pass empirical test schedule if and only if the empirical priority of $c$ is either immediate or high.

background

The module supplies a single certificate for the first-pass empirical program attached to Option A. Earlier modules establish the queue, schedule, actions, deliverables, pipelines, and readiness separately; this file assembles them to prove the program is complete and collision-free at the metadata layer, with zero sorrys and zero axioms.

proof idea

The proof is a one-line wrapper that applies the theorem firstPassSchedule_mem_iff_high_or_immediate to the input combination identifier.

why it matters

This theorem feeds the first_pass_complete field inside the empiricalProgramCert definition. It confirms the assembled first-pass program begins exactly with the high-or-immediate tests required by the Option A structure. The upstream schedule membership result, whose doc-comment states that the first-pass schedule contains exactly the high-or-immediate tests, supplies the concrete list and priority cases.

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