priorityBucketTotal
The priorityBucketTotal theorem asserts that the four empirical test buckets sum to exactly nine items in total. Researchers auditing the Option A queue for C1-C9 cross-domain coverage would cite it to confirm queue completeness. The proof is a one-line term reduction that substitutes the four precomputed bucket lengths.
claimLet $I$ be the list of immediate empirical tests, $H$ the high-priority tests, $M$ the medium-priority tests, and $D$ the deferred tests. Then $|I| + |H| + |M| + |D| = 9$.
background
The Option A Empirical Queue module constructs a priority queue for empirical tests attached to the C1-C9 cross-domain theorems. It records which protocols to test first and proves every queued item is already covered by the formal empirical protocol. Immediate tests are the oncology tensor and Miller span combinations; high-priority tests are planet strata, attention tensor, and regulatory ceiling; deferred tests are quantum molecular depth and Erikson reverse.
proof idea
The proof is a one-line term proof that rewrites the sum by applying the four length theorems immediateTests_length, highPriorityTests_length, mediumPriorityTests_length, and deferredTests_length. Each length theorem is discharged by decide.
why it matters in Recognition Science
This result feeds the empiricalQueueCert definition that certifies the four-priority structure and specific test placements. It closes the queue-size accounting step inside the Option A empirical protocol, ensuring the total test count is fixed before any downstream certification of coverage.
scope and limits
- Does not establish the empirical outcomes or validity of any listed test.
- Does not derive the test lists from the Recognition Science forcing chain or J-cost axioms.
- Does not prove protocol coverage for the queued items.
- Does not address ordering or execution within each priority bucket.
formal statement (Lean)
143theorem priorityBucketTotal :
144 immediateTests.length + highPriorityTests.length +
145 mediumPriorityTests.length + deferredTests.length = 9 := by
proof body
Term-mode proof.
146 rw [immediateTests_length, highPriorityTests_length,
147 mediumPriorityTests_length, deferredTests_length]
148