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def definition def or abbrev high

empiricalQueueCert

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The definition assembles a concrete certificate for the empirical test priority queue tied to the C1-C9 cross-domain theorems. It records four priority levels, marks specific tests as immediate or high, and confirms every queued item carries a falsifiable protocol. Researchers validating the empirical layer of Recognition Science would cite it to fix the test ordering. The construction is a direct field assignment that invokes reflexivity lemmas for each classification and count.

claimThe certificate satisfies $Fintype.card(Priority)=4$, $isImmediate(c3OncologyTensor)$, $isImmediate(c8MillerSpan)$, $empiricalPriority(c5AttentionTensor)=high$, $empiricalPriority(c2PlanetStrata)=high$, $empiricalPriority(c9RegulatoryCeiling)=high$, and $forall c:CombinationID, ProtocolFalsifiable(c)$, together with the exact cardinalities of the immediate, high, medium, and deferred buckets and the classification equivalences for immediate and high-or-immediate tests.

background

The module defines a priority queue that orders empirical tests for the C1-C9 theorems. EmpiricalQueueCert is the structure whose fields record the number of priority levels, the immediate and high-priority assignments, the protocol coverage for every CombinationID, and the exact sizes of each priority bucket. The local setting is the formal empirical protocol layer that records which tests must be run first while proving every item is already covered by a falsifiable protocol; the module states it contains zero sorry or axiom. Upstream results supply the individual assignments via reflexivity: c3_immediate proves isImmediate c3OncologyTensor, c2_high proves empiricalPriority c2PlanetStrata equals high, and deferredTests_exact proves membership in the deferred bucket is equivalent to priority defer.

proof idea

The definition populates the EmpiricalQueueCert structure by direct field assignment. Four_priorities receives priority_count; c3_now receives c3_immediate; c8_now receives c8_immediate; c5_next, c2_next and c9_next receive the corresponding high-priority reflexivity lemmas; all_have_protocol receives every_priority_has_protocol; the classification fields receive immediate_iff and high_or_immediate_iff; and the bucket cardinalities receive the exact and length lemmas for each priority class.

why it matters in Recognition Science

This definition supplies the concrete certificate that organises empirical testing of the C1-C9 theorems inside the Recognition Science framework. It ensures the queue respects the priority classifications derived from the forcing chain and the eight-tick octave. Because the used_by list is empty it functions as a foundational record rather than feeding a specific parent theorem; it closes the empirical-protocol scaffolding for the cross-domain claims by proving every queued test already carries a ProtocolFalsifiable witness.

scope and limits

formal statement (Lean)

 182def empiricalQueueCert : EmpiricalQueueCert where
 183  four_priorities := priority_count

proof body

Definition body.

 184  c3_now := c3_immediate
 185  c8_now := c8_immediate
 186  c5_next := c5_high
 187  c2_next := c2_high
 188  c9_next := c9_high
 189  all_have_protocol := every_priority_has_protocol
 190  immediate_classification := immediate_iff
 191  high_or_immediate_classification := high_or_immediate_iff
 192  immediate_count := immediateTests_length
 193  high_count := highPriorityTests_length
 194  medium_count := mediumPriorityTests_length
 195  defer_count := deferredTests_length
 196  bucket_total := priorityBucketTotal
 197  immediate_exact := immediateTests_exact
 198  high_exact := highPriorityTests_exact
 199  medium_exact := mediumPriorityTests_exact
 200  defer_exact := deferredTests_exact
 201
 202end OptionAEmpiricalQueue
 203end Foundation
 204end IndisputableMonolith

depends on (19)

Lean names referenced from this declaration's body.