crossDomainModuleCount
The cross-domain module count is fixed at 27 for the wave-64 layer in Recognition Science. Meta-theorem analysts cite this constant when confirming the equality to three cubed or the bounds 25 to 45. The definition is a direct numeric assignment with no reduction steps.
claimLet $N$ denote the number of cross-domain modules in the wave-63/64 layer. Then $N = 27$.
background
The module lists 27 cross-domain structural theorems C1 through C27. These include CognitiveStateSpace (5×5×5=125), PlanetStratification (5+5+5=15), JEquilibriumUniversality, PhiLadderUniversality, and RecognitionGenerators (spectrum from {2,3,5}). The local setting is the meta-count claim for the cross-domain layer, presented as C28 itself, with the explicit statement that the total is 27 and Lean status shows zero sorrys and zero axioms.
proof idea
The definition is a direct constant assignment of the natural number 27. No lemmas are applied and no tactics are invoked beyond the declaration itself.
why it matters in Recognition Science
This constant supplies the input value for downstream results including count_is_D_cubed (equality to 3^3) and count_in_spectrum (interval 25 to 45). It links to T8 of the forcing chain where D equals 3 spatial dimensions, since 27 equals 3 cubed. The module doc positions the count as closing the meta-theorem enumeration for the wave-64 layer.
scope and limits
- Does not derive the number 27 from the forcing chain or Recognition Composition Law.
- Does not verify that the listed C1-C27 modules are exhaustive.
- Does not extend the count to layers beyond wave 64.
- Does not supply a general formula for module counts in other domains.
Lean usage
theorem count_eq : crossDomainModuleCount = 27 := rflformal statement (Lean)
48def crossDomainModuleCount : ℕ := 27
proof body
Definition body.
49