count_eq
The cross-domain layer of Recognition Science contains exactly 27 joint structural theorems. Meta-structure analysts cite this equality to anchor the enumeration of modules C1 through C27. The proof is a one-line reflexivity on the explicit natural-number definition of the module count.
claimThe number of cross-domain modules in the wave-64 layer equals 27.
background
This module supplies a structural meta-claim that the cross-domain layer holds a countable set of joint structural theorems. The module documentation enumerates 27 modules, each carrying a specific structural property such as 5×5×5 lattices in CognitiveStateSpace or phi-ratio sharing in PhiLadderUniversality, running from C1 to C27 RecognitionGenerators with spectrum drawn from {2, 3, 5}. The local setting is the wave-64 cross-domain layer whose total is witnessed here as C28.
proof idea
The proof is a one-line wrapper that applies reflexivity to the definition crossDomainModuleCount := 27.
why it matters in Recognition Science
This equality anchors the MetaTheoremCountCert structure, which supplies the count field for downstream certifications in urban density from the phi-ladder and hurricane categories. It completes the meta-claim for the wave-64 layer and notes the numerical match 27 = 3³ with the spatial dimension D forced in the unified forcing chain. The result ties the enumeration to upstream universality statements on J-convexity and spectral emergence.
scope and limits
- Does not prove the content of any of the 27 individual theorems.
- Does not guarantee the count stays fixed if further cross-domain modules are added.
- Does not derive the number 27 from the forcing chain or recognition composition law.
- Does not address physical interpretations or applications of the listed theorems.
formal statement (Lean)
50theorem count_eq : crossDomainModuleCount = 27 := rfl
proof body
Term-mode proof.
51
52/-- 27 = 3³ (cube of D_spatial). Coincidence? -/