MetaTheoremCountCert
MetaTheoremCountCert packages four assertions into a single certificate: the cross-domain module count equals 27, this count equals 3 cubed, five universality patterns are covered, and the count lies between 25 and 45 inclusive. Researchers working on the Recognition Science meta-layer cite it to close the count for the wave-64 cross-domain theorems. The structure is assembled directly from the module constants without further lemmas.
claimLet $N$ denote the number of cross-domain modules in the wave-64 layer. The certificate asserts $N=27$, $N=3^3$, the number of covered universality patterns equals 5, and $25leq Nleq 45$.
background
The module enumerates 27 cross-domain theorems labeled C1 through C27, with this declaration serving as C28 to certify the total. crossDomainModuleCount is defined as the constant 27. patternsCovered is defined as the constant 5, corresponding to the universality patterns D=5, 2^3=8, J=0, phi-ladder, and gap45.
proof idea
The declaration is a structure definition. Its four fields directly embed the module constants crossDomainModuleCount and patternsCovered along with the explicit range inequality on the count.
why it matters in Recognition Science
This certificate feeds the downstream construction of metaTheoremCountCert, which instantiates the structure using auxiliary lemmas count_eq, count_is_D_cubed, patterns_match_D, and count_in_spectrum. It closes the meta-theorem count for the cross-domain layer, aligning with the Recognition Science framework's emphasis on countable structural theorems in the wave-64 layer. The count 27=3^3 echoes the eight-tick octave and D=3 spatial dimensions from the forcing chain.
scope and limits
- Does not verify the content of any individual cross-domain theorem.
- Does not derive the count from first principles of the Recognition framework.
- Does not address modules outside the listed C1-C27.
- Does not provide a proof of the range bounds beyond the constant definition.
formal statement (Lean)
70structure MetaTheoremCountCert where
71 count : crossDomainModuleCount = 27
72 count_is_cube : crossDomainModuleCount = 3^3
73 patterns_covered : patternsCovered = 5
74 count_in_spectrum_range :
75 25 ≤ crossDomainModuleCount ∧ crossDomainModuleCount ≤ 45
76