metaTheoremCountCert
The metaTheoremCountCert definition assembles a certificate asserting that the cross-domain layer contains exactly 27 structural theorems. This count equals 3 cubed and lies inside the spectrum interval 25 to 45 while covering five universality patterns. A researcher verifying completeness of the C1-C28 layer would cite the certificate when checking the enumeration. The construction is a direct record instantiation that applies reflexivity lemmas to each field.
claimLet $N$ denote the cross-domain module count. Then $N=27$, $N=3^3$, the number of covered patterns equals 5, and $25leq Nleq45$.
background
The module enumerates 27 cross-domain theorems labeled C1 through C27, each tied to structural results on J-functions, phi-ladders, cube patterns, and gap relations, with this declaration serving as C28. The MetaTheoremCountCert structure packages four assertions: the exact count equals 27, the count equals the cube of spatial dimension D, five patterns are covered, and the count falls inside the closed interval from 25 to 45. Upstream results supply each piece: count_eq establishes the equality to 27 by reflexivity, count_is_D_cubed confirms the cube relation, patterns_match_D fixes the pattern count at 5, and count_in_spectrum verifies the bounds via decision procedures.
proof idea
The definition is a direct instantiation of the MetaTheoremCountCert structure. It supplies the count field from count_eq, the cube property from count_is_D_cubed, the pattern coverage from patterns_match_D, and the spectrum bounds from count_in_spectrum.
why it matters in Recognition Science
This declaration closes the cross-domain enumeration by certifying that the layer contains 27 theorems, matching the framework expectation of D cubed for D=3. It completes the list of modules C1-C27 that each encode universality statements on J-equilibrium, phi-ladders, and cube-based patterns. The certificate supports higher-level meta-claims about the architecture of Recognition Science, though no downstream uses are recorded yet.
scope and limits
- Does not establish the content or proofs of any individual cross-domain theorem.
- Does not derive the count from first principles beyond the enumerated modules.
- Does not address theorems outside the cross-domain layer.
- Does not supply a general counting mechanism applicable to arbitrary layers.
formal statement (Lean)
77def metaTheoremCountCert : MetaTheoremCountCert where
78 count := count_eq
proof body
Definition body.
79 count_is_cube := count_is_D_cubed
80 patterns_covered := patterns_match_D
81 count_in_spectrum_range := count_in_spectrum
82
83end IndisputableMonolith.CrossDomain.MetaTheoremCount