metaTheoremCountCert
plain-language theorem explainer
This definition assembles a certificate asserting that the cross-domain layer of Recognition Science contains exactly 27 structural theorems, equal to 3 cubed, covering 5 universality patterns and lying in the interval [25,45]. Cross-domain unification researchers cite it as the C28 meta-count witness. The construction is a direct structure instantiation that wires four sibling theorems into the MetaTheoremCountCert record.
Claim. Let $N$ be the number of cross-domain modules. The certificate asserts $N=27$, $N=3^3$, the number of covered patterns equals 5, and $25leq Nleq 45$.
background
The module lists 27 cross-domain theorems (C1-C27) whose individual cardinalities sum to 27, with examples such as 5x5x5=125 for CognitiveStateSpace and 5+5+5=15 for PlanetStratification. The structure MetaTheoremCountCert packages four properties: count equals 27, count equals 3 cubed, patterns covered equals 5, and the count lies in [25,45]. Upstream results supply the four ingredients: count_eq proves equality to 27 by reflexivity, count_is_D_cubed proves equality to 3^3 by decide, patterns_match_D proves patterns covered equals 5 by reflexivity, and count_in_spectrum proves the interval bounds by unfolding and decide.
proof idea
The definition constructs the MetaTheoremCountCert record by direct field assignment: count from count_eq, count_is_cube from count_is_D_cubed, patterns_covered from patterns_match_D, and count_in_spectrum_range from count_in_spectrum. It is a one-line wrapper that assembles the certificate from these four prior results.
why it matters
This declaration supplies the meta-level certificate for the count of cross-domain theorems, closing the C28 module in the Recognition Science framework. It records the numerical outcome of the cross-domain layer and links to the forcing chain where D=3 is forced as spatial dimensions. No downstream uses are recorded yet; the declaration touches the open question whether the equality 27=3^3 is forced by the phi-ladder or remains a numerical coincidence.
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