MetaTheoremCountCert
plain-language theorem explainer
MetaTheoremCountCert packages four assertions on the cross-domain layer count in Recognition Science: the module total equals 27, equals 3 cubed, five universality patterns are covered, and the total sits in [25,45]. Meta-theorists cite the certificate when confirming the C1-C27 enumeration completeness. The declaration is a plain structure definition with no lemmas or computational steps.
Claim. Let $N$ be the number of cross-domain modules and $P$ the number of covered universality patterns. The certificate asserts $N=27$, $N=3^3$, $P=5$, and $25≤N≤45$.
background
The module states a structural meta-claim: the cross-domain layer (C1–C27 plus this C28) contains a countable set of joint structural theorems. It enumerates 27 modules with explicit cardinalities such as 5×5×5=125 for C1 and 5+5+5=15 for C2, summing to 27. Upstream, crossDomainModuleCount is defined as the constant 27 and patternsCovered as the constant 5 for the patterns D=5, 2³=8, J=0, φ-ladder, and gap45.
proof idea
Structure definition with four fields. No lemmas or tactics are applied; the fields directly record the numerical assertions supplied by the sibling definitions crossDomainModuleCount and patternsCovered.
why it matters
The structure feeds the downstream metaTheoremCountCert constructor that instantiates it. It supplies the meta-claim witness for the C28 module, confirming the cross-domain layer size and its alignment with the five universality patterns. The count 27=3³ ties to the eight-tick octave and D=3 spatial dimensions in the forcing chain.
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