MetaTheoremCountCert
plain-language theorem explainer
The structure certifies that the cross-domain layer contains 27 modules, equal to three cubed, covering five universality patterns and lying in the interval from 25 to 45. Researchers verifying completeness of the wave-64 layer in Recognition Science would cite this certificate when auditing the enumerated theorems. The declaration is realized as a structure definition that simply bundles the four assertions.
Claim. Let $N$ be the number of cross-domain modules and $P$ the number of covered universality patterns in the Recognition Science wave-64 layer. The certificate asserts $N=27$, $N=3^3$, $P=5$, and $25≤N≤45$.
background
The module lists 27 cross-domain theorems (C1–C27) that exhibit shared structural features such as five-dimensional lattices, cube cardinalities, J-positivity, phi-ladder relations, and gap-45 ceilings. The upstream definition sets the module count to the constant 27 and the pattern count to the constant 5, where the five patterns are D=5, the 2^3 cube, J=0, the phi ladder, and gap45. The local setting is a meta-count of the cross-domain layer whose total is stated to be 27 with zero sorry or axiom.
proof idea
The declaration is a structure definition. Its four fields directly embed the two upstream constant definitions together with the arithmetic relation 27=3^3 and the interval check 25≤27≤45; no lemmas or tactics are applied.
why it matters
The structure supplies the record type instantiated by the downstream metaTheoremCountCert definition, thereby closing the meta-claim that the cross-domain layer comprises exactly 27 theorems. It records the explicit count 27=3^3, which aligns with the framework landmark that spatial dimension D=3 forces the eight-tick octave and the cube cardinality 27. The module doc presents this as the structural meta-claim for wave 64 with no open scaffolding.
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