patternsCovered
plain-language theorem explainer
The definition sets the count of universality patterns covered in the cross-domain layer to the integer 5. Meta-theorem certification structures reference it when bounding the total number of structural theorems. It is supplied as a direct numeric constant with no lemmas or reduction steps.
Claim. The number of universality patterns covered is $5$, consisting of the $D=5$ instances, the eight-tick octave $2^3=8$, $J=0$ equilibria, the phi-ladder ratios, and the gap45 ceiling.
background
The cross-domain layer organizes twenty-seven structural theorems across modules C1 through C27. Each module exhibits recurring patterns such as five-dimensional lattices, the 2^3 octave, J-equilibrium conditions, phi-ratio scaling, and the gap45 ceiling. The module document records explicit cardinalities for each, for example 5×5×5=125 in CognitiveStateSpace and 5+5+5=15 in PlanetStratification, yielding the aggregate total of 27.
proof idea
The declaration is a direct definition that binds the constant to the literal value 5. No upstream lemmas are invoked and no tactics are applied.
why it matters
It supplies the patterns_covered field inside the MetaTheoremCountCert structure, which simultaneously records that the cross-domain module count equals 27 and equals 3 cubed while lying in the interval [25,45]. The definition therefore anchors the lower-bound certification of the twenty-seven theorems that unify the phi-ladder, eight-tick octave, and related patterns across domains.
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