count_is_D_cubed
plain-language theorem explainer
The cross-domain layer of Recognition Science enumerates exactly 27 structural theorems, which equals three cubed. Meta-theorists checking dimensional consistency in unified models cite this to link the enumeration to the forced spatial dimension. The proof is a direct decision procedure that evaluates the numerical equality after the count definition unfolds to the constant 27.
Claim. Let $N$ be the number of cross-domain structural theorems in the wave-64 layer. Then $N = 3^3$.
background
The module supplies a meta-claim for the cross-domain layer, which assembles 27 theorems labeled C1 through C27. The sibling definition crossDomainModuleCount sets this number to the constant 27. The local setting is a structural meta-claim that witnesses the count and proves a lower bound, with the module documentation confirming zero sorry or axiom across the layer.
proof idea
The proof is a one-line term proof that applies the decide tactic to verify the equality after unfolding the count definition to 27.
why it matters
This theorem supplies the count_is_cube field inside the MetaTheoremCountCert structure. It connects the enumeration of 27 theorems to the framework landmark T8 that forces D = 3 spatial dimensions. The module documentation notes the numerical coincidence with 3 cubed while recording the layer's formal status.
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