third_primorial
plain-language theorem explainer
The product of the three primitive generators equals 30. Researchers decomposing the RS cardinality spectrum into polynomials over {2,3,5} cite this as the base primorial case. The proof is a one-line decision procedure that evaluates the constant definitions directly.
Claim. Let $G_2=2$ be the binary face generator, $G_3=3$ the spatial dimension generator, and $G_5=5$ the configuration dimension generator. Then $G_2 G_3 G_5 = 30$.
background
The module states a structural meta-claim: every integer in the RS cardinality spectrum is generated by operations on three primitive generators G = {2, 3, 5} (binary face, spatial dim, configDim). Operations include addition, multiplication, exponentiation and choose. Spectrum members such as 4=2², 6=2·3, 8=2³, 10=2·5, 12=2²·3, 15=3·5, 16=2⁴, 25=5² and 360=2³·3²·5 are exhibited as examples. The module proves the listed decompositions for spectrum members enumerated in C21, with zero sorry or axiom.
proof idea
One-line wrapper that applies the decide tactic to the arithmetic equality on natural numbers after unfolding the three constant definitions.
why it matters
It supplies the base primorial identity required by the module's meta-claim that no RS spectrum member lies outside polynomials in {2,3,5}. The generators align with the binary face, spatial dimension and configuration dimension landmarks used across the Recognition framework. No downstream theorems are recorded.
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