totalRank
plain-language theorem explainer
The declaration certifies that the ranks of the three Standard Model gauge factors sum to six. A researcher closing the gauge-group derivation in Recognition Science would cite this to confirm the (3,2,1) decomposition. The proof is a one-line decision procedure that evaluates the three constant natural-number definitions.
Claim. $rank(SU(3)) + rank(SU(2)) + rank(U(1)) = 6$
background
Module StandardModelGroupStructure certifies the SM gauge group SU(3)×SU(2)×U(1) obtained from the RS GaugeGroupCube construction. Local definitions set rankSU3 = 3 (matching spatial dimension D), rankSU2 = 2, and rankU1 = 1. Upstream constants rankSU2 and rankU1 are imported from ElectrowealUnificationFromRS; the module also depends on the meta-realization structure for in UniversalForcingSelfReference.
proof idea
One-line wrapper that applies the decide tactic to the arithmetic on the three natural-number constants rankSU3, rankSU2, and rankU1.
why it matters
The equality is referenced by smGroupCert to supply the rank_decomp field alongside the five gauge-boson types and gluon count of eight. It completes the group-rank match required by the RS derivation of the Standard Model, aligning with T8 (D = 3) and the eight-tick octave in the forcing chain.
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