gluon_count
plain-language theorem explainer
The theorem asserts that the gluon count equals eight, matching the dimension of the SU(3) adjoint representation. Researchers deriving Standard Model gauge boson multiplicities from Recognition Science would cite this to fix the color octet structure. The proof is a one-line decision procedure that evaluates the arithmetic identity directly.
Claim. The gluon count satisfies $3^2 - 1 = 8$, where the count is defined as colorCount squared minus one and colorCount equals three for the SU(3) color group.
background
The module certifies the Standard Model gauge group SU(3)×SU(2)×U(1) via rank decomposition from the Recognition Science GaugeGroupCube construction, with SU(3) rank equal to spatial dimension D=3. gluonCount is the sibling definition gluonCount : ℕ := colorCount ^ 2 - 1. Upstream results supply the numerical value of colorCount via the forcing chain and wallpaper-group constants W appearing in MassTopology, LeptonGenerations, and Anchor.
proof idea
The proof is a one-line wrapper that applies the decide tactic to the concrete arithmetic equality 3² - 1 = 8.
why it matters
This populates the gluon_8 field inside smGroupCert and gluonCert, confirming eight gluons among the five gauge-boson types whose total carrier count is twelve. It closes the SU(3) piece of the rank decomposition (3+2+1=6) that matches the framework's T8 spatial dimension D=3 and the eight-tick octave structure. No open scaffolding remains for this numerical fact.
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