su3Rank
plain-language theorem explainer
Recognition Science assigns the rank of SU(3) the value 3 to coincide with the spatial dimension D. This constant is cited by researchers deriving gauge theory vertices from the Recognition Science forcing chain. It establishes that the strong interaction is non-Abelian, permitting three-gluon and four-gluon vertices. The definition is introduced by direct assignment of the natural number 3.
Claim. The rank of the Lie group $SU(3)$ equals the natural number 3, identified with the spatial dimension $D$.
background
The module derives Feynman diagrams as the perturbative expansion of the S-matrix in Recognition Science, with each vertex realized as a J-cost coupling event. Five canonical vertex types appear in the Standard Model (3-gluon, 4-gluon, quark-gluon, W-fermion, Higgs-fermion), whose total equals the configuration dimension 5. The 3-gluon and 4-gluon vertices exist because SU(3) is non-Abelian, which holds when its rank equals D (non-commutative for D ≥ 2).
proof idea
The declaration is a direct definition that assigns the constant value 3 in the natural numbers. No lemmas are invoked; the companion equality theorem reduces immediately by reflexivity.
why it matters
This definition supplies the numerical value required by the su3_rank_D field inside the FeynmanCert structure, which also records five_vertices = 5 and non_abelian = 2. It thereby links the forcing-chain result T8 (D = 3) to the presence of non-Abelian gauge vertices in the RS-derived QFT. The parent result is the certification that the diagram expansion reproduces the Standard Model vertex set.
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