IndisputableMonolith.Foundation.SMGaugeAlgebra
The SMGaugeAlgebra module supplies generator counts for the Standard Model gauge groups inside the Recognition Science foundation. It states that su(N) has N squared minus one generators and extends the count to U(1) and the full SM factor. Researchers assembling gauge degrees of freedom for mass formulas or interaction counts cite these values. The module contains only definitions and no proof obligations.
claimThe Lie algebra of the special unitary group satisfies $dim(su(N)) = N^2 - 1$.
background
This module sits in the Foundation layer and introduces the generator-counting functions for the Standard Model gauge algebra. It defines suGenCount(N) as the dimension of su(N), uGenCount for the U(1) factor, and SMGaugeFactor together with the combined smTotalGenCount. The setting imports basic Lie-algebra facts from Mathlib and applies them to the groups SU(3), SU(2), and U(1) that appear in the SM gauge structure.
proof idea
This is a definition module, no proofs.
why it matters in Recognition Science
The generator counts supplied here are prerequisites for the SM gauge algebra certification and total generator tally used in downstream particle-mass and interaction calculations. They furnish the algebraic degrees of freedom that enter the Recognition Science treatment of gauge bosons on the phi-ladder.
scope and limits
- Does not derive the choice of SU(3) x SU(2) x U(1) from the forcing chain.
- Does not include representation theory or charge assignments.
- Does not connect the counts to the J-function or RCL.