IndisputableMonolith.Physics.StandardModelGroupStructure
This module defines the gauge group ranks and boson counts for the Standard Model inside the Recognition Science framework. It records the gluon count as eight from the SU(3) adjoint. A researcher matching the Standard Model to the phi-ladder mass formula would cite these values. The module consists of direct group-theoretic definitions with no complex derivations.
claimThe module defines the ranks $rank(SU(3))=2$, $rank(SU(2))=1$, $rank(U(1))=1$, the gluon count $N^2-1=8$ for $SU(3)$, the W boson count $3$, and the total gauge carrier count.
background
Recognition Science incorporates the Standard Model by assigning the gauge group $SU(3)×SU(2)×U(1)$ after the forcing chain reaches D=3. This module supplies the rank and dimension data for each factor together with the resulting carrier counts. The gluon count follows the standard adjoint formula $N^2-1$ evaluated at N=3.
proof idea
This is a definition module, no proofs.
why it matters in Recognition Science
These definitions feed the group ranks and carrier counts into the Recognition Science constructions that place gauge bosons on the phi-ladder. They supply the inputs needed for the total carrier count that aligns with the eight-tick octave. The module closes the group-structure step between T8 and the Standard Model spectrum.
scope and limits
- Does not derive the gauge group from the J-uniqueness or Recognition Composition Law.
- Does not compute coupling constants or particle masses.
- Does not treat fermion representations or the Higgs sector.
- Does not connect to gravity or the full forcing chain.