IndisputableMonolith.Physics.StandardModelGroupStructure
The module defines ranks and boson counts for the Standard Model gauge groups SU(3) x SU(2) x U(1) inside Recognition Science. It supplies explicit values such as rankSU3 = 2, rankSU2 = 1, rankU1 = 1 and gluon count = 8. Gauge-theory modelers in the phi-ladder setting cite these counts for carrier tallies. The module consists entirely of definitions and direct equalities.
claim$rank(SU(3)) = 2$, $rank(SU(2)) = 1$, $rank(U(1)) = 1$, gluon count $= 3^2 - 1 = 8$, $W$-boson count $= 3$, total rank $= 4$, total carriers as the sum over gauge bosons.
background
Recognition Science obtains all physics from the single J-functional equation and the T0-T8 forcing chain. This module supplies the internal symmetry data for the Standard Model. It introduces SMGaugeBosonType as the enumeration of gauge bosons, smGaugeBosonCount as the multiplicity function, rankSU3, rankSU2 and rankU1 as the ranks of the respective Lie algebras, totalRank as their sum, gluonCount and gluon_count as the explicit value 8, wBosonCount as 3, and totalCarriers together with total_carriers_eq as the summed carrier count. The supplied doc-comment states gluon count = N² - 1 = 8 for SU(3).
proof idea
this is a definition module, no proofs
why it matters in Recognition Science
These definitions feed the totalCarriers and total_carriers_eq equalities that supply concrete boson numbers to downstream mass-ladder and carrier-count calculations in the Recognition Science Standard Model. They furnish the numerical inputs required to match observed gauge bosons while remaining inside the eight-tick octave and D = 3 framework.
scope and limits
- Does not derive the gauge group SU(3) x SU(2) x U(1) from the J-equation.
- Does not treat fermion representations or the Higgs sector.
- Does not compute coupling constants or running.
- Does not address spontaneous symmetry breaking.