IndisputableMonolith.Foundation.GaugeGroupCube
The module defines the ranks of the three standard model gauge groups SU(3), SU(2), U(1) along with their sum and a cube-face decomposition. A particle physicist working in Recognition Science would cite these when embedding the gauge sector. The module consists entirely of definitions and elementary equalities with no tactic proofs.
claimThe module introduces the gauge ranks $\mathrm{rank}(SU(3))$, $\mathrm{rank}(SU(2))$, $\mathrm{rank}(U(1))$, the total rank, the 3-2-1 partition, and the cube face-pair relation certified by GaugeCubeCert.
background
Recognition Science places gauge structure inside the Foundation layer that precedes the forcing chain T0-T8. The module supplies the concrete ranks for the standard-model gauge group SU(3)×SU(2)×U(1) and encodes them as a geometric cube whose six faces correspond to the rank sum. Sibling definitions include gaugeRankSU3, gaugeRankSU2, gaugeRankU1, totalGaugeRank, rankDecomposition, cubeFacePairs, and the certificate GaugeCubeCert.
proof idea
this is a definition module, no proofs
why it matters in Recognition Science
These rank definitions supply the gauge-sector input required by later Recognition Science results on the standard-model spectrum and the D=3 spatial structure. The module therefore sits directly beneath any theorem that invokes the 3-2-1 gauge partition inside the unified forcing chain.
scope and limits
- Does not derive the gauge groups from the J-functional equation.
- Does not prove uniqueness of the 3-2-1 partition.
- Does not compute numerical values of the gauge couplings.
- Does not link ranks to the phi-ladder or mass formula.