IndisputableMonolith.Physics.IsospinSymmetryFromRS
This module constructs the isospin symmetry structure inside Recognition Science by tying SU(2) representations to the forced spatial dimension D=3. It introduces su2Rank, su2Generators, IsoSpinMultiplet, and the IsospinCert predicate along with their basic counting and equality lemmas. The definitions follow from the dimension-forcing step of the unified chain without additional hypotheses.
claimThe isospin symmetry is realized by the Lie algebra su(2) of rank $D-1=2$ with three generators matching the spatial dimensions $D=3$. An isospin multiplet is a finite set of states classified by their dimension, counted by isoSpinMultipletCount and certified by the predicate IsospinCert.
background
Recognition Science forces D=3 through the eight-tick octave and the self-similar fixed point phi after J-uniqueness. This module sits in the physics layer and introduces the SU(2) structure that arises once three dimensions are fixed. The sibling definitions su2Rank_eq_Dm1 and su2Generators_eq_D make the rank and generator count explicit consequences of that dimension. IsoSpinMultiplet and IsospinCert supply the representation-theoretic language used downstream for particle classification.
proof idea
This is a definition module, no proofs.
why it matters in Recognition Science
The module supplies the isospin symmetry layer that feeds the mass formula and multiplet counting used in later particle derivations. It closes the step from the T8 dimension result to concrete SU(2) representations without introducing new constants or hypotheses.
scope and limits
- Does not derive the full electroweak gauge group.
- Does not compute numerical mass values or mixing angles.
- Does not address color SU(3) or higher symmetries.
- Does not treat time-reversal or parity violation.