Calculation record
Verify geometric projections, spin bilinears and moment fixed points.
These are mathematical controls for stated models, not fitted particle
couplings or an observational neutrino test.
Research context
- Nested moment coupling
The dot-square kernel on centered isotropic nested subspaces gives a minimum-depth Gram matrix of full rank, despite factorized bare coefficients.
- Five-dimensional spinor bilinears
Explicit five-dimensional Clifford matrices have an invariant antisymmetric bilinear and a quaternionic reality map; allowed interaction terms additionally depend on field statistics and the full symmetry representation.
- Hopf fibre and invariant channel projectors
Circle averaging selects a definite fibre weight, while a colour singlet requires invariance under the full colour action; explicit projectors separate these conditions.
- Self-consistent functional
A reusable harmonic mean-field closure with explicit norm and variation assumptions.
Interpret numerical checks within the assumptions and limitations documented in these notes.