Scope
This sub-programme asks which internal symmetries, if any, are selected by admissible non-injective projection. It contains fibre-fixed-point proposals, charge and chirality constructions, and a heat-kernel derivation of Yang–Mills equations conditional on a supplied compact group and connection.
Corrected status. The programme does not derive $G_{\mathrm{SM}}=\mathrm{SU}(3)\times\mathrm{SU}(2)\times\mathrm{U}(1)$. O31 version 2.0 withdraws the colour-triplet co-admissibility, $\mathrm{SU}(3)$ uniqueness and complete-group chain. Colour, commutation, direct-product structure and the complete gauge group remain open.
Surviving chain
- Q6a organises phase and conjugate-pair symmetries as proposed $\mathrm{U}(1)$ and $\mathrm{SU}(2)$ fixed points, subject to explicit carrier and identification assumptions.
- O27 supplies the canonical representation action $\mathfrak{su}(2)\to\operatorname{End}(V_\rho)$ only after the conditional carrier and identification are supplied; the relevant equivariant intertwiner is unique only up to a scalar. It does not construct a vector lift.
- Q12 derives the local Yang–Mills equation from vertical spectral variation for a supplied compact gauge group and admissible connection. It does not select the group.
- O32 retains finite-$q$ numerical measurements, without the withdrawn pointwise co-admissibility or $\mathrm{SU}(3)$ interpretation.
Constituent papers
Open problems
- Construct a canonical causal carrier and the required inter-sector identifications.
- Identify a colour representation and compact group without importing the withdrawn O31 claims.
- Prove determinant, commutation and direct-product properties if a multi-factor group is proposed.
- Derive the weak-current $V-A$ structure and extend the monopole analysis beyond the canonical model.