Schur functions at (1,-1,t,1/t): a closed form on the non-identity component of O(4) (Part IV).

What the Higgs Potential Cannot See: bulk matter that cannot help select a boundary condition (Part V).

Three self-contained pages for 6D SU(4) gauge-Higgs unification on T^2/Z_2: the alpha-domain selection rule (Part III), a model calculator that takes a matter content and returns the Higgs (Parts IV-V), and an eta-meter that predicts what the boundary sign does in closed form and checks itself against the loop sum.

A centre-charge selection rule for the Wilson-line potential: the fundamental domain of gauge-Higgs unification is representation-dependent (Part III).

Anomaly- and tadpole-compatible fermion completion of 6D SU(4) gauge-Higgs unification (exact, Lean-checked) (Part I).

Three Gates to a Quark Generation: an exact criterion for which SU(4) representations contain the Standard Model (Part II).

Reproducible verification for the paper Gap-protected spectral invariants on T^d/Z_2 (doi:10.5281/zenodo.20597195)