higgsHypercharge6

The module continues the cube-completion gauge skeleton (SU(3)×SU(2)×U(1) with recognition-axis counts (3,2,1) and carrier counts (8,3,1)) by asking whether SM fermion multiplets and hypercharges fit the same arithmetic. Every hypercharge is stored as the integer $Y_6 = 6Y$, so all anomaly sums become exact integer arithmetic.

One left-handed generation (including a sterile $\nu^c_L$ at $Y_6 = 0$) is listed with multiplicities and $Y_6$ values that total 16 Weyl states and cancel the usual $SU(3)^2U(1)$, $SU(2)^2U(1)$, mixed gravitational-$U(1)$, and $U(1)^3$ anomalies. The Higgs doublet is the scalar that must sit in the same unit system; its textbook value $Y = 1/2$ becomes $Y_6 = 3$.

This layer is still only a faithful encoding of the anomaly-free SM hypercharge assignment in cube units, not a uniqueness proof that those charges are forced.

Pure definition: the constant is the integer literal 3. No lemmas, tactics, or computation. The companion equality theorem is just rfl.

Supplies the Higgs entry in the cube-unit hypercharge table used by the local certificate SMHyperchargeCert (six multiplets, 16 states per generation, anomaly vanishing) and by the equality wrapper higgsHypercharge6_eq. Downstream it feeds the gauge/SM routing bridge T8_To_GaugeStandardModel_Bridge in the unified forcing chain, which ties T8 (D = 3) to the compact gauge skeleton and SM multiplet layer. Framework role: after T8 forces three spatial dimensions and the cube, this constant is the scalar hypercharge needed so the SM layer sits in the same 1/6 units as the fermion $Y_6$ list. It does not close uniqueness of hypercharges; the module doc is explicit that the assignment is the standard anomaly-free layer, not a forcing theorem.