ew_boson_dof_eq

This module records exact arithmetic identities that rewrite imported Standard Model degree-of-freedom counts in D-flavored notation at the forced spatial dimension D = 3 (T8 / DimensionForcing). It does not derive the SM spectrum: gauge representations, polarizations, and thermal weights are imported physics; only the numerical re-expressions are kernel-checked here.

The local definition counts unbroken-phase EW gauge bosons as $2(D-1)^2$. Physically that is SU(2)×U(1) with four generators and two transverse polarizations each, totaling 8; the formula is bookkeeping of that imported content, not an RS derivation of the group or the polarization count. Sibling identities in the same file re-express fermionic DOF, the 7/8 Fermi–Dirac weight as $(2^D-1)/2^D$, and the assembled $g_\star = 106.75$ identity.

One-line native_decide proof. Unfolding the definition gives $2((D-1)^2)$ with $D = 3$, so $2(2^2) = 8$, which the kernel evaluates directly.

Closes the EW-boson side of the module’s DOF arithmetic bridge: the unbroken-phase gauge count is pinned at 8 in the same D = 3 language used for eight-tick cadence ($2^D = 8$) and generation count. Downstream assembly of high-T $g_\star$ (bosonic 28 plus $(7/8)\times 90$) needs this 8 as part of the bosonic total; the module’s honest split keeps the identity as verified bookkeeping, not a claim that RS forced SU(2)×U(1) or transverse polarizations. No used_by edges are recorded yet; the value is available for any later $g_\star$ or EW-threshold lemma that sums bosonic DOF.