w14

Module setting is Gate C-A3 of the QG full-theory campaign (Paper C / Pillar 1, Lane C): close the hinge-aware zero mode for the assembled Regge TT constant block. The stencil-only constant residual at the reported TT witness does not vanish; the hinge term cancels it under the relative-minus assembly convention, so the assembled $k=0$ block is zero on TT.

The raw coefficient is the single-entry radical form $J_{fg}/(2\sqrt{a^*_f})$, not a fiber sum. Independently, the full 36-entry rational stencil table records the radical-free normal forms of those coefficients; the entry at left=1, right=4 is the literal rational $1/4$. The universal evaluation theorem states every raw coefficient equals the corresponding table entry cast to $\mathbb{R}$.

One-line wrapper. Rewrite by the universal evaluation theorem rawJacobianCoefficient_eval at indices $(1,4)$, which replaces the radical form by the rational stencil weight of bucket $\langle 1,4\rangle$. Then norm_num on that table definition discharges the equality to $1/4$.

Supplies one concrete table entry used when the free-coefficient contraction of the six tetrahedron types is expanded into the perfect square $(c_0+c_1+c_2-c_3-c_4-c_5+c_6)^2/2$. That identity is the algebraic shape of the assembled constant block: it vanishes exactly on the alternating-sum hyperplane where geometric edge-class coefficient vectors live.

Downstream, the same coefficient table feeds the full-star homothety stationarity theorems in the 4D star-kernel modules (support-restricted and full 15-class sums). Within Gate C-A3 this is scaffolding for the zero-mode headline: assembled constant block equals zero at the TT witness after hinge cancellation of the recorded stencil residual.