w43

This module closes Gate C-A3 of the QG full-theory campaign (Paper C / Pillar 1): the hinge-aware zero mode of the assembled Regge TT constant block. The raw Jacobian coefficient is the single-entry radical form $J_{fg}/(2\sqrt{a^*_f})$, used before full fiber aggregation. Independently, a literal rational stencil table records the radical-free normal form of every slot pair; the evaluation theorem identifies each raw coefficient with the corresponding table entry as a real.

Only the assembled (hinge minus stencil) block is claimed to vanish at the TT witness. The free-coefficient contraction over six tetrahedron types is expanded entrywise from these rationals, so each concrete pair such as $(4,3)$ must be pinned before the perfect-square identity can be stated.

One-line wrapper. Rewrite by the universal evaluation theorem rawJacobianCoefficient_eval at arguments $4,3$, which replaces the radical coefficient by the cast of the literal rational stencil weight at bucket $\langle 4,3\rangle$. Then norm_num on that table entry yields $-1/4$.

Feeds zeroMode_free_coefficients, the algebraic identity that the raw-table contraction over six tetrahedron types equals $(c_0+c_1+c_2-c_3-c_4-c_5+c_6)^2/2$. That perfect square vanishes exactly on the alternating-sum hyperplane inhabited by geometric edge-class coefficient vectors, and is the shape of the assembled constant block at $k=0$. Pinning every rational entry (including this off-diagonal $-1/4$) is required before the free-coefficient expansion can be discharged by simp and arithmetic. Sits inside the Gate C-A3 zero-mode headline that the Schlaefli-reduced assembled constant block vanishes for TT data.