e_331111

This module is chunk 15 of the 256 kernel decides that establish $m_2^{\mathrm{num}}=8\cdot Z$ pointwise on $(\mathbb{F}_4)^6$. The ambient setting is 4D Regge calculus at the exact midpoint: discrete curvature couplings are reduced to an integer-valued numerator on six finite indices.

The numerator $m_2^{\mathrm{num}}(a,b,c,d,i,j)$ is defined by folding a fixed coupling list and summing each term's contribution at those indices. The comparison object $Z$ is an explicit pattern-matched integer table on the same six $\mathrm{Fin},4$ arguments (sample clauses include $Z(0,0,1,1,2,2)=4$ and $Z(0,0,1,2,1,2)=-2$).

Both definitions live in the kernel certificate module; this chunk only discharges one concrete sextuple.

One-line computational proof: decide evaluates both sides as concrete integers (the fold defining the numerator versus eight times the matched $Z$ entry) and closes the equality in the kernel. No algebraic lemmas are invoked beyond the decidable integer arithmetic of the two closed definitions.

Feeds the assembly theorem m2Num_eq_eight_explicitZ, which states $\forall a,b,c,d,i,j,; m_2^{\mathrm{num}}=8Z$ and is proved by exhaustive fin_cases on all six indices. Each chunk theorem such as this one is a leaf of that case split.

In the Recognition gravity stack, the identity certifies that the midpoint Regge mass-squared numerator is exactly eight copies of the explicit kernel, a discrete bookkeeping step toward the continuum TT-sector match. It is pure finite enumeration, not a continuum limit argument, and does not itself invoke the forcing chain (T0–T8) or the Recognition Composition Law.