e_013131

This module is chunk 1 of a 256-cell kernel certification that the midpoint Regge mass-squared numerator equals eight times an explicit integer coupling table on $(\mathrm{Fin},4)^6$.

The numerator m2Num is defined by folding a fixed coupling list: it sums contribution terms contrib t a b c d i j over that list, yielding an integer. The comparison target explicitZ is a closed-form case table on the same six indices (sample values include $4$, $-2$, and so on for the listed patterns).

The local goal is purely algebraic bookkeeping in 4D discrete gravity analysis: verify the scalar identity cell-by-cell so a later assembly theorem can quantify over all index sextuples.

One-line computational proof: decide. Both sides reduce to concrete integers once the six Fin 4 arguments are fixed at $(0,1,3,1,3,1)$, so the kernel equality checker discharges m2Num ... = 8 * explicitZ ... with no manual case split or rewrite.

Feeds the assembly theorem m2Num_eq_eight_explicitZ, which states the identity for every $(a,b,c,d,i,j)$ in $(\mathrm{Fin},4)^6$ and is proved by exhaustive fin_cases. Each chunk theorem such as this one is a named kernel cell in that cover.

In the Recognition gravity stack this is infrastructure for the exact midpoint Regge $M^2$/TT identity in 4D: it certifies that the folded numerator matches the explicit $Z$ table (scaled by 8) at one lattice point, with no analytic remainder. It does not itself invoke the forcing chain (T0–T8) or the J-cost; it is a discrete tensor-identity brick those continuum claims sit on once the Regge calculus side is closed.