e_323201

In the 4D Regge midpoint analysis, two integer-valued kernels on six Fin-4 indices are compared. The numerator $m_2^{\mathrm{num}}$ is the fold of a fixed coupling list: each term contributes an integer via a local weight, and the fold starts at 0. The companion table $Z$ is an explicit pattern-matched function on the same six indices, returning small integers (e.g. $\pm 2,4$) on the nonzero support and (by default) zero elsewhere.

This module is chunk 14 of the 256-way kernel split that discharges $m_2^{\mathrm{num}}=8Z$ by concrete decision at each multi-index. The local setting is pure integer arithmetic on Fin-4 labels; no continuum limit or metric signature is invoked here.

One-line computational proof: decide evaluates both sides at the fixed indices $(3,2,3,2,0,1)$. The left side runs the fold that defines $m_2^{\mathrm{num}}$; the right side looks up $8\cdot Z$ in the explicit table. Both reduce to the same Int, so the equality is closed by the kernel decision procedure. No lemmas beyond the two definitions are required.

Feeds the parent assembly theorem m2Num_eq_eight_explicitZ, which states $\forall a,b,c,d,i,j,, m_2^{\mathrm{num}}=8Z$ and proves it by six nested fin_cases sweeps. Each concrete residue class (including this $(3,2,3,2,0,1)$ cell) is discharged by a chunk decide of this form. Closing the pointwise table is a bookkeeping step toward the exact midpoint $M_2$ TT identity in 4D Regge calculus used in the Gravity analysis stack; it does not itself touch the T0–T8 forcing chain or the Recognition Composition Law.