e_312231

This module is chunk 13 of a 256-cell kernel certifying that the folded numerator of the 4D Regge midpoint M2TT identity agrees with a closed integer table, scaled by eight. Indices run over $\mathrm{Fin},4$, labeling discrete edge/face slots in the midpoint stencil.

The numerator $N=m2Num$ is defined by folding a fixed coupling list: start at 0 and add each local contribution at the six-index slot. The table $Z=explicitZ$ is a pattern-matched integer function on the same six $\mathrm{Fin},4$ arguments (sample values include $4$, $-2$, and so on for distinguished index patterns).

The local claim is one concrete cell of $N=8Z$. The parent assembly theorem quantifies over all six indices by exhaustive fin_cases.

One-line computational proof: decide. Both sides reduce to concrete integers once the six $\mathrm{Fin},4$ arguments are fixed at $(3,1,2,2,3,1)$, so the kernel equality checker discharges $N=8Z$ with no manual algebra.

Feeds the assembler m2Num_eq_eight_explicitZ, which states $\forall a,b,c,d,i,j,, N=8Z$ by six nested fin_cases over the 256 cells. Each chunk theorem such as this one is a named kernel witness the assembler (or an equivalent decide sweep) relies on.

In the gravity analysis stack this closes the algebraic identity between the summed midpoint coupling numerator and the explicit integer table used in the 4D Regge M2TT midpoint certification. It is bookkeeping infrastructure, not a new physical law: once all cells match, the midpoint identity can quote a single universal equality instead of a fold.