e_022030

This module is chunk 2 of a 256-cell kernel certification that the 4D Regge midpoint numerator $N_2$ equals eight times an explicit closed-form table $Z$ on every sextuple of indices in $\mathrm{Fin},4$.

Upstream, $N_2(a,b,c,d,i,j)$ is defined by folding a fixed coupling list and summing each term's contribution at those indices. The companion table $Z$ is a pattern-matched integer function on the same six $\mathrm{Fin},4$ arguments (sample clauses include $Z(0,0,1,1,2,2)=4$ and $Z(0,0,1,2,1,2)=-2$).

The local goal is purely algebraic bookkeeping: discharge one concrete index cell so a later exhaustive fin_cases assembly can conclude the identity for all $4^6$ inputs.

One-line computational proof: decide evaluates both sides at the fixed indices $(0,2,2,0,3,0)$. The left side reduces by unfolding the fold over the coupling list; the right side multiplies the matched table entry by 8. Both are concrete integers, so the kernel closes the equality with no lemmas beyond definitional reduction.

Feeds the parent assembly theorem m2Num_eq_eight_explicitZ, which states $\forall a,b,c,d,i,j,, N_2=8Z$ and proves it by six nested fin_cases over $\mathrm{Fin},4$, each leaf a chunk cell like this one.

In the Recognition gravity stack, that global identity is the certified algebraic core of the exact midpoint M2 TT relation in 4D Regge calculus. Without the cell-by-cell kernel, the assembly cannot discharge the numerator side. This is scaffolding closure for a proved identity, not an open physical hypothesis; it does not itself invoke the forcing chain (T5–T8) or the RCL, but sits downstream in the discrete gravity analysis those landmarks motivate.