e_321121

This module is chunk 14 of a 256-cell kernel certification that the 4D Regge midpoint M2TT numerator equals eight times an explicit integer table. Indices run over Fin 4 (four spacetime directions).

The numerator $N(a,b,c,d,i,j)$ is defined by folding a fixed coupling list: each term contributes an integer via a local contribution map, and the fold starts at 0. The explicit kernel $Z$ is a pattern-matched table on six Fin-4 indices, returning small integers such as $4$, $-2$, and so on for the nonzero support.

The local claim is one concrete cell of the identity $N=8Z$. Upstream, both $N$ and $Z$ are pure definitions in the kernel certificate module; no analytic lemma is required beyond evaluating those definitions at fixed indices.

One-line computational proof: decide evaluates both sides at the literal indices $(3,2,1,1,2,1)$ and checks integer equality. No lemmas are invoked; the kernel reduces the fold defining the numerator and the pattern match defining the explicit table to concrete Int values, then confirms they stand in the ratio $8$.

Parent theorem is the full assembly m2Num_eq_eight_explicitZ, which states $\forall a,b,c,d,i,j,, N=8Z$ by exhaustive fin_cases on all six indices. Each chunk theorem such as this one discharges one cell so the assembly case split stays modular and kernel-checkable.

In the Recognition gravity stack this identity is bookkeeping for the exact midpoint Regge calculus in 4D: it certifies that the discrete curvature/mass-side numerator matches the closed-form kernel used downstream. It does not itself invoke the forcing chain (T5–T8) or the Recognition Composition Law; it is pure discrete-geometry arithmetic supporting the gravity analysis layer.