e_220321

In the 4D Regge midpoint analysis, the $M_2$ numerator is an integer-valued six-index array on $\mathbb{F}_4$. It is defined by folding a fixed coupling list: each term contributes an integer contrib and the fold accumulates the total. Independently, an explicit kernel $Z$ is given by a finite pattern-match table of small integers (entries such as $4$, $-2$, and so on).

The local module is chunk 10 of a 256-way case split: the claim is that the folded numerator equals eight times the table value at every multi-index. Upstream, m2Num is exactly that fold, and explicitZ is the table. The factor eight is the global normalization relating the summed coupling contributions to the closed kernel.

One-line computational proof: decide. Both sides are closed integer expressions once the six Fin 4 arguments are concrete literals, so the kernel evaluates the fold defining the numerator and the pattern match defining $Z$, then checks equality with $8Z$. No lemmas are invoked beyond the definitions of the two sides.

This is one atomic cell in the exhaustive verification that $m_2=8Z$ on all of $(\mathbb{F}_4)^6$. The parent theorem m2Num_eq_eight_explicitZ introduces six free Fin 4 indices and discharges them by nested fin_cases, each leaf citing a chunk identity of this form. That global equality is the algebraic content of the Regge exact midpoint $M_2$ TT identity in 4D: the numerator built from couplings collapses to a sparse explicit kernel. Within Recognition gravity, such exact discrete identities underwrite continuum limits and curvature bookkeeping on the causal lattice; they sit downstream of the forcing chain's $D=3$ spatial claim only insofar as the 4D spacetime scaffolding is fixed. No open sorry remains on this leaf.