e_221302

This module is chunk 10 of a 256-way kernel certification that the midpoint Regge $m_2$ numerator equals eight times an explicit integer table on all six-index combinations in $(\mathrm{Fin},4)^6$.

Upstream, $m_2\mathrm{Num}(a,b,c,d,i,j)$ is defined by folding a fixed coupling list: it accumulates every local contribution at those indices into a single integer. The companion table $\mathrm{explicit}Z$ is a pattern-matched $\mathrm{Fin},4^6\to\mathbb{Z}$ function that records the closed-form values the fold is expected to hit (e.g. $4$, $-2$, and sparse zeros elsewhere).

The local claim is one concrete cell of that comparison, at multi-index $(2,2,1,3,0,2)$.

One-line kernel proof: decide evaluates both sides as concrete integers (the fold defining the numerator versus eight times the matched table entry) and discharges equality by computation. No lemmas beyond the two definitions are required.

Parent theorem m2Num_eq_eight_explicitZ quantifies over all six Fin-4 indices and proves $m_2\mathrm{Num}=8\cdot\mathrm{explicit}Z$ by exhaustive fin_cases; each chunk theorem such as this one supplies one decided cell of that case tree. In the Recognition gravity stack this identity is the algebraic certificate that the midpoint Regge mass-squared numerator collapses to a sparse explicit kernel, the discrete input needed before continuum or continuum-limit gravity statements. It does not itself touch the forcing chain (T5–T8) or the RCL; it is pure 4D combinatorial bookkeeping inside the Regge analysis layer.