e_010003

This module is chunk 1 of a 256-case kernel certification that the 4D Regge midpoint numerator agrees with an explicit integer table, up to the universal factor 8. The ambient setting is discrete gravity analysis: curvature and stress-energy contributions on a 4-simplex lattice are reduced to integer couplings indexed by six $\mathrm{Fin},4$ labels.

The numerator $m_2^{\mathrm{num}}$ is defined by folding a fixed coupling list: start at 0 and add each term's contribution at the given multi-index. The comparison object $Z_{\mathrm{explicit}}$ is a pattern-matched integer table on the same six indices (typical nonzero entries are $\pm 2,\pm 4$). The claim is pure integer equality at one concrete slot.

One-line computational proof: decide evaluates both sides as concrete Int values and checks equality in the kernel. No algebraic lemmas are invoked; the definitions of m2Num (fold of contributions) and explicitZ (table lookup) reduce to numerals at this fixed multi-index.

Feeds the assembly theorem m2Num_eq_eight_explicitZ, which states the identity for every six-tuple in $(\mathrm{Fin},4)^6$ by exhaustive fin_cases. That universal equality is the certified form of the Regge exact-midpoint M2–TT identity in 4D: the folded numerator is exactly eight times the closed-form table. Each chunk theorem such as this one discharges one leaf of the case tree, so the full gravity identity is only as strong as the conjunction of these decides. Landmark contact is the discrete 4D geometry side of Recognition gravity (spatial $D=3$ plus time), not the T5–T8 forcing chain directly.