e_311022

In the 4D Regge exact-midpoint analysis, the numerator m2Num is obtained by folding a fixed coupling list: each term contributes an integer depending on six Fin-4 indices, and the fold starts at 0. The companion table explicitZ assigns a sparse pattern of small integers (typically $\pm 2,,4$, or 0) to the same six-index slots.

The module is chunk 13 of a 256-cell kernel certification: every concrete sextuple must satisfy m2Num = 8 · explicitZ so that the global identity can be assembled by exhaustive fin_cases. The local setting is pure integer arithmetic on Fin 4; no continuum limit or physical units enter at this layer.

One-line kernel proof: by decide. Both sides reduce to concrete Int values (m2Num by folding the coupling list at the fixed indices; explicitZ by table lookup), and the equality $N = 8Z$ is discharged by the decidable equality instance on integers. No lemmas beyond the two definitions are invoked.

This cell is consumed by m2Num_eq_eight_explicitZ, which states the identity for all six Fin-4 arguments and proves it by nested fin_cases, each branch hitting one chunk theorem such as this one. Closing every cell certifies that the folded midpoint numerator is exactly eight times the explicit kernel, a numerical identity needed for the Regge exact-midpoint M2TT analysis in the Gravity domain. It is bookkeeping infrastructure rather than a new physical law; once the full 256-case cover is in place, the assemble theorem becomes a pure case split with no sorry.