e_023031

In the 4D Regge midpoint analysis, two integer-valued kernels on six $\mathrm{Fin},4$ indices are compared. The numerator $\mathrm{m2Num}$ is defined by folding a fixed coupling list and summing each term's contribution at the given indices. The comparison target $\mathrm{explicitZ}$ is a piecewise closed-form integer table on the same six indices (typical nonzero entries are $\pm 2$ or $4$).

The local module is chunk 2 of a 256-cell decide grid that discharges $\mathrm{m2Num}=8\cdot\mathrm{explicitZ}$ pointwise. The identity is purely combinatorial on finite index sets; no continuum limit or variational argument is invoked inside the chunk.

One-line kernel proof: decide evaluates both sides at the concrete sextuple $(0,2,3,0,3,1)$ and checks integer equality. No lemmas beyond the definitions of $\mathrm{m2Num}$ and $\mathrm{explicitZ}$ are required; the Fin 4 values are closed under reduction to bare integers.

Feeds the assembler m2Num_eq_eight_explicitZ, which states the identity for all six $\mathrm{Fin},4$ arguments by exhaustive fin_cases and invokes each chunk cell such as this one. That global equality is the algebraic core of the Regge-exact midpoint M2–TT identity in the gravity analysis stack: it certifies that the folded coupling numerator is exactly eight copies of the explicit kernel, so midpoint curvature bookkeeping matches the closed form used downstream.

Within Recognition Science gravity work this is scaffolding for discrete curvature identities on the eight-tick / $D=3$ side, not a forcing-chain (T0–T8) step. It closes one of 256 decide obligations rather than an open physical hypothesis.