e_010210

This module is chunk 1 of a 256-way kernel certification that the midpoint M2 numerator coincides with eight times a sparse explicit table on $(\mathrm{Fin},4)^6$. The numerator is defined by folding a coupling list and summing a local contribution at each multi-index; the explicit table hard-codes the nonzero integer values that the identity is expected to match (e.g. $\pm 2,,4$ on selected patterns, zero elsewhere).

The ambient setting is exact algebraic bookkeeping for a 4D Regge/TT midpoint identity in the Gravity analysis layer: once every concrete multi-index satisfies numerator $= 8Z$, the global identity follows by exhaustive case split rather than by a closed-form symbolic argument.

One-line computational proof: decide evaluates both sides at the fixed six-tuple of Fin 4 values and checks integer equality. No lemmas are invoked beyond the definitions of the folded numerator and the explicit table.

Feeds the assembly theorem m2Num_eq_eight_explicitZ, which states the identity for all six Fin 4 arguments by nested fin_cases and dispatches each leaf to a chunk theorem of this form. Without the full 256-case cover, the midpoint M2–TT numerator identity stays uncertified. This is pure algebraic scaffolding inside the Gravity analysis path; it does not itself invoke the RS forcing chain (T5–T8) or the Recognition Composition Law, but it locks a concrete 4D discrete-gravity identity used downstream in that stack.