e_030333

In the 4D Regge exact-midpoint analysis, the numerator m2Num is the fold of a fixed coupling list: it sums contribution terms over six indices in $\mathrm{Fin},4$. The companion table explicitZ is a sparse pattern-matched integer kernel on the same six indices (typical nonzero entries are $\pm 2$ or $4$).

This module is chunk 3 of the certification that the numerator is identically eight times the explicit kernel. The local setting is pure finite enumeration: 256 kernel decides, one per index sextuple, with no analytic remainder.

Upstream, both sides are already defined in the kernel-cert module; the present lemma only pins one concrete point of the identity.

One-line wrapper: by decide. With all six indices ground, both sides reduce to concrete integers (m2Num by folding a finite list, explicitZ by pattern match). Lean’s decision procedure checks numeral equality; no lemmas are invoked beyond the definitions.

Feeds the assembly theorem m2Num_eq_eight_explicitZ, which states the identity for every sextuple in $\mathrm{Fin},4$ and proves it by nested fin_cases, landing on these pointwise chunk lemmas. That global equality is the algebraic core of the exact midpoint M2TT identity in the gravity analysis stack. It sits in the discrete Regge sector that supports Recognition Science continuum limits; it does not itself touch the forcing chain (T0–T8) or the J-cost, but supplies a certified numerator identity those continuum arguments rely on when they specialize to 4D midpoint stencils.