e_201100

In the 4D Regge midpoint analysis, the M2 numerator at six discrete indices is defined by folding a fixed coupling list: each term contributes an integer, and the fold starts from zero. The companion object is an explicit integer kernel $Z$ on the same six $\mathrm{Fin},4$ arguments, given by a finite pattern-match table (e.g. diagonal-type slots map to $4$ or $-2$).

The local module is chunk 8 of a 256-way case split: the claim is that the folded numerator equals $8\cdot Z$ at every multi-index. This file discharges one concrete slot by kernel decision rather than by a symbolic identity.

Upstream, both the fold definition and the explicit table live in the kernel certificate module; the present theorem only evaluates them at $(2,0,1,1,0,0)$.

One-line computational proof: decide evaluates both sides as concrete Int expressions (the fold of contributions versus eight times the table entry) and closes the equality by kernel reduction. No lemmas are invoked beyond the definitions of the numerator fold and the explicit kernel.

Parent theorem m2Num_eq_eight_explicitZ assembles all 256 index cases into the universal statement that the M2 numerator equals eight times explicit $Z$ on every six-tuple in $(\mathrm{Fin},4)^6$. That assembly is the algebraic backbone of the Regge exact midpoint M2–TT identity in 4D gravity analysis inside the monolith.

Within Recognition Science gravity work, such identities constrain discrete curvature and coupling bookkeeping on the lattice side of the continuum limit. This chunk does not itself touch the forcing chain (T0–T8) or the J-cost; it is pure integer kernel hygiene supporting the gravity layer.