e_013333

In the 4D Regge midpoint analysis, two integer kernels on six Fin-4 indices are compared. The numerator $N(a,b,c,d,i,j)$ is obtained by folding a fixed coupling list, accumulating a contribution at each term for the given indices. The explicit kernel $Z$ is a closed pattern-match table on the same six indices, returning small integers (e.g. $4$, $-2$, and so on).

This module is chunk 1 of the identity $N=8Z$: it discharges 256 concrete sextuples by kernel decision. The local claim is the single sextuple $(0,1,3,3,3,3)$. Upstream, $N$ and $Z$ are defined in the kernel certificate module; no analytic identity is assumed beyond those definitions.

One-line computational proof: decide evaluates both sides at the concrete Fin-4 constants and checks integer equality. No lemmas beyond the definitions of the folded numerator and the explicit table are required; both reduce to closed integer expressions at this point.

Feeds the parent assembly theorem that states $\forall(a,b,c,d,i,j)\in(\mathbb{F}_4)^6$, $N=8Z$, proved by exhausting all sextuples (via fin-cases / chunk decides). That global identity is the algebraic backbone of the exact midpoint M2 TT identity in 4D Regge gravity analysis inside the monolith. The chunk decomposition keeps each decide goal tiny and machine-checkable. No Recognition forcing-chain landmark (T5–T8, RCL, phi) is invoked here; the result is pure discrete kernel arithmetic supporting the gravity side.