e_011330

In the 4D Regge midpoint M2 TT analysis, two integer-valued kernels on six Fin-4 indices are compared. The numerator $m_2^{\mathrm{num}}$ is defined by folding a fixed coupling list: it sums a local contribution at each coupling triple against the six free indices. The companion $Z_{\mathrm{expl}}$ is an explicit pattern-matched table of small integers (entries such as $4$, $-2$, and so on) that is meant to be the closed form of that fold, up to a universal factor of eight.

This module is chunk 1 of the 256 kernel decides: each declaration pins one concrete sextuple. The local claim is only the equality at $(0,1,1,3,3,0)$; the surrounding chunks cover the rest of $(\mathbb{F}_4)^6$.

One-line computational proof: decide. Both sides reduce to concrete Int values once the six Fin-4 arguments are substituted into the fold definition of $m_2^{\mathrm{num}}$ and the pattern table for $Z_{\mathrm{expl}}$, so the kernel decision procedure closes the equality with no further lemmas.

Feeds the assembly theorem m2Num_eq_eight_explicitZ, which states $\forall a,b,c,d,i,j:\mathbb{F}4,; m_2^{\mathrm{num}}=8,Z{\mathrm{expl}}$ by exhaustive fin_cases on all six indices and dispatch to the chunk cells. Without each pointwise decide, the global identity that certifies the Regge midpoint M2 TT numerator against its explicit table would not close. In the gravity stack this is bookkeeping infrastructure for the exact discrete curvature identities, not a new physical law; it sits downstream of the kernel certificate definitions and upstream of the assembled equality used by later midpoint analyses.