e_110233

In the 4D Regge midpoint M2TT analysis, two integer-valued maps on six indices in $\mathrm{Fin},4$ are compared. The numerator is obtained by folding a fixed contribution functional over a coupling list; the comparison target is an explicit pattern-matched integer table whose nonzero values are small constants such as $4$ and $-2$.

This module is chunk 5 of a partitioned decide sweep that checks the pointwise identity numerator $= 8\cdot$ table on the full $4^6$ index space. The local setting is pure computational verification of discrete gravity kernel equalities, imported from the kernel-certificate module that defines both maps.

Upstream, the numerator is the fold of contributions over the coupling list, and the table is the closed-form case table used as the right-hand side of the identity.

One-line proof by decide. The kernel evaluates both sides of the integer equality at the concrete sextuple $(1,1,0,2,3,3)$ from the definitions of the folded numerator and the explicit table, and accepts the equality. No intermediate lemmas are applied.

Supplies one concrete case to the universal assembly theorem that states the numerator equals eight times the explicit table for every sextuple in $(\mathrm{Fin},4)^6$. That assembly runs nested fin_cases on all six indices and lands each residual goal on a chunk theorem of this form. The universal equality is the algebraic backbone of the Regge exact midpoint M2TT identity in 4D, inside the discrete-curvature layer of the Recognition gravity stack. The case is fully closed; no scaffolding remains.