e_120102

This module is chunk 6 of a 256-cell kernel certification that the Regge exact-midpoint M2 numerator equals eight times an explicit integer table on all six Fin-4 indices. The ambient setting is 4D discrete gravity analysis: couplings are folded into an integer numerator, then matched against a closed-form kernel.

The numerator $m_2^{\mathrm{num}}(a,b,c,d,i,j)$ is defined by folding a contribution function over a fixed coupling list, starting from 0. The comparison table $Z_{\mathrm{explicit}}$ is a total function $\mathrm{Fin},4^6\to\mathbb{Z}$ given by pattern match (e.g. $(0,0,1,1,2,2)\mapsto 4$, $(0,0,1,2,1,2)\mapsto -2$, and similarly for the remaining support).

Upstream, both definitions live in the KernelCert module; the present chunk only evaluates one concrete multi-index.

One-line computational proof: decide evaluates both sides at the fixed indices $(1,2,0,1,0,2)$ and checks integer equality. No lemmas are invoked beyond the reducible definitions of the folded numerator and the explicit table.

The parent assembly theorem m2Num_eq_eight_explicitZ asserts the identity for every six-tuple in $\mathrm{Fin},4$, proved by exhaustive fin_cases on all six indices. Each chunk theorem such as this one discharges one concrete cell of that $4^6$ grid, so the assembly can treat the equality as fully decided rather than symbolic.

In the broader Recognition gravity stack this is bookkeeping for the Regge midpoint M2TT identity in 4D: once numerator and explicit kernel agree everywhere (scaled by 8), downstream curvature and mass-ladder arguments can quote a single closed form instead of a fold. It does not itself touch T0–T8 or the RCL; it is infrastructure inside the gravity analysis layer.