e_123012

This module is chunk 6 of a brute-force certification that the 4D midpoint Regge TT identity holds at the level of integer kernels: $m_2^{\mathrm{num}}=8\cdot Z$ on every sextuple in $(\mathrm{Fin},4)^6$.

The numerator $m_2^{\mathrm{num}}$ is defined by folding a fixed coupling list: start at $0$ and add a contribution term for each coupling entry evaluated at the six indices. The comparison target explicitZ is a closed-form integer table on the same six $\mathrm{Fin},4$ arguments (sample values include $4$, $-2$, and so on for the listed patterns).

The local setting is pure finite enumeration: no continuum limit, no metric signature choice beyond the discrete kernel already fixed upstream in the KernelCert module.

One-line computational proof: decide evaluates both sides at the concrete sextuple $(1,2,3,0,1,2)$ and checks integer equality. No lemmas are invoked; the fold defining the numerator and the pattern match defining explicit $Z$ reduce to numerals that the kernel compares.

Parent theorem is m2Num_eq_eight_explicitZ, which states $\forall a,b,c,d,i,j,; m_2^{\mathrm{num}}=8Z$ and discharges the claim by nested fin_cases over all six indices. Each chunk theorem such as this one supplies one branch of that case split.

In the Recognition gravity stack this identity is bookkeeping for the exact midpoint Regge TT sector in four dimensions: once every cell matches, the assembled equality licenses replacing the folded numerator by the closed $Z$ table in later curvature and mass-ladder arguments. It does not itself touch the forcing chain (T0–T8) or the RCL; it is infrastructure under the discrete gravity side.