e_130310

This module is chunk 7 of a 256-case kernel certifying that the folded midpoint numerator equals eight times an explicit integer table on all of $(\mathbb{F}_4)^6$. The setting is the 4D Regge exact-midpoint M2TT identity analysis.

The numerator $N=\mathrm{m2Num}$ is defined by folding a fixed coupling list: start at 0 and add a local contribution at each coupling triple for the six indices. The table $Z=\mathrm{explicitZ}$ is a hand-written integer function on six $\mathrm{Fin},4$ arguments (sample values include $4$, $-2$, and so on on the diagonal and off-diagonal patterns).

Upstream, both $N$ and $Z$ live in the kernel-cert module; this chunk only evaluates one concrete sextuple.

One-line computational proof: decide. Lean reduces both sides on the concrete indices $(1,3,0,3,1,0)$ (the fold for $N$ and the match table for $Z$) and checks integer equality. No lemmas are invoked beyond the decidable equality instance on $\mathbb{Z}$.

Feeds the assembly theorem $\mathrm{m2Num_eq_eight_explicitZ}$, which states $\forall a,b,c,d,i,j,, N(a,b,c,d,i,j)=8,Z(a,b,c,d,i,j)$ and discharges the universal quantifier by exhaustive $\mathrm{fin_cases}$ on the six $\mathrm{Fin},4$ arguments. Each chunk such as this one is one of the 256 kernel points that make that global identity hold by computation.

In the Recognition gravity stack this closes a numerator identity used in the Regge midpoint / M2TT 4D analysis; it is bookkeeping infrastructure rather than a new physical law, but without the pointwise certs the assembly theorem cannot stand.