e_330322

In the 4D Regge midpoint analysis, two integer-valued maps on six Fin-4 indices are compared. The numerator $m_2$ is defined by folding a fixed coupling list: each term contributes an integer depending on the six indices, and the fold starts at 0. The comparison target is an explicit piecewise kernel $Z$ that returns small integers (typically $\pm 2$ or $4$) on the nonzero support and is used as a closed form.

The local module is one of the decide chunks that discharge the pointwise identity $m_2 = 8Z$ on a block of the $4^6 = 4096$ index tuples (here framed as 256 kernel decides per chunk). Upstream, both $m_2$ and $Z$ are pure definitions in the kernel certificate module; no analytic hypothesis is left open at this layer.

One-line proof by decide. Lean evaluates both sides on the concrete sextuple $(3,3,0,3,2,2)$: the fold that defines $m_2$ and the pattern-match that defines $Z$, then checks integer equality with the factor $8$. No lemmas beyond the two definitions are invoked.

This is one atomic cell in the exhaustive case split that proves $m_2 = 8Z$ for every six-index argument. The parent theorem m2Num_eq_eight_explicitZ introduces all six Fin-4 variables and runs nested fin_cases; each leaf is a chunk theorem of this form. Establishing the exact midpoint M2–TT identity in 4D Regge calculus depends on every such cell matching, so the chunk closes a finite but necessary fragment of the gravity kernel certificate. It does not itself touch the RS forcing chain (T0–T8) or the J-cost; it is pure discrete tensor algebra supporting the continuum limit story.