e_030321

In the 4D Regge exact-midpoint analysis, two integer-valued kernels on six $\mathrm{Fin},4$ indices are compared. The numerator side $m_2^{\mathrm{num}}$ is the fold of a fixed coupling list: each term contributes an integer via a local contribution map, summed from zero. The comparison side is an explicit sparse table $Z$ that hard-codes the nonzero pattern (e.g. diagonal blocks $4$, selected off-diagonal pairs $-2$).

This module is chunk 3 of the 256-cell kernel certification that $m_2^{\mathrm{num}}=8Z$ holds at every multi-index. The local setting is pure finite enumeration: no continuum limit, no metric variation, only integer equality after folding.

One-line computational proof: decide evaluates both sides at the concrete six-tuple $(0,3,0,3,2,1)$. The left side runs the fold that defines $m_2^{\mathrm{num}}$; the right side looks up $8Z$ at those indices. No lemmas are invoked beyond kernel reduction of closed integer terms.

Feeds the assembly theorem m2Num_eq_eight_explicitZ, which states $\forall a,b,c,d,i,j., m_2^{\mathrm{num}}=8Z$ by exhaustive fin_cases over all six indices. Each chunk cell such as this one discharges one branch of that case split. In the gravity stack this identity is the algebraic core of the Regge midpoint M2–TT comparison: once the numerator matches eight times the explicit table everywhere, downstream curvature and mass-coupling identities can quote a single closed form rather than a fold. It is bookkeeping, not a new physical law, but without the full 256-cell cover the assembly theorem does not close.