e_110331

In the 4D Regge exact-midpoint analysis, two integer-valued maps on six Fin-4 indices are compared cellwise. The numerator $m_2^{\mathrm{num}}$ is defined by folding a fixed coupling list: each term contributes an integer via a local contrib rule, and the fold starts at 0. The comparison target $Z_{\mathrm{ex}}$ is an explicit piecewise integer table on the same six indices (sample clauses include values $4$, $-2$, and so on).

The local module is chunk 5 of the 256-cell kernel certification that $m_2^{\mathrm{num}}=8,Z_{\mathrm{ex}}$ everywhere. Each chunk theorem pins one concrete sextuple so the later assembly can discharge the universal statement by exhaustive fin_cases.

One-line kernel proof: decide evaluates both sides at the concrete Fin-4 sextuple $(1,1,0,3,3,1)$ and checks integer equality. No lemmas are invoked beyond the definitions of $m_2^{\mathrm{num}}$ (the fold over couplingZList) and $Z_{\mathrm{ex}}$ (the explicit case table).

Feeds the assembly theorem $m_2^{\mathrm{num}}=8,Z_{\mathrm{ex}}$ for all Fin-4 sextuples, which is proved by nested fin_cases over the six indices and therefore depends on every cell identity of this form. That universal equality is the algebraic core of the Regge exact-midpoint M2TT identity in 4D gravity analysis inside the monolith. It is bookkeeping, not a new physical law: it certifies that the folded coupling numerator matches the closed kernel used downstream in the midpoint identity chain.