e_203001

In the 4D Regge exact-midpoint analysis, two integer kernels are compared cellwise on $(\mathrm{Fin},4)^6$. The numerical side $m_2^{\mathrm{num}}$ is the fold of a fixed coupling list: each term contributes an integer via a local contribution function, summed from zero. The closed form $Z$ is an explicit case table on the six indices, returning small integers such as $4$, $-2$, and so on.

The module is chunk 8 of a 256-cell decide kernel whose sole job is to discharge $m_2^{\mathrm{num}}=8Z$ at concrete sextuples. The ambient claim is the full identity over all indices, assembled downstream by exhaustive fin_cases.

One-line computational proof: decide evaluates both sides at the fixed indices $(2,0,3,0,0,1)$ and checks integer equality. No lemmas are invoked beyond the definitions of the fold $m_2^{\mathrm{num}}$ and the case table $Z$; the kernel reduces to concrete arithmetic.

Feeds the assembler theorem that states $\forall a,b,c,d,i,j,, m_2^{\mathrm{num}}=8Z$ on $(\mathrm{Fin},4)^6$, proved by six nested fin_cases over the 256 cells. That global identity is the numerical half of the Regge exact-midpoint M2–TT certification in 4D gravity analysis. Within Recognition Science this sits in the gravity sector that must match discrete curvature bookkeeping to continuum limits; it does not itself touch the forcing chain T0–T8, but supplies certified arithmetic infrastructure those continuum claims rely on when gravity is reconstructed from recognition data.