e_021101

In the 4D Regge exact-midpoint analysis, two integer-valued maps on six $\mathrm{Fin},4$ indices are compared. The numerator $m_2^{\mathrm{num}}$ is defined by folding a fixed coupling list: each term contributes via a local kernel, and the fold starts at zero. The comparison target $Z_{\mathrm{explicit}}$ is a sparse pattern-matched table of small integers (entries such as $4$, $-2$, and so on on selected multi-indices).

The module is chunk 2 of a 256-cell kernel certification that $m_2^{\mathrm{num}}=8,Z_{\mathrm{explicit}}$ pointwise. Each cell is an independent equality at one multi-index; the present declaration treats $(0,2,1,1,0,1)$.

One-line kernel proof: decide evaluates both sides as concrete Int values (the fold for $m_2^{\mathrm{num}}$ at this tuple, and the pattern match for $Z_{\mathrm{explicit}}$) and discharges the equality by computation. No lemmas beyond the two definitions are invoked.

The parent theorem m2Num_eq_eight_explicitZ assembles the universal statement $\forall a,b,c,d,i,j,, m_2^{\mathrm{num}}=8,Z_{\mathrm{explicit}}$ by exhaustive fin_cases on all six indices. Each chunk cell such as this one supplies one branch of that case split. In the gravity stack this identity is the algebraic backbone of the Regge midpoint M2TT certification: once the numerator matches eight times the explicit table everywhere, downstream curvature and mass-response identities can quote a single closed form rather than a fold. It is pure discrete linear algebra on the 4D index set, not a continuum GR claim.