e_021102

This module is chunk 2 of a 256-cell kernel that certifies $m_2^{\mathrm{num}}=8\cdot Z_{\mathrm{expl}}$ pointwise on $(\mathrm{Fin},4)^6$. The setting is the exact midpoint evaluation of the 4D Regge M2–TT identity used in the gravity analysis stack.

Upstream, $m_2^{\mathrm{num}}(a,b,c,d,i,j)$ is the integer obtained by folding couplingZList and summing the local contribution of each coupling term at those indices. $Z_{\mathrm{expl}}$ is the sparse closed-form table that returns a fixed integer (e.g. $4$, $-2$, or $0$ by default) on each six-tuple; only a handful of patterns are nonzero.

The full identity is assembled later by exhaustive fin_cases over all six indices, each leaf discharging one concrete equality of this form.

One-line kernel proof: by decide. Both sides reduce to concrete Int values (the fold for m2Num and the match for explicitZ at $(0,2,1,1,0,2)$), so the decision procedure closes the equality with no lemmas or rewriting.

Feeds the parent assembly theorem m2Num_eq_eight_explicitZ, which states $\forall a,b,c,d,i,j,; m_2^{\mathrm{num}}=8,Z_{\mathrm{expl}}$ and proves it by six nested fin_cases whose leaves are exactly these chunk equalities. That global identity is the algebraic backbone of the Regge exact-midpoint M2–TT certification in 4D gravity analysis. It does not itself touch the RS forcing chain (T5–T8) or the RCL; it is pure discrete curvature bookkeeping supporting the continuum limit claims higher in the gravity stack.