e_211000

This module is one chunk of a 256-cell kernel certification that the midpoint Regge mass-squared numerator coincides with eight times a closed-form integer table on all of $(\mathbb{F}_4)^6$. The local setting is pure finite enumeration: every index runs over four values, so the full identity is a finite check split across chunk files.

The numerator $m_2^{\mathrm{num}}$ is defined by folding a fixed coupling list: start at $0$ and add a contribution term for each coupling triple at the six indices. The comparison target $\mathrm{explicitZ}$ is a pattern-matched integer table on six $\mathrm{Fin},4$ arguments (sample entries include $4$, $-2$, and so on for distinguished index patterns).

Upstream, both $m_2^{\mathrm{num}}$ and $\mathrm{explicitZ}$ live in the kernel certificate module; this chunk only evaluates one concrete six-tuple.

One-line computational proof: decide. After the six indices are substituted by the literals $2,1,1,0,0,0$, both sides reduce to concrete integers (the fold over the coupling list on the left; the pattern match on the right). Lean’s decision procedure discharges the resulting integer equality with no lemmas and no case split inside this declaration.

Parent theorem m2Num_eq_eight_explicitZ assembles the universal statement $\forall a,b,c,d,i,j,; m_2^{\mathrm{num}}=8,Z$ by exhaustive fin_cases on all six indices. Each chunk cell such as this one supplies (or is aligned with) one of those $4^6=256$ kernel points; the module doc labels this file chunk 9 of that decide grid.

In the Recognition gravity stack this identity is bookkeeping for the exact midpoint Regge M2TT analysis in 4D: it certifies that the folded coupling numerator is a pure multiple of the explicit Z table, so later continuum or continuum-limit arguments can quote the closed form instead of the fold. It does not itself invoke the forcing chain (T0–T8), RCL, or $\varphi$-ladder mass formula; it is infrastructure under the discrete gravity kernel.