e_200131

This module is chunk 8 of a 256-cell decide grid that checks $m_2^{\mathrm{num}}=8\cdot Z_{\mathrm{explicit}}$ pointwise on $(\mathrm{Fin},4)^6$. The setting is the exact midpoint evaluation of the Regge M2 TT identity in four dimensions.

The numerator $m_2^{\mathrm{num}}(a,b,c,d,i,j)$ is defined by folding a fixed coupling list: start at 0 and add each contribution term at those six indices. The closed form $Z_{\mathrm{explicit}}$ is a sparse integer table on the same six $\mathrm{Fin},4$ arguments (typical nonzero values $\pm 2,,4$).

Upstream, both definitions live in the kernel certificate module; this chunk only evaluates one concrete sextuple against that table.

One-line computational proof: by decide. Lean reduces both sides of the equality on the fixed indices $(2,0,0,1,3,1)$ to concrete integers (the fold for $m_2^{\mathrm{num}}$ versus the pattern match for $Z_{\mathrm{explicit}}$) and checks equality in the kernel. No lemmas are invoked beyond the two definitions.

Feeds the assembly theorem $m_2^{\mathrm{num}}=8\cdot Z_{\mathrm{explicit}}$ for all six $\mathrm{Fin},4$ arguments, which exhausts the grid by fin_cases and dispatches each cell to a chunk decide such as this one. That global identity is the algebraic core of the Regge exact-midpoint M2 TT certificate in 4D gravity analysis inside the monolith. It is pure discrete tensor algebra on the coupling kernel, not a continuum GR derivation, and does not itself invoke the T0–T8 forcing chain or the Recognition Composition Law.