e_201113

This module is chunk 8 of a 256-cell kernel that certifies the pointwise identity $m_2=8\cdot Z$ on all sextuples of $\mathrm{Fin},4$ indices. The setting is the exact midpoint form of the 4D Regge M2–TT identity used in the gravity analysis stack.

The numerator $m_2(a,b,c,d,i,j)$ is defined by folding a fixed coupling list: start from $0$ and add each contribution term at those six indices. The companion table $Z$ is an explicit case-split function $\mathrm{Fin},4^6\to\mathbb{Z}$ that records the closed-form integer expected at each cell (examples in the kernel include $4$, $-2$, and other small integers).

The local claim is only the single cell $(2,0,1,1,1,3)$. Sibling theorems cover the other cells in the same chunk; the assemble layer quantifies over all indices.

One-line kernel proof: decide. Both sides reduce to concrete integers once the six Fin-4 arguments are substituted into the fold definition of $m_2$ and the case table for $Z$, so the equality is a decidable closed computation with no lemmas beyond evaluation.

Parent theorem m2Num_eq_eight_explicitZ assembles every cell by nested fin_cases on the six indices and dispatches each branch to a chunk theorem of this form. Without the full 256-cell cover, the universal identity $m_2=8Z$ on $\mathrm{Fin},4^6$ does not close.

That identity is the algebraic core of the exact midpoint M2–TT certificate in the 4D Regge analysis. It sits in the gravity domain of the monolith, downstream of the kernel definitions and upstream of any continuum or continuum-limit statements that quote the midpoint form. No forcing-chain landmark (T5–T8, RCL, $\phi$) is invoked here; the work is pure finite integer bookkeeping for the discrete curvature side.