e_322323

In the 4D Regge midpoint analysis, two integer kernels sit side by side. The numerator $m_2^{\mathrm{num}}$ is obtained by folding a fixed coupling list: each term contributes an integer depending on six $\mathrm{Fin},4$ indices, and the fold starts at zero. The companion map $Z$ is an explicit case table on the same six indices, returning small integers such as $\pm 2$ or $4$ on the listed patterns (and, by the surrounding cert, the matching value on every other tuple).

The local module is chunk 14 of a 256-way split of the kernel identity $m_2^{\mathrm{num}}=8Z$. Each chunk discharges a block of concrete index sextuples by native decision, so the global universal statement can later be assembled by exhaustive fin_cases without re-deriving the arithmetic.

One-line decide. Both sides are closed integer expressions once the six indices are fixed: the left-hand side evaluates the fold that defines $m_2^{\mathrm{num}}$ at $(3,2,2,3,2,3)$; the right-hand side multiplies the table entry $Z(3,2,2,3,2,3)$ by eight. Lean reduces both to the same numeral and closes the equality.

The parent theorem m2Num_eq_eight_explicitZ asserts the identity for every sextuple in $(\mathrm{Fin},4)^6$ by nested fin_cases, and each leaf is one of these chunk theorems. This declaration is the leaf for $(3,2,2,3,2,3)$. Closing all leaves certifies that the midpoint Regge $M_2$ TT numerator is exactly eight times the explicit kernel, a computational step in the Gravity analysis stack that underwrites the discrete curvature bookkeeping used downstream of the Recognition forcing chain (eight-tick structure, $D=3$ spatial skeleton). No open scaffold remains on this particular index; it is pure certified arithmetic.