e_210321

In the 4D Regge exact-midpoint analysis, the numerator $m_2^{\mathrm{num}}$ is defined by folding a fixed coupling list: each term contributes an integer weight at a six-tuple of Fin-4 indices, and the fold starts from zero. The companion table $Z_{\mathrm{ex}}$ is an explicit pattern-matched integer function on the same six indices (sample values include $\pm 2,4$ on diagonal and off-diagonal slots).

The module is chunk 9 of a 256-case kernel certification that $m_2^{\mathrm{num}}=8,Z_{\mathrm{ex}}$ pointwise. The local setting is pure finite enumeration over $(\mathrm{Fin},4)^6$, not continuum GR: each chunk discharges a block of concrete equalities so the global identity can be assembled by case split.

One-line proof by decide. Both sides reduce to closed integer expressions at the fixed indices $(2,1,0,3,2,1)$: the left via the fold definition of the numerator, the right via the pattern match in the explicit table (scaled by 8). The kernel checks integer equality; no lemmas beyond the two definitions are invoked.

Feeds the parent assembly theorem $m_2^{\mathrm{num}}=8,Z_{\mathrm{ex}}$ for all six Fin-4 indices, whose proof case-splits on every coordinate and lands on these chunk decides. That identity is the certified algebraic core of the Regge exact-midpoint $M_2$ TT kernel in 4D inside the Gravity analysis stack. It does not itself touch the T0–T8 forcing chain or the J-cost; it is infrastructure that keeps the discrete curvature bookkeeping exact before continuum or phenomenological limits are taken.