e_233333

This module is chunk 11 of the 256-point kernel certification that the midpoint Regge mass-squared numerator equals eight times an explicit integer table. The ambient setting is 4D discrete gravity analysis: six indices each run over $\mathbb{F}_4$ (values $0..3$), labeling edge/face data in the midpoint identity.

The numerator $m_2^{\mathrm{num}}$ is defined by folding a fixed coupling list and summing a local contribution at each tuple. The comparison object $Z$ is an explicit case-table $\mathbb{F}_4^6\to\mathbb{Z}$ (sample entries include $4$ on diagonal-type patterns and $-2$ on crossed patterns). The claim is the pointwise equality at one concrete six-tuple.

Both sides are closed integer terms once the six $\mathbb{F}_4$ arguments are fixed to $2,3,3,3,3,3$. The tactic decide evaluates the fold that defines the numerator and the matching clause of the explicit kernel, then checks integer equality. No lemmas beyond the two definitions are required; the goal is pure computation.

The parent theorem is the assembled identity: for every six-tuple in $\mathbb{F}_4^6$, the numerator equals eight times the explicit kernel. That proof runs nested fin_cases on all six indices and dispatches each leaf to a chunk theorem of this form. Without the point checks, the global midpoint mass-squared identity in the 4D Regge analysis does not close. In the Recognition gravity stack this is bookkeeping infrastructure for the discrete curvature/mass kernel, not a new physical law; it certifies that the tabulated $Z$ correctly reproduces the folded coupling sum everywhere, including this off-diagonal pattern.