e_100223

This module is one chunk of the exhaustive check that the 4D Regge midpoint numerator equals eight times a sparse explicit integer table. The ambient setting is the exact midpoint M2TT identity for discrete gravity on a 4-index kernel.

The numerator $N(a,b,c,d,i,j)$ is defined by folding a fixed coupling list and summing a local contribution at each tuple. The comparison table $Z$ is a total function $\mathbb{F}_4^6\to\mathbb{Z}$ given by a finite pattern of nonzero entries (mostly $\pm 2,\pm 4$) and zeros elsewhere. Both live in the kernel certificate module imported here.

Chunk 4 packages 256 such pointwise equalities so the assembler can discharge the universal statement by fin_cases without re-deciding the whole kernel in one go.

One-line computational proof: decide evaluates both sides at the concrete Fin-4 sextuple $(1,0,0,2,2,3)$ and checks integer equality in the kernel. No lemmas are invoked beyond the reducible definitions of the folded numerator and the explicit table.

Parent theorem is m2Num_eq_eight_explicitZ, which asserts $N=8Z$ for every sextuple in $\mathbb{F}_4^6$ by nested fin_cases; each case lands on a chunk identity such as this one. Without the pointwise facts the assembler cannot close the universal midpoint identity used in the Regge gravity analysis stack.

In the broader Recognition gravity line this is bookkeeping infrastructure, not a forcing-chain step (T0–T8). It certifies that the discrete curvature/coupling numerator matches the closed-form table factor of eight, so downstream continuum or continuum-limit arguments can quote a single clean identity rather than a raw fold.