e_311301

This module sits inside the 4D Regge exact-midpoint analysis for the M2TT identity. The numerator $N=\mathrm{m2Num}$ is the integer obtained by folding a fixed coupling list: each term contributes via a local weight depending on the six Fin-4 indices, and the fold starts at 0. The comparison value $Z=\mathrm{explicitZ}$ is a sparse lookup table on the same six indices, returning small integers such as $4$, $-2$, and so on for the nonzero cells.

The local setting is chunk 13 of a 256-cell kernel certification: every concrete index sextuple is discharged separately so that a later assembly theorem can recombine them by exhaustive fin_cases. Upstream, both $N$ and $Z$ are pure definitions with no hypotheses; equality is a numerical fact about those definitions at one point.

One-line kernel proof: decide evaluates both sides as concrete integers (the fold that defines the numerator on the left, the table lookup on the right) and checks equality in Int. No lemmas are invoked beyond the elaborator’s evaluation of the two upstream definitions at the fixed indices $(3,1,1,3,0,1)$.

The parent theorem is the full pointwise identity $\forall a,b,c,d,i,j,,N=8Z$, proved by six nested fin_cases that ultimately land on cells such as this one. Without the chunk lemmas, the assembly cannot close. In the Recognition gravity stack this identity is bookkeeping for the exact midpoint form of the 4D Regge M2TT relation, not a new physical postulate; it certifies that the folded coupling numerator matches the closed explicit kernel everywhere, so later curvature and mass-ladder arguments may quote a single clean factor of 8 rather than an opaque fold.