e_130231

This module is chunk 7 of a 256-cell kernel certification that the midpoint numerator equals eight times an explicit integer table on every sextuple of Fin 4 indices. The setting is the 4D Regge exact midpoint analysis of the M2 TT identity in the gravity stack.

The numerator $N=\mathrm{m2Num}$ is defined by folding a fixed coupling list and summing a local contribution at $(a,b,c,d,i,j)$. The table $Z=\mathrm{explicitZ}$ is a pattern-matched integer function on the same six indices (sample values include $4$, $-2$, and so on). The claim under audit is one concrete cell of $N=8Z$.

Upstream, both $N$ and $Z$ live in the kernel certificate module; downstream assembly will quantify over all $4^6$ cells by fin_cases.

One-line kernel decision: by decide. Both sides reduce to concrete integers once the six Fin 4 arguments are fixed, so the equality is a closed arithmetic fact with no lemmas beyond evaluation of m2Num and explicitZ.

Feeds the universal identity m2Num_eq_eight_explicitZ, which states $\forall a,b,c,d,i,j,, N(a,b,c,d,i,j)=8Z(a,b,c,d,i,j)$ and is proved by exhausting all six Fin 4 coordinates. That assembler is the bridge from 256 decide-chunks to a single quantified certificate used in the Regge exact midpoint M2 TT identity pipeline.

In the Recognition gravity analysis this cell-level equality is pure bookkeeping: it locks the discrete coupling numerator to the explicit kernel so later continuum or continuum-limit arguments can quote a fully discharged integer identity rather than an open fold. No forcing-chain landmark (T5–T8) is at stake here; the stake is mechanical completeness of the 4D midpoint kernel.