e_000320

In the 4D Regge exact-midpoint stack, the M2TT identity is reduced to a pointwise integer equality on six indices in $\mathrm{Fin},4$. The left-hand side is a numerator obtained by folding a contribution map over a fixed coupling list, starting from zero. The right-hand side is eight times an explicit pattern-matched integer table on the same six indices (sample values include $4$ on diagonal pairs such as $(0,0,1,1,2,2)$ and $-2$ on mixed pairs).

This module is chunk 0 of the kernel-decide grid that discharges that equality cell by cell. The local claim is only the single cell with indices $(0,0,0,3,2,0)$.

Both sides are closed integer terms once the six $\mathrm{Fin},4$ arguments are fixed literals. The tactic decide normalizes the fold that defines the numerator and the pattern match that defines the explicit table, then checks $\mathrm{Int}$ equality in the kernel. No named lemmas are applied; the proof is pure decidable computation on this one cell.

The parent theorem asserts $N_2(a,b,c,d,i,j)=8,Z(a,b,c,d,i,j)$ for all six indices, proved by exhaustive fin_cases whose leaves are these per-cell decides. This declaration is the leaf for $(0,0,0,3,2,0)$ inside chunk 0. Closing every cell certifies the algebraic numerator identity that the 4D Regge midpoint M2TT analysis rests on in the gravity stack. It is bookkeeping infrastructure, not a new physical law: it locks one discrete identity needed upstream of continuum or observational claims.