e_313000

This module is one chunk of a 256-case kernel certification that the 4D Regge midpoint M2 TT numerator equals eight times a sparse explicit integer table. Indices run over Fin 4 (the four discrete directions of the lattice).

The numerator $N=\mathrm{m2Num}$ is defined by folding a fixed coupling list: each term adds a local contribution depending on the six indices. The table $Z=\mathrm{explicitZ}$ is a pattern-matched integer function on the same six Fin 4 arguments (typical nonzero values are $\pm 2,\pm 4$).

The local setting is pure integer arithmetic: no continuum limit is taken here. The chunk isolates one concrete sextuple so the full universal identity can be assembled by exhaustive case split downstream.

One-line kernel proof: decide evaluates both sides at the concrete indices $(3,1,3,0,0,0)$. The left side reduces by unfolding the fold over the coupling list; the right side multiplies the pattern-matched integer from the explicit table by 8. Equality of the resulting integers is discharged by the decidable instance on Int.

Feeds the parent assembly theorem m2Num_eq_eight_explicitZ, which states the identity for every sextuple of Fin 4 indices by fin_cases and invokes each chunk lemma such as this one. That universal equality is the algebraic core of the exact midpoint M2 TT identity in the 4D Regge analysis stack.

In the broader Recognition gravity line, certifying the discrete curvature/mass numerator against a closed kernel supports exact (not approximate) identities on the lattice before continuum or phenomenological limits. The module title marks this as chunk 13 of the 256 decides; closing all chunks discharges the full kernel certificate.