e_313121

This module is chunk 13 of a 256-case kernel certification that the midpoint Regge numerator in 4D equals eight times a sparse explicit integer table. The ambient setting is discrete gravity analysis: couplings on six Fin-4 indices are summed, then matched to a closed form.

The numerator m2Num is defined by folding a fixed coupling list and adding each contribution at the six indices. The target table explicitZ is a pattern-matched integer function on the same six indices (typical values 4, -2, and zeros off the listed patterns). The claim is one concrete six-tuple equality inside that table match.

Upstream, both definitions live in the kernel-cert module; this chunk only discharges one decide instance rather than re-deriving the fold.

One-line tactic proof: by decide. Lean evaluates both sides as concrete Int expressions (the fold of m2Num at fixed Fin-4 values versus 8 * explicitZ at the same values) and closes by kernel computation. No lemmas are invoked beyond the definitions of the two sides.

Feeds the assembly theorem m2Num_eq_eight_explicitZ, which states the identity for every six-tuple in Fin 4 by exhaustive fin_cases and dispatches each leaf to a chunk equality of this form. Without the per-slot decides, the global numerator-to-kernel match does not close.

In the Recognition gravity stack this is bookkeeping infrastructure for the exact midpoint Regge identity in 4D, not a new physical law. It supports later continuum or continuum-limit arguments that rely on the certified discrete kernel, sitting downstream of the forcing chain only indirectly (D=3 spatial plus time gives the 4-index structure). No open physics question is settled here; the open work is completing all 256 decides and wiring them into the assemble proof.