e_013300

This module is one chunk of the 4D Regge exact-midpoint M2TT identity certification: the claim that the folded numerator m2Num equals eight times a sparse explicit integer table explicitZ, discharged cell-by-cell over $(\mathrm{Fin},4)^6$.

m2Num a b c d i j is defined by folding couplingZList, accumulating each term's contribution contrib t a b c d i j into an Int. explicitZ is the matching closed-form table on six Fin 4 indices (nonzero only on a short list of patterns such as $(0,0,1,1,2,2)\mapsto 4$, $(0,0,1,2,1,2)\mapsto -2$, and so on).

The local setting is pure integer bookkeeping for the midpoint discrete-gravity kernel; no continuum limit or physical units enter these cells.

One-line kernel proof: by decide. Lean reduces both sides of the equality on the concrete six-tuple $(0,1,3,3,0,0)$ to integers and checks equality by the decidable instance on Int. No lemmas beyond the definitions of m2Num and explicitZ are invoked.

Parent theorem m2Num_eq_eight_explicitZ assembles the full universal statement $\forall a,b,c,d,i,j,;\mathrm{m2Num}=8\cdot\mathrm{explicitZ}$ by exhaustive fin_cases on all six indices; each leaf is one of these chunk cells (here e_013300). Closing the cells certifies the algebraic identity underlying the 4D Regge midpoint M2TT kernel used in the gravity analysis stack. It is bookkeeping infrastructure, not a forcing-chain (T0–T8) step, but it is required before continuum or phenomenological gravity claims that quote the certified kernel can be trusted.