e_123331

This module is chunk 6 of a 256-cell decide grid that certifies the algebraic identity between two integer-valued kernels on six Fin-4 indices. The setting is the 4D Regge midpoint analysis of the M2TT gravity identity: one side is a fold of coupling contributions, the other an explicit sparse table.

The numerator $N=\mathrm{m2Num}$ is defined by folding a fixed coupling list, accumulating a contribution at each term for the six indices. The closed form $Z=\mathrm{explicitZ}$ is a pattern-matched integer table on those same indices (typical values $\pm 2,\pm 4$, and zero off the listed patterns).

The local claim is one concrete six-tuple equality $N=8Z$. The full quantified statement is assembled downstream by exhausting all Fin-4 cases.

One-line kernel proof: decide evaluates both sides as concrete integers for the fixed indices $(1,2,3,3,3,1)$ and checks equality. No lemmas are invoked beyond the definitions of the fold numerator and the explicit table; the checker reduces the fold and the match arms to numerals and compares.

Feeds the assembler theorem that states $\forall a,b,c,d,i,j:\mathrm{Fin},4,, N(a,b,c,d,i,j)=8,Z(a,b,c,d,i,j)$, which is proved by nested fin_cases over the six indices and dispatch into these chunk cells. That global identity is the certified numerator half of the Regge-exact midpoint M2TT relation in 4D gravity analysis inside the Recognition Science monolith.

Within the framework this sits in the gravity domain rather than the T0–T8 forcing chain; it is bookkeeping that makes the discrete curvature/coupling identity machine-checkable. Closing all 256 decide cells removes scaffolding risk from the M2 numerator side of the midpoint certificate.