e_001033

The ambient module certifies, cell by cell, that the 4D Regge exact-midpoint M2 numerator equals eight times an explicit sparse kernel on $(\mathrm{Fin},4)^6$. Module doc: "m2Num = 8·explicitZ, chunk 0 (256 kernel decides)."

The numerator is the integer fold of a fixed coupling list: each term contributes via a local weight at the six indices. The explicit kernel is a pattern-matched integer table on the same six Fin-4 arguments (typical nonzero entries are $\pm 2,\pm 4$; unmatched cells are zero).

This declaration is one concrete cell of that table. Upstream definitions supply both sides; the full universal statement is assembled downstream by exhaustive fin-cases over all $4^6$ index tuples.

One-line computational proof: by decide. After unfolding the fold that defines the numerator and the pattern match that defines the explicit kernel at $(0,0,1,0,3,3)$, both sides reduce to concrete integers; the kernel decision procedure discharges the equality.

Feeds the parent assembly theorem m2Num_eq_eight_explicitZ, which states $\forall a,b,c,d,i,j,; m_2^{\mathrm{num}}=8,Z_{\mathrm{ex}}$ and proves it by nested fin-cases, each leaf a chunk decide such as this one. That identity is the algebraic core of the 4D Regge exact-midpoint TT kernel certification in the Gravity analysis stack. It sits inside the discrete geometric side of Recognition gravity (Regge calculus on the eight-tick / $D=3$ lattice), not the T0–T8 forcing chain itself, but it is required machinery for exact curvature bookkeeping once the continuum limit is discretized.