e_101322

In the 4D Regge midpoint analysis, two integer-valued kernels on six Fin-4 indices are compared. The numerator $m_2^{\mathrm{num}}(a,b,c,d,i,j)$ is defined by folding a fixed coupling list: each term contributes an integer via a local contribution function, and the fold starts at zero. The companion kernel $Z(a,b,c,d,i,j)$ is an explicit case table of small integers (entries such as $4$, $-2$, and so on) on the same six-index domain.

The local module is chunk 4 of a 256-cell decide grid whose sole job is to discharge $m_2^{\mathrm{num}}=8Z$ pointwise. The ambient claim is the exact midpoint M2–TT identity in four dimensions; this file only handles one concrete cell of that grid.

Both sides evaluate to concrete integers once the six Fin-4 arguments are fixed at $(1,0,1,3,2,2)$. The tactic decide runs the kernel decision procedure on that closed arithmetic equality and closes the goal. No lemmas beyond the definitions of the numerator fold and the explicit table are required.

The parent theorem is the universal statement that $m_2^{\mathrm{num}}(a,b,c,d,i,j)=8Z(a,b,c,d,i,j)$ for every six-tuple in $(\mathrm{Fin},4)^6$. That assembly proof introduces all six indices and splits by fin_cases; each leaf is one of these chunk theorems. Establishing the factor-of-eight match cell by cell is the computational spine of the exact midpoint M2–TT identity in the gravity analysis layer. It does not itself invoke the Recognition forcing chain (T5–T8) or the mass ladder; it is pure discrete kernel bookkeeping needed before continuum or phenomenological claims can be attached.