e_012001

In the 4D Regge midpoint analysis, the mass-squared numerator $m_2^{\mathrm{num}}$ is defined by folding a coupling list: sum the local contributions over that list at a six-tuple of $\mathrm{Fin},4$ indices. The companion map $Z$ is an explicit piecewise integer function on the same six indices (sample values include $4$, $-2$, and other small integers on diagonal and off-diagonal patterns).

The module is chunk 1 of a 256-cell kernel certification whose sole job is to prove $m_2^{\mathrm{num}}=8,Z$ pointwise. Each cell fixes one concrete multi-index; the present cell is $(0,1,2,0,0,1)$. Upstream, both sides are pure definitions in the kernel certificate module, so equality is a finite integer check rather than an analytic argument.

One-line computational proof: decide evaluates both the folded sum defining $m_2^{\mathrm{num}}$ at $(0,1,2,0,0,1)$ and the product $8,Z(0,1,2,0,0,1)$, then confirms the two concrete integers coincide. No lemmas beyond the definitions of $m_2^{\mathrm{num}}$ and $Z$ are required.

This cell is consumed by the assembly theorem $m_2^{\mathrm{num}}=8,Z$ for all six $\mathrm{Fin},4$ arguments, which proceeds by exhaustive fin_cases and dispatches each branch to a chunk identity of this form. That global identity is the algebraic backbone of the Regge exact midpoint M2 TT certification in four dimensions: it replaces a summed coupling expression by a closed integer kernel, enabling exact (non-numeric) gravity identities downstream.

Within Recognition Science gravity work, such kernel equalities sit under the discrete geometric side of the framework (Regge-type curvature and mass-squared bookkeeping), not under the T0–T8 forcing chain itself. The declaration closes one of 256 decide obligations; none remain open once the full assemble theorem typechecks.