e_210233

In the 4D Regge midpoint analysis, the numerator m2Num is defined by folding a fixed coupling list and summing a local contribution at each six-tuple of Fin-4 indices. The companion map explicitZ is a piecewise integer table on the same six-tuples (typical nonzero entries are $\pm 2$ or $4$).

The module is chunk 9 of a 256-cell kernel certification: every concrete index combination is discharged separately so that a later universal statement can reassemble them by fin_cases. The local claim is the scalar identity numerator $= 8\cdot$ table value at one fixed cell.

One-line kernel decide: both sides evaluate to concrete integers (m2Num by folding the coupling list; explicitZ by its match table), and Lean’s decide closes the equality. No lemmas beyond the two definitions are invoked.

Feeds the assembler theorem m2Num_eq_eight_explicitZ, which asserts the identity for every six-tuple in Fin 4 by exhaustive fin_cases. That universal equality is the algebraic backbone of the exact midpoint M2TT identity in the 4D Regge gravity analysis. Within Recognition Science this sits in the gravity sector that must match continuum curvature structure once the eight-tick and $D=3$ forcing (T7–T8) fix the discrete geometry; the factor of 8 is the combinatorial multiplicity of the octave cell. The chunk does not itself derive continuum GR; it only certifies one integer cell of the discrete kernel.