e_310033

This module sits in the Gravity analysis layer that certifies an exact midpoint identity for the 4D Regge M2TT mass-matrix numerator. The local goal, per the module doc, is the pointwise equality of that numerator with eight times an explicit integer kernel, discharged by 256 concrete kernel decisions (this file is chunk 13).

The numerator is defined by folding a fixed coupling list: at six Fin 4 indices it sums a contribution functional over every coupling term, yielding an Int. The explicit kernel is a piecewise integer table on the same six indices (sample clauses send e.g. $(0,0,1,1,2,2)$ to $4$ and $(0,0,1,2,1,2)$ to $-2$). Both objects are imported from the kernel-certificate module; this theorem only evaluates them at one tuple.

One-line proof by decide. Both sides reduce to closed integer expressions once the six concrete Fin 4 arguments are substituted into the fold definition of the numerator and the pattern match of the explicit kernel; the kernel decision procedure checks the resulting Int equality.

Parent consumer is the assembled universal statement that the numerator equals eight times the explicit kernel for every six-tuple in Fin 4. That assembler introduces the six indices and runs fin_cases on each; the present lemma is the discharged cell for $(3,1,0,0,3,3)$ inside chunk 13 of that case tree.

In the broader Recognition gravity stack this is bookkeeping infrastructure for an exact discrete identity (Regge midpoint M2TT in 4D), not a continuum or phenomenological claim. It does not itself invoke the forcing chain (T5–T8), the Recognition Composition Law, or the phi-ladder mass formula; it only clears one arithmetic obligation those higher layers rely on when the discrete kernel is quoted.