e_313032
plain-language theorem explainer
For the Fin-4 index sextuple (3,1,3,0,3,2), the folded coupling numerator equals eight times the explicit integer table value. Gravity analysts certifying the 4D Regge midpoint M2TT identity cite this as one cell of the 256-case kernel. Proof is a single kernel `decide` on concrete integers.
Claim. For indices $(a,b,c,d,i,j)=(3,1,3,0,3,2)$ with each entry in $\{0,1,2,3\}$, the folded coupling numerator at those indices equals $8$ times the corresponding entry of the explicit integer table.
background
In the Regge-exact midpoint analysis of the 4D M2TT identity, two integer maps on six Fin 4 indices are compared. The numerator folds a fixed coupling list, summing each contribution at the given indices. Its companion is a sparse case table of small integers (values such as $4$ and $-2$) proposed as the closed form.
This module is chunk 13 of a 256-case kernel certification that the numerator equals eight times the table pointwise. The universal statement is assembled downstream by exhaustive case split on all six indices.
proof idea
One-line kernel decision. Both sides reduce to concrete integers once the six Fin 4 arguments are substituted, so decide discharges the equality in Int with no further lemmas.
why it matters
Supplies one dispatch cell for the assembler theorem that states the numerator equals eight times the explicit table for every sextuple of Fin 4 indices. That assembler runs fin_cases on all six arguments and lands on chunk lemmas such as this one. The identity is bookkeeping inside Gravity.Analysis: it closes a discrete kernel cell so the global algebraic M2TT midpoint relation can be cited without gaps. No new continuum physics is claimed here; the landmark is certification completeness for the 4D Regge kernel.
Switch to Lean above to see the machine-checked source, dependencies, and usage graph.