e_232020
plain-language theorem explainer
Pointwise identity: the folded Regge coupling numerator at multi-index (2,3,2,0,2,0) equals eight times the explicit integer table entry. Gravity analysts cite it as one of the 256 kernel cells that assemble the global m2Num = 8·explicitZ statement. The proof is a single kernel decide on concrete Fin-4 integers.
Claim. For indices $(a,b,c,d,i,j)=(2,3,2,0,2,0)$ in $(\mathrm{Fin}\,4)^6$, the folded coupling numerator equals eight times the explicit closed-form integer: $N(2,3,2,0,2,0)=8\,Z(2,3,2,0,2,0)$.
background
In the 4D Regge midpoint M2TT analysis, two integer-valued kernels on six $\mathrm{Fin},4$ indices are compared. The numerator $N=m2Num$ is obtained by folding a fixed coupling list and summing local contributions at $(a,b,c,d,i,j)$. The comparison target $Z=explicitZ$ is an explicit pattern-matched integer table (typical nonzero entries $\pm 2,\pm 4$).
The module is chunk 11 of a 256-cell partition of the kernel: each cell asserts $N=8Z$ at one concrete sextuple. The local setting is pure integer arithmetic on a finite discrete index set, with no continuum limit taken inside the chunk.
proof idea
Both sides evaluate to concrete integers once the six $\mathrm{Fin},4$ arguments are fixed. The proof is the single tactic decide, which runs the kernel decision procedure on the equality of those integers. No algebraic rewriting or intermediate lemmas are invoked beyond the definitions of the folded numerator and the explicit table.
why it matters
The parent assembly theorem m2Num_eq_eight_explicitZ proves $\forall$ sextuples $N=8Z$ by exhaustive fin_cases on all six indices; each leaf is one of these chunk identities. Closing the 256 cells discharges the discrete algebraic core of the Regge exact midpoint M2TT identity in 4D, which sits in the gravity analysis layer of the Recognition Science mirror (spatial $D=3$ plus time, eight-tick discrete structure upstream). Without the pointwise cells, the global fold-versus-table comparison remains open.
Switch to Lean above to see the machine-checked source, dependencies, and usage graph.