e_200013
plain-language theorem explainer
Pointwise check that the Regge midpoint mass-squared numerator at multi-index (2,0,0,0,1,3) equals eight times the explicit integer kernel value. Gravity analysts cite it when assembling the global 4D identity m2Num = 8·explicitZ over all Fin-4 indices. The proof is a single kernel decide on concrete integers.
Claim. For the multi-index $(a,b,c,d,i,j)=(2,0,0,0,1,3)$ with each entry in $\{0,1,2,3\}$, the folded coupling numerator $m_2^{\mathrm{num}}(a,b,c,d,i,j)$ equals $8$ times the explicit integer table entry $Z(a,b,c,d,i,j)$.
background
In the 4D Regge exact-midpoint analysis, the mass-squared numerator $m_2^{\mathrm{num}}$ is defined by folding a fixed coupling list: sum the local contributions of each coupling term at a six-index slot $(a,b,c,d,i,j)\in(\mathbb{F}_4)^6$. The companion table $Z$ is an explicit integer-valued kernel on the same index set (nonzero only on a sparse pattern of matched pairs, with entries in ${4,-2,\ldots}$).
The module is one of several decide-chunks whose sole job is to certify $m_2^{\mathrm{num}}=8Z$ at a block of concrete indices. Module doc: "m2Num = 8·explicitZ, chunk 8 (256 kernel decides)." Upstream, $m_2^{\mathrm{num}}$ is the fold over couplingZList, and $Z$ is the case-table of closed-form integers.
proof idea
One-line computational proof: decide. Both sides reduce to concrete Int values at the fixed Fin-4 sextuple $(2,0,0,0,1,3)$, so the kernel equality checker discharges the goal with no lemmas or rewriting.
why it matters
Feeds the assembly theorem m2Num_eq_eight_explicitZ, which states $\forall a,b,c,d,i,j,; m_2^{\mathrm{num}}=8Z$ by exhausting all Fin-4 cases. That global identity is the algebraic backbone of the Regge exact-midpoint $M_2$ TT certificate in 4D gravity analysis inside Recognition Science. Each chunk (here index pattern 200013) closes one of the 256 kernel cells so the assemble step can finish without sorry. It is pure discrete linear-algebra bookkeeping on the coupling kernel, not a continuum GR claim, but it is required scaffolding for the discrete curvature/mass-squared identities used downstream in the gravity sector.
Switch to Lean above to see the machine-checked source, dependencies, and usage graph.