e_200231
plain-language theorem explainer
For the multi-index (2,0,0,2,3,1), the midpoint M2 numerator equals eight times the explicit Z kernel value. Gravity analysts checking the 4D Regge exact-midpoint TT identity cite this as one cell of the chunk-8 table. The proof is a pure kernel decision: both sides evaluate to the same numeral.
Claim. For the index tuple $(2,0,0,2,3,1)$, the midpoint $M_2$ numerator equals eight times the corresponding explicit $Z$ value: $\mathrm{m2Num}(2,0,0,2,3,1)=8\,\mathrm{explicitZ}(2,0,0,2,3,1)$.
background
The ambient module is a finite chunk of the 4D Regge exact-midpoint $M_2$ TT-identity certification. The global claim being assembled is that the midpoint $M_2$ numerator coincides with eight times an explicitly expanded $Z$ kernel on every multi-index that appears in the expansion.
Each sibling theorem fixes one concrete six-tuple of indices and asserts the same scalar identity at that point. Chunk 8 is one of the 256-kernel decide blocks that discharge these equalities by direct evaluation rather than by symbolic rewriting.
The imported kernel-cert module supplies the concrete definitions of the numerator and of explicit $Z$; this file only records the evaluated instances.
proof idea
One-line decide proof. Both sides are closed numeric terms once the six indices are substituted, so the kernel reduces the equality to true by computation. No lemmas are invoked.
why it matters
The declaration is a single cell in the chunk-8 table that fills the identity $\mathrm{m2Num}=8\cdot\mathrm{explicitZ}$ across the full multi-index range needed for the 4D Regge midpoint TT analysis. Downstream assembly of the exact-midpoint identity depends on every such cell succeeding; a single mismatch would break the global certificate. Within Recognition Science gravity work this is bookkeeping infrastructure, not a new physical law: it underwrites the discrete curvature bookkeeping that later feeds continuum limits and the forced $D=3$ spatial sector.
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