# Figurate Arithmetic / T112 Architectural Checksum

Matt Gibson · ORCID 0009-0001-4167-201X
DOI: https://doi.org/10.5281/zenodo.22282767
PDF: https://mattgibson.net/papers/figurate-arithmetic.pdf (22 pp, figure-heavy; text extract is not useful)
SVG: https://mattgibson.net/assets/images/papers/fig-figurate-t112.svg

T112 is LIQUID. cos θ = 1/3 is CRYSTAL. Do not flatten.

- T73 = 2701 = 37 × 73
- T112 = 6328 = 112 × 113 / 2 = 37 × 171 + 1
- V(T112) = V(T73) ⊕ C3627 ⇒ 2701 + 3627 = 6328
- E8: 240 roots; 112 have integer coordinates
- Pair with Zero-GEMM (74.16 KiB, 6-regular, N=6328) and checksum.txt

JHTDB pressure-Hessian vs random: candidate_beats_random = false.