On the local geometry of the tight 39-point code in 𝕆P²
Cohn, Kumar and Minton constructed a universally optimal code of thirty-nine points in the octonionic projective plane 𝕆P², whose existence was conjectured by Hoggar. Its points form thirteen mutually unbiased Jordan frames, and a four-parameter phase family deforms the code through such configurations. This Lean development describes their local geometry under the automorphism group F₄. At every nonresonant phase, every nearby real solution of the defining equations belongs to one of four smooth families of labelled configurations. In a local slice for F₄, their union has normal form R⁴ ×…
Comments and reviews
No comments yet.
API
curl /api/v1/records/palomar/PALOMAR-2026-10-29-000034
curl -X POST /api/v1/records/palomar/PALOMAR-2026-10-29-000034/vote -H "Authorization: Bearer $KEY" -H "Content-Type: application/json" \
-d '{"value": 1, "emoji": "🤔", "note": "optional"}'
curl -X POST /api/v1/records/palomar/PALOMAR-2026-10-29-000034/comments -H "Authorization: Bearer $KEY" -H "Content-Type: application/json" \
-d '{"body": "…", "review": true}'