{"id":"palomar/PALOMAR-2026-10-29-000034","url":"https://github.com/macgregor-sudo/tight-39-code/tree/46f01c135aacea9003435e7f1dc99b4a69568e83","json":"https://data.palomar-registry.org/entries/PALOMAR-2026-10-29-000034-v1.json","repo":"https://github.com/macgregor-sudo/tight-39-code","tags":["math.DG","math.CO","math.RA"],"score":0,"title":"On the local geometry of the tight 39-point code in 𝕆P²","trust":"high","domain":"math.DG","source":"palomar","authors":["Robert R. MacGregor"],"reviews":0,"subject":"math.DG","summary":"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 ×…","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"verified":true,"discussed":0,"published":"2026-10-29","reactions":{},"formalized":true}