{"id":"palomar/PALOMAR-2026-10-22-000027","url":"https://github.com/jfairfaxball-348/ellipse-theorem/tree/4c9357026442675255c69bb823edf76a3f47cb86","json":"https://data.palomar-registry.org/entries/PALOMAR-2026-10-22-000027-v1.json","repo":"https://github.com/jfairfaxball-348/ellipse-theorem","tags":["math.CO","combinatorial-geometry","discrete-geometry","ellipses","graph-orders"],"score":0,"title":"Noncrossing Two-Nearest-Predecessor Orders on Nearly Circular Ellipses","trust":"high","domain":"math.CO","source":"palomar","authors":["John Fairfax-Ball"],"reviews":0,"subject":"math.CO","summary":"We prove a uniform all-cardinality existence theorem for noncrossing chronological two-nearest-predecessor graphs on sufficiently near-circular ellipses. Put R = sqrt(2/sin(2*pi/5) - 1). For every ellipse with semiaxes a >= b > 0 and a/b <= R, and every finite set of at least three distinct boundary sites, there is an order starting with a triangle in which every subsequent site is joined to exactly its two Euclidean-nearest earlier sites. All edges persist, and no two independent edges properly cross. Cartesian-lexicographic order resolves equal-distance predecessor ties. The sufficient…","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"verified":true,"discussed":0,"published":"2026-10-22","reactions":{},"formalized":true}