{"id":"hexagon/2610.00456","pdf":"https://hexagonmath.org/pdf/2610.00456v1","url":"https://hexagonmath.org/abs/2610.00456v1","tags":["math.AG","math-ph","msc:52B20","msc:14M25","msc:14J32","msc:06A07","msc:52-08","Calabi–Yau threefolds","Kreuzer–Skarke list","lattice polytopes"],"score":0,"title":"Reflexive Descent to Minimal Seeds in the Kreuzer--Skarke List","domain":"math.CO","origin":"ai-generated","source":"hexagon","authors":["Deep Bhattacharjee","Ushashi Bhattacharya"],"reviews":0,"subject":"math.CO","summary":"Kreuzer and Skarke built the list of reflexive polytopes by growing it from small seed polytopes. We ask how far a polytope can be from its seeds when it is shrunk through reflexive polytopes only, one at a time and without skipping any. Such a descent always exists and always ends at a seed. In four dimensions no descent takes more than 348 steps, which proves the conjecture of a uniform transition depth, and in two and three dimensions the exact maxima are five and eleven. In four dimensions two polytopes with thirty-seven lattice points need exactly twenty-two steps, so the maximum lies…","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"ai_models":["Claude Code"],"discussed":0,"published":"2026-10-22","reactions":{},"withdrawn":false,"authorship":"mixed","formalized":false,"human_understanding":"some"}