{"id":"palomar/PALOMAR-2026-09-04-000004","url":"https://github.com/stalex444/chiral-padovan-histories/tree/14711e6cffdc74669d15f808d4aec8cbb373d71f","json":"https://data.palomar-registry.org/entries/PALOMAR-2026-09-04-000004-v1.json","repo":"https://github.com/stalex444/chiral-padovan-histories","tags":["math.DS","math.NT","msc:37B10","msc:11K16","msc:52C23","msc:11E04","padovan-sequences","dynamical-systems","algebraic-number-theory"],"score":0,"title":"Sharp arithmetic separation in chiral Padovan histories","trust":"high","domain":"math.DS","source":"palomar","authors":["Stephanie Alexander"],"reviews":0,"subject":"math.DS","summary":"Sixteen compared statements establish quantitative recurrence for the actual infinite Padovan prefix path and compare cubic and quartic arithmetic record windows. For 0 =1, and Padovan substitution stages attain equality at arbitrarily large clocks. The full cubic record window is relatively dense with uniformly discrete differences; the identical positive-real window in the quartic case admits nonzero inverse-unit points arbitrarily close to zero, while its other real embedding grows. Scalar prefix coordinates factor the included faithful chiral timelike history in the genuine quartic trace…","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"verified":true,"discussed":0,"published":"2026-09-04","reactions":{},"formalized":true}