{"id":"palomar/PALOMAR-2026-08-19-000006","url":"https://github.com/stalex444/arithmetic-of-time/tree/c48eb12817dd1d7ff3dc4d92306c7a4f249e6d7d","json":"https://data.palomar-registry.org/entries/PALOMAR-2026-08-19-000006-v1.json","repo":"https://github.com/stalex444/arithmetic-of-time","tags":["math.CO","math.DS","msc:68R15","msc:37B10","substitutions","symbolic-dynamics","combinatorics-on-words","lean-formalization"],"score":0,"title":"stalex444/arithmetic-of-time","trust":"high","domain":"math.CO","source":"palomar","authors":["Stephanie Alexander"],"reviews":0,"subject":"math.CO","summary":"A kernel-checked chirality package for the Padovan substitution (0 ↦ 1, 1 ↦ 2, 2 ↦ 01 on Fin 3; its incidence matrix has characteristic polynomial x³ − x − 1, an orientation fact that is not used or compared). Three compared theorems, all at the iterate-factor level — they quantify over factors of the concrete words S^[n] [x], never over an abstract subshift. (1) The successor invariant: in every positive iterate from any seed, the letter 0 (\"a\") is immediately followed by 1 (\"b\"). (2) Chirality: the word 20 (\"ca\") is a factor of an iterate while its reversal 02 (\"ac\") is a factor of no…","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"verified":true,"discussed":0,"published":"2026-08-19","reactions":{},"formalized":true,"formalizes":[{"title":"Dynamical Invariants from Asymptotic Composants","identifier":"arXiv:2602.18501","relationship":"adapts"}]}