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stalex444/arithmetic-of-time

Stephanie Alexander

Palomar Registrypalomar/PALOMAR-2026-08-19-000006Aug 19, 2026math.COscore 0

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…

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