Open Research Index

Sharp arithmetic separation in chiral Padovan histories

Stephanie Alexander

Palomar Registrypalomar/PALOMAR-2026-09-04-000004Sep 4, 2026math.DSscore 0

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…

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