Local Dynamics and Periodic Lifts of Carry Depths in Canonical PLRS Numeration

For a canonical positive linear recurrence numeration system with threshold-reset legality automaton and maximal boundary block P = p1 pL, we give an exact local grammar for the reset-depth sequence produced by lexicographic succession. Every positive reset depth determines its predecessor s branch-point state and depth exactly (Theorem A); every carry-depth excursion collapses to depth 0 in [ ]…