Year: 2026
Type: preprint
Abstract: The single-seed Rule 30 cone has unbounded least diagonal periods in both directions. On the finite-support side, first contact fixes the least Newton index and an integer polynomial lift gives a Fibonacci ceiling. On the reflected Rule 86 side, a backward map on periodic tail profiles retains the zero boundary and bounds the largest period from below, independently of transient lengths. This argument extends the reset/integration criterion for period doubling. The physical Rule 135 orbit is a translated complement of Rule 30 after its first step, yielding finite or cofinite supports. A separately initialized auxiliary recurrence admits exact index-by-index stabilization. Residue tables and block formulas describe the remaining structure and permit evaluation from supplied representations. Their construction and minimum size remain distinct quantitative questions.
Source: arXiv (Cornell University)
Author: Nersissian, Tigran
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7212423700
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