A Ternary (4k+1(2))/3 Collatz-Type Map and Its 4^r-Scaled Family

This repository contains the supplementary materials for the research paper titled “A Ternary (4k+1(2))/3 Collatz-Type Map and Its 4^r-Scaled Family”. The paper introduces and rigorously analyzes a novel family of Collatz-type ternary maps, denoted as TrT_rTr, which are 4r4^r4r-scaled versions of a base ternary map T0T_0T0. The core contribution is the proof of a precise one-step conjugacy relation: Tr(4ry)=4rT0(y)T_r(4^r y) = 4^r T_0(y)Tr(4ry)=4rT0(y) for all relevant domains and scaling factors r≥0r \ge 0r≥0. This conjugacy establishes that every trajectory of TrT_rTr is a direct, scaled replica of the corresponding trajectory of T0T_0T0. Consequently, fundamental dynamical properties such as cycle structures, stopping times, and basin memberships are shown to be preserved across all scales. The paper also derives the heuristic geometric drift rate of approximately 0.76980.76980.7698 (−23.02%-23.02\%−23.02% per step) and discusses the transfer of convergence conjectures from the base map to its scaled family. The accompanying files in this archive are provided to ensure the full reproducibility of the research, adhering to best practices in experimental mathematics: Source Code (verify_conjugacy.py): A Python script that numerically verifies the key conjugacy relations (Tr(4ry)=4rT0(y)T_r(4^r y) = 4^r T_0(y)Tr(4ry)=4rT0(y)) for various values of rrr and yyy. Scaling Rules (SCALING_RULES.txt): Machine-readable definitions of the base map and its scaled variants, including the exact mathematical identities used. Computational Summary (BASE_COMPUTATIONAL_SUMMARY.txt): Numerical data summarizing the computational experiments for the base map T0T_0T0 up to N=109N=10^9N=109, consistent with the results presented in the paper. LaTeX Source Files (.tex): The complete source code for generating the paper, allowing users to compile it themselves. Compiled PDF (.pdf): The final, peer-ready version of the research paper. This release ensures that all computational and theoretical claims made in the paper can be independently verified.