Residue Recurrence in the Odd-Only Collatz Dynamics: Reference Implementation

This record provides a fully reproducible reference implementation and complete supporting material for the empirical study “Residue Recurrence in the Odd-Only Collatz Dynamics: An Empirical Note via Modular Projection.” The package is designed to serve as a self-contained research object, enabling independent verification and reuse. It includes: a complete and deterministic Python implementation reproducing all experiments reported in the accompanying paper, row-level CSV datasets and automatically generated CCDF (complementary cumulative distribution function) plots, a fixed, non-optional observation rule for odd-only (Syracuse) Collatz trajectories, and detailed documentation specifying experimental parameters, boundary-case handling, and reproducibility constraints. The study reports distribution-level and tail-level recurrence behavior observed when odd-only Collatz trajectories are viewed through a finite modular projection modulo 2^k. Recurrence is quantified via a residue self-intersection statistic (“backwash ratio”) and a length-normalized score compared against a conservative i.i.d. uniform-residue baseline conditioned on observed trajectory length. Importantly, no claim of convergence, divergence, periodicity, or proof of the Collatz conjecture is made. All results are strictly empirical and descriptive. Observed differences between arithmetic classes (e.g., primes vs. composites) are interpreted as differences in the induced distribution of odd-part orbit drivers, not as direct dynamical dependence on multiplicative structure. The primary contribution of this record is methodological: it provides a transparent, falsifiable experimental protocol and a reference implementation that can be reused, extended, or challenged in future investigations of Collatz-type dynamics, modular residue behavior, and orbit-level constraints under finite observational lenses.