Why the Odd-Only Collatz Map Lacks Persistent Growth Tubes

This repository accompanies the paper “Why the Odd-Only Collatz Map Lacks Persistent Growth Tubes”.

The work presents an empirical and structural analysis of the odd-only Collatz map,
focusing on the stability of growth-supporting residue structures under 2-adic refinement.
Rather than claiming convergence or a proof of the Collatz conjecture,
the paper isolates refinement stability as a diagnostic criterion.

Empirically, residue classes that exhibit positive expected log-drift at a coarse modulus
(e.g. mod 36) fail to remain dominant when refined to mod 72 for the map n ↦ 3n + 1,
while the variant n ↦ 3n + 5 exhibits stable lifting of its dominant structure.

The repository includes the paper, the analysis code, and the residue-conditioned
drift data used to generate the figures.
The results are intended as a structural perspective on the difficulty of sustaining
persistent growth in Collatz-type dynamics.