# 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–structural analysis of the odd-only Collatz map,
focusing on the stability (or failure thereof) of growth-supporting residue
structures under 2-adic refinement.

Rather than claiming convergence or a proof of the Collatz conjecture,
the paper isolates and analyzes *refinement stability* as a structural obstruction
to persistent growth.

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## Contents

- `Why_the_Odd_Only_Collatz_Map_Lacks_Persistent_Growth_Tubes.pdf`  
  The main paper.

- `scc_export.py`  
  Python script used to construct residue transition graphs and extract
  strongly connected components (SCCs) for the odd-only Collatz map.

- `drift_mod72_b1.csv`  
  Residue-conditioned empirical drift statistics for the map  
  \( n \mapsto 3n + 1 \) (odd-only), modulo 72.

- `drift_mod72_b5.csv`  
  Residue-conditioned empirical drift statistics for the map  
  \( n \mapsto 3n + 5 \) (odd-only), modulo 72.

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## Summary of Results

- At coarse modulus (e.g. mod 36), both \(3n+1\) and \(3n+5\) exhibit
  apparent growth-favorable residue classes.

- Under refinement to mod 72, these similarities break sharply:
  - The dominant SCC associated with \(3n+1\) fragments and loses dominance.
  - The dominant SCC associated with \(3n+5\) lifts stably and remains dominant.

- This demonstrates that **positive expected log-drift at a fixed modulus
  does not guarantee refinement stability**, highlighting a structural
  obstruction to persistent growth tubes in the odd-only Collatz dynamics.

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## Reproducibility

- The script `scc_export.py` reproduces the SCC structures analyzed in the paper.
- The CSV files contain the residue-conditioned drift statistics used to generate
  the figures in Sections 4–5.
- All figures involving mod 36 and mod 72 drift comparisons are generated directly
  from these CSV files.

The analysis is empirical but structurally constrained; no probabilistic
measure-theoretic assumptions are made.

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## Scope and Limitations

- This work does **not** claim a proof of the Collatz conjecture.
- It does **not** assert convergence of individual trajectories.
- The results concern **residue-level structural behavior under refinement**,
  not pointwise dynamics.

The contribution is intended as a structural diagnostic for understanding
why apparent growth mechanisms fail to persist under refinement.

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## Keywords

Collatz conjecture, odd-only Collatz map, residue classes,  
strongly connected components, 2-adic refinement, dynamical systems

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## Author

Independent researcher.

Released via Zenodo to support reproducibility and further analysis.