collatzprefixverification
Computational verification of base-3 prefix class contraction for the Collatz map.
https://github.com/the-math-gremlin/collatzprefixverification
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Repository
Computational verification of base-3 prefix class contraction for the Collatz map.
Basic Info
- Host: GitHub
- Owner: the-math-gremlin
- License: mit
- Language: Python
- Default Branch: main
- Size: 805 KB
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- Stars: 1
- Watchers: 1
- Forks: 0
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Metadata Files
README.md
Collatz Prefix Verification
This repository contains the data and code used to verify the contraction of all base-3 prefix classes under the Collatz map, supporting the paper:
"From Infinite to Finite: A Proof of the Collatz Conjecture via Prefix Partition and Height Descent"
by Sadie A. Sherratt
📌 Overview
Every base-3 prefix of length 10 was tested for contraction under the modified Collatz map:
For each prefix r in the range [0, 3^10), the minimal representative n₀ = 3^10 × r was generated.
The Collatz map T(n) was defined as:
T(n) = n / 2 if n is even
T(n) = (3n + 1) / 2 if n is odd
Each trajectory was checked for one of the following outcomes:
A strict drop in the symbolic height function
Entry into the known terminal cycle {1, 2, 4}
No prefix failed to contract.
🔍 Purpose
This computational experiment supports the main theoretical claim of the paper:
Every ternary prefix class contracts in symbolic height, providing a finite partition of the natural numbers under the Collatz map and proving universal convergence.
⚙️ How to Use
- Make sure you have Python 3.10+ installed.
- Run the script:
python prefix_verification.py
- This will generate a new file
prefix_summary.csvwith the results of all 59,049 prefix class checks.
📂 Files
prefix_verification.py– Verifies symbolic height contraction for each prefix class.prefix_summary.csv– Output: contraction type and stats for each prefix.README.md– This file.LICENSE.txt– MIT License.citation.bib– BibTeX citation for the paper.
📖 Citation
If you use this code or data, please cite:
@misc{sherratt2025collatz,
author = {Sadie A. Sherratt},
title = {From Infinite to Finite: A Proof of the Collatz Conjecture via Prefix Partition and Height Descent},
year = {2025},
note = {Preprint},
url = {https://sherrattmath.org/collatz-paper}
}
📝 License
This project is licensed under the MIT License. See LICENSE.txt for full terms.
© 2025 Sadie A. Sherratt. All rights reserved.
Owner
- Login: the-math-gremlin
- Kind: user
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Citation (citation.bib)
@misc{sherratt2025collatz,
author = {Sadie A. Sherratt},
title = {From Infinite to Finite: A Proof of the Collatz Conjecture via Prefix Partition and Height Descent},
year = {2025},
note = {Preprint},
url = {https://sherrattmath.org/collatz-paper}
}
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