upper-bound-unknotting

A self-contained repository for improving upper bounds on unknotting numbers with an RL-based reducer.

This version is set up to run locally and does not rely on Google Drive.

Included files

This repository already contains:

• data/unknotting.xlsx
• models/best_model.zip
• notebooks/upper_bound_unknotting_v6_local.ipynb

So the notebook can be run directly after installing the dependencies.

Repository layout

upper-bound-unknotting/
├─ README.md
├─ requirements.txt
├─ .gitignore
├─ notebooks/
│  ├─ upper_bound_unknotting_v6_local.ipynb
│  └─ upper_bound_unknotting_v5_original.ipynb
├─ data/
│  └─ unknotting.xlsx
├─ models/
│  └─ best_model.zip
├─ training_data/                            # optional extra training files
│  ├─ hard_unknots.csv
│  ├─ very_hard_unknots.csv
│  └─ random_diagrams.csv
└─ outputs/

What the notebook does

The notebook

1. loads data/unknotting.xlsx
2. fills missing Jones vectors from PD presentations when possible
3. finds unresolved unknotting-number ranges such as [a,b] with a != b
4. inflates the PD diagram
5. flips one crossing at a time
6. runs the RL unknotter / reducer
7. computes the Jones vector of the reduced knot
8. matches against the local workbook database, allowing mirrors
9. updates the upper bound while preserving the lower bound, for example [2,3] -> [2,2]
10. overwrites data/unknotting.xlsx

Quick start

Create an environment and install dependencies:

python -m venv .venv
source .venv/bin/activate
pip install -r requirements.txt

Then launch Jupyter:

jupyter lab

and open:

notebooks/upper_bound_unknotting_v6_local.ipynb

Model behavior

The notebook first looks for a pretrained model in:

• models/best_model.zip
• models/ppo_knot_rl_spherogram_continued.zip
• outputs/best_model.zip

Since models/best_model.zip is already included here, it should run without retraining.

Optional training data

If you want to retrain or continue training, you can additionally place files such as

• training_data/hard_unknots.csv
• training_data/very_hard_unknots.csv
• training_data/random_diagrams.csv

If no external training files are present, the notebook can fall back to PD data already stored inside unknotting.xlsx.

Notes

• The notebook is designed to work from inside this repository.
• The main editable parameters are in the configuration cell near the top of the notebook.
• Results are written back into data/unknotting.xlsx.