didericis
74030a5b8f
Adds experiments/test_conj_5_26_n_21_22.py, a clause-4 checker that re-uses find_all_36_witnesses + check_clause_4 from check_conj_final_scaled.py and runs them on n = 21, 22 with incremental JSONL output and a 10-minute PROGRESS heartbeat. Results (139 min wall, single thread): n=21: 192 tri, 392,370 colourings w/ clause-1–3 witness, all pass n=22: 651 tri, 1,786,314 colourings w/ clause-1–3 witness, all pass total at n ≤ 22: 2,321,496 / 2,321,496 (combined with the existing 142,812 at n ≤ 20 from check_conj_final_scaled.py) Paper edits: - Abstract: "|V(G)| ≤ 20 (142,812)" → "|V(G)| ≤ 22 (2,321,496)" for the strengthening; clauses-1–3 count unchanged at 535,182 / n ≤ 21. - Intro paragraph: matching update. - Remark rem:conj-3-8-empirical table: added n=21 and n=22 rows; new total ($n \le 22$) = 959 triangulations, 2,321,496 colourings. - Updated script reference in that remark to point at check_conj_final_scaled.py + test_conj_5_26_n_21_22.py. COMMENTARY.md summary table: Conjecture 5.26 row bumped to 2,321,496 / 2,321,496 (n ≤ 22). Also commits the test_*_results.jsonl artifacts (with per-tri records + n-summaries + grand summary) for reproducibility. Co-Authored-By: Claude Opus 4.7 <noreply@anthropic.com>
math-research
Personal mathematics research repository by Eric Bauerfeld. Papers are written in AMS-LaTeX using the amsart document class.
Papers
kempe_style_search_for_smaller_contradiction
Humans Suffice: A Novel Proof of the Four Color Theorem
An in-progress proof of the Four Color Theorem via a minimal counterexample argument. The paper builds on Kempe's 1879 strategy — establishing valid cases for vertices of degree ≤ 4, then extending the argument to the degree-5 case using properties of non-adjacent degree-5 vertices, merged subgraphs, and locked colorings.
plane_depth_labelling
Plane Depth Labelling
Early-stage paper. Title and author information set; content in progress.
Creating a New Paper
Use run.sh to scaffold a new paper from the AMS-LaTeX template:
./run.sh init_paper "Your Paper Title"
This creates a new directory (name derived from the title) containing a paper.tex pre-filled with the title and author.
Setup
The Python library code in lib/ requires SageMath. Run setup once per machine:
./run.sh setup <sage_python_path> <sage_site_packages> [system_name]
sage_python_path— path to the SageMath Python interpreter (e.g./opt/sage/local/bin/python3)sage_site_packages— path to SageMath's site-packages directorysystem_name— optional label for this machine (defaults tohostname -s); used to store per-machine env files as.env.<system_name>
On subsequent runs the paths default to whatever was saved in .env, so ./run.sh setup alone re-runs setup with the existing configuration.
Setup also compiles the plantri submodule via make.
Running Sage
To run a Sage script with plantri available on PATH:
./run.sh sage <script.py> [args...]
Or to open an interactive Sage session:
./run.sh sage
Linting
./run.sh lint
Runs pyright and pylint on lib/ using the SageMath Python interpreter.
Shell Completion
To enable tab-completion for run.sh in zsh, add this to your .zshrc:
eval "$(path/to/run.sh completion)"
Or source it once in the current shell session:
eval "$(./run.sh completion)"
Building
Papers are compiled with LaTeX. From within a paper directory:
latexmk -pdf paper.tex