didericis
c6d4eb06fb
The complete tire dual D*(T) and Tait correspondence material was giving exact counts but only via Tait colorings with XOR-to-0 conditions at high-degree vertices -- not proper edge colorings, which was the original goal. Removed: - Definition 1.13 (Complete tire dual) and its figure. - Proposition 1.14 (Tait correspondence on complete tire dual). - Remark 1.15 (Tait construction). - Remark 1.16 (octahedron verification). - Tait1880 bibitem (no longer cited; the body-text mention of Tait's theorem in the introduction remains). - experiments/draw_complete_tire_dual.py + its PNG. - experiments/draw_tait_coloring_example.py + its PNG. - fig_complete_tire_dual.png from the paper root. The partial tire dual definition (Def 1.7), structure proposition (Prop 1.8), figure, and associated scripts (tire_graph.py, draw_partial_tire_dual.py) are retained. Paper shrinks from 9 to 7 pages. 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