didericis
95d020b113
NEW NOTE: birkhoff_internally_6_connected.tex (3 pages) NEW SCRIPT: experiments/draw_internally_6_connected.py NEW FIGURE: icosahedron_internally_6_connected.pdf States and illustrates the Birkhoff (1913) condition that any minimum 4CT counterexample must be internally 6-connected: - No separating 3-cycle. - No separating 4-cycle. - No separating 5-cycle isolating ≥ 2 vertices on either side. - Only separating 5-cycles isolating exactly 1 vertex. The icosahedron is the canonical example: 12 vertices all of degree 5; the 5 neighbors of every vertex form a 5-cycle whose removal isolates that vertex. Sage verification confirms this: Vertex 0 has 5 neighbors: [1, 5, 7, 8, 11] Induced subgraph on neighbors: 5 edges, is_cycle=True After removing the 5 neighbors: 2 components, sizes=[1, 6] Note also lists the graphs used in our framework testing: - Icosahedron (12 v, dual = dodecahedron) - Pentakis dodecahedron (32 v, dual = Buckyball) - Holton-McKay graphs (21 v primal, 38 v dual) All are internally 6-connected, hence in the framework's intended domain. 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