didericis
8faf37a9dc
Adds fig_facial_dual_choices.png showing T'_{f'} for the three faces
A, B, C of T'_ann = θ(1, 3, 3) in the bridge case:
Face A (outer): V(A) = all 6 vertices; T'_A pulls in all four
external neighbors u_1, u_2, u_4, u_5.
Face B (inner right): V(B) = {v_0, v_1, v_2, v_3}; T'_B pulls in
only u_1, u_2 and the cycle-neighbors v_4, v_5.
Face C (inner left): mirror image of B.
The figure also visually conveys that the chord endpoints v_0, v_3
(= the two annular faces sharing the bridge edge) have all three
G'-edges inside T'_ann, so neither contributes an external u_v.
Adds:
- experiments/draw_facial_dual_choices.py
- notes/fig_facial_dual_choices.png
- Figure 5 in paper.tex referencing the new image.
Paper grows from 9 to 10 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