didericis
adafecc75b
Replaces the spoke-only Figure 4 with a true barbell example:
Setup:
- B_out: hexagon u_0..u_5 (red).
- O = barbell: triangle {a_1, a_2, a_3} + triangle {b_1, b_2, b_3}
+ bridge a_3-b_1 (light red).
- 14 spokes triangulate the annulus into 14 annular triangles:
6 outer-cap + 6 inner-cap + 2 bridge-cap.
Dual placement is precise:
- All 14 blue dots at exact triangle centroids (via TikZ
barycentric cs).
- 13 edges of the Hamilton cycle wrap around the annulus
crossing each spoke.
- The bridge dual edge connects the two bridge-cap triangles
directly (dashed blue chord across the cycle).
Resulting Γ ≅ Θ(1, 7, 7): Hamilton cycle of length 14 with a
single length-1 chord. Outerplanar (the length-1 chord has no
internal degree-2 vertex, so no K_{2,3} minor).
This now properly demonstrates the chord arising from a real
bridge, exactly as the theorem and Remark 1.14 describe.
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