didericis
8dd9d537f9
Previous figures drew σ as VERTEX colors on a 6-cycle. This was misleading: σ = (1,2,3,2,3,1) is not a proper vertex 3-coloring of a hexagon (σ_5 = σ_0 = 1 at adjacent vertices), and the user correctly flagged this. σ is the coloring of the 6 *spoke edges* -- the G'-edges of G' that cross γ, equivalently the 6 edges of γ ⊂ G under the duality γ-edge ↔ crossing G'-edge. Adjacent γ-edges meet at γ-vertices, which are not G'-vertices, so σ has NO proper-coloring constraint on itself. Proper-edge-coloring constraints live on each tire's full annular cycle, which is longer than 6 (T_1's is 12, T_2's is 9), with γ-spokes interleaved among non-γ spokes; that's where the extendibility of σ is actually checked. Redrawn figures: - fig_rainbow_orbit.png: σ drawn as edge colors of γ (not vertex colors), all 6 orbit elements. - fig_rainbow_pattern.png: abstract pattern abcbca as edge labels, with explanatory text in the legend. - fig_rainbow_setup.png: shows γ between the two tires with each tire's full annular cycle (length 12 and 9), the interleaved non-γ dual vertices, the dashed G'-spoke edges crossing γ colored by σ, and T_1's antipodal chord in O_1. 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