didericis
a8af5612c4
Concrete picture demonstrating "low-side faces span multiple
parent faces of H_{d-1}":
- H_{d-1} drawn as the outer blue circle.
- H_d as a smaller nested orange circle inside.
- Face A of H_d (high-side, inside inner cycle): a small disk,
sits entirely inside face X of H_{d-1}. Unique parent. ✓
- Face B of H_d (low-side, outside inner cycle): RED REGION
spanning across the H_{d-1} cycle. It is one connected face
of ℝ² \ H_d, but it intersects BOTH face X (annulus between
cycles) and face Y (exterior of H_{d-1}). Neither X nor Y
contains all of B → no unique parent. ✗
This makes the uniqueness step's failure visible: the forest
proposition's containment argument works for high-side (= face A,
nested inside) but fails for low-side (= face B, spanning across).
The motivation section of the note now has 3 figures:
1. Low-side spans uniqueness failure (this commit, page 1)
2. T_∂ thick-H_1 hexagon (page 2)
3. T_∂ thin-H_1 tree (page 2)
Plus the nested-cut-tires figure on page 3.
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
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eval "$(path/to/run.sh completion)"
Or source it once in the current shell session:
eval "$(./run.sh completion)"
Building
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latexmk -pdf paper.tex