didericis
36be3e14cb
Per user's request: try option 3 (push case analysis) as a sanity
check on the G'-pentagon fallback conjecture. Result: trivial
pigeonhole closes the |S| ≤ 1 case but no further.
Added:
- Lemma (Partial proof, |S| ≤ 1): a single uncovered vertex hits
at most 3 of the ≥ 6 G'-pentagons of the reduced dual, so 3
pentagons remain fully covered. Trivial pigeonhole.
- Remark "The pigeonhole stops at |S| = 1; the proof begins to
resemble discharging": Theorem deciding-face-partial-extended
+ Lemma gprime-pigeonhole cover ~91% of chord-apex+Kempe
configurations (73.87% with |S|=0 + 17% with |S|=1). The
remaining ~9% have |S| ≥ 2 and need finer graph-structural
input, exactly the discharging flavour Appel-Haken / RSST /
Gonthier used for 4CT. We stop the case-by-case route here.
So the sanity check confirms the user's intuition: continuing the
case analysis would replay the irreducible-configurations approach
in different vocabulary. Pivoting to option 2 (global argument)
next.
Paper stays at 22 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