didericis
85497c38f2
Three verification scripts: experiments/check_30_residual.py and check_30_residual_v2.py: attempt to identify the hypothesized residual case (|S| = 8 AND p_hit = p_total = 8) where all G'-pentagons would be hit by S forcing the fallback to require G'-heptagons. Result: 0 such colourings — the conditional doesn't occur empirically. experiments/check_gprime_pentagon_always_works.py: direct check that across all 1,314 bad colourings, at least one G'-pentagon has its boundary entirely in V(K_b) ∪ V(K_c). RESULT: 1,314 / 1,314 = 100.00% have an uncovered G'-pentagon. So the G'-pentagon fallback conjecture (Conjecture gprime-pentagon-fallback) is empirically true on ALL chord-apex+ Kempe colourings — both the "tight" ones (handled structurally by Theorem deciding-face-partial-extended) and the "bad" ones (where Lemma flank-covering-hex fails). Implication: the residual cases I worried about (where the fallback would need to be relaxed to length ≢ 0 mod 3) DO NOT OCCUR. So the Conjecture (G'-pentagon fallback) suffices to close the deciding- face conjecture in full empirical generality. 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