didericis
984655fd3d
Backward bridge-switch search (sharded over valid parity partitions) found an Even Level Graph witness for each of the four previously-open duals: dual 0: partition 12, witness orbit 9458 dual 3: partition 9, witness orbit 388 dual 4: partition 23, witness orbit 3842 dual 5: partition 12, witness orbit 165668 So all four are bridge-derived level graphs, hence valid derived level graphs. Combined with the two duals that are Even Level Graphs outright, the disjunction is now confirmed for ALL SIX critical iso classes at n=21 -- the first nontrivial test of the conjecture passes. Why it worked where exhaustion failed: a witness, when it exists, tends to sit in a SMALL orbit (here a few hundred to ~1.7e5 states) reachable quickly, while other parity partitions of the same triangulation have orbits >1e6. We only need one good partition. The bridge restriction both shrinks orbits ~100x and guarantees validity, so any ELG found in a backward orbit is an immediate witness. - Update paper n=21 subsection to report the resolution. - Add shard_hunt.py (partition-sharded parallel witness hunt). 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