didericis
1a71658349
Findings at n=9 (50 triangulations, orbits fully exhaustible): - 36 bridge-derived, 14 NOT bridge-derived. So bridge-derived is a PROPER subclass of derived (49 derived at n=9). All 14 non-bridge graphs are intertwining trees -- as are all 50, necessarily: intertwining tree <=> dual Hamiltonian, and the smallest non-Hamiltonian 3-connected cubic planar graph has 38 vertices, i.e. dual on 2n-4=38 => n=21. Hence every triangulation with n<=20 is an intertwining tree, and the disjunction "bridge-derived OR intertwining" is trivially true below n=21. The 4 Holton-McKay duals are the first non-intertwining triangulations. - Static parity-subgraph invariants (Betti numbers, component counts, cross-edge count, existence of an all-forest partition) do NOT separate bridge-derived from non-bridge-derived -- both classes realize beta=0 partitions and identical ranges. Bridge-derivability is dynamical, not a simple static invariant; no easy obstruction. - Side lemma: every valid parity partition of an n-vertex triangulation has exactly 2n-4 cross edges (intra-edges = n-2). Holds for all n=9 graphs. 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