didericis
a36271a2cf
- Step 1: local CW structure at u, w (F_R = F_{ab}^u = F_{ca}^w, etc.)
- Step 2 (new, complete): K_1 \ e leaves u into In(K_0) and arrives at w
from Out(K_0), so it crosses K_0 an odd number of times. Each crossing
uses a shared a-edge, so |E(K_0) ∩ E(K_1)| is even and ≥ 2. Closes
the case of a single shared edge.
- Step 3 (new, complete): Heawood's face-sum identity ∑ h_φ ≡ 0 (mod 3)
applied to every H-face inside a face Φ of K_0 ∪ K_1, with
multiplicity bookkeeping at degree-3 vs degree-2 boundary vertices,
yields ν_{2,Φ} ≡ -ℓ_Φ (mod 3) for every face Φ.
- Step 4 (open): use Lemma 5.2 alternation to force ν_{2,Φ} on some
face, and exhibit a violation.
Literature search via research-analyst confirms the theorem is novel
(Heawood face-sum and the +/-1 rotation sign are classical; no result
relating intersecting Kempe cycles via vertex signs found).
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