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. To set up the linting environment, run:

./run.sh setup

This creates a .venv using the SageMath Python interpreter and installs pylint into it.

Linting

To lint the lib/ directory:

./run.sh lint

This runs pyright (via npx) and pylint using the SageMath Python interpreter.

Building

Papers are compiled with LaTeX. From within a paper directory:

latexmk -pdf paper.tex