T

didericis 65f79f2e65 papers: split coloring_nested_tire foundations into separate paper

NEW PAPER: papers/coloring_nested_tire_graphs/ ("Coloring Nested
Tire Graphs", 5 pages).

Contains foundational definitions 1.1 through 1.7 from the dual
paper, plus the four illustrative figures:
  - 1.1 Level source
  - 1.2 Levels
  - 1.3 Dual (with label def:dual added — was missing in original)
  - 1.4 Dual depth
  - 1.5 Tire graph
  - 1.6 Remark (tire counts)
  - 1.7 Partial tire dual

Also: the dual-depth figure, the tire-example figure, and both
partial-tire-dual figures (vanilla + bridge case).

MODIFIED: papers/coloring_nested_tire_dual_graphs/paper.tex now a
follow-up:
  - Abstract recasts the paper as building on the foundational paper.
  - Intro no longer recapitulates definitions; lists them as
    citations to the new paper.
  - Removes definitions 1.1-1.7 and their figures (now in
    foundational paper).
  - Internal \ref{...} to removed labels converted to
    \cite[Definition N.M]{bauerfeld-nested-tires}.
  - Bibliography adds the new paper as a reference.
  - Renumbering: theorems/propositions now start at 1.1 (formerly
    1.8). Paper down from 14 to 8 pages.

Both papers compile cleanly with no broken references.

Co-Authored-By: Claude Opus 4.7 <noreply@anthropic.com>

2026-05-27 00:54:53 -04:00

ams-latex-template @ 2aebb46d6a

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lib

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papers

papers: split coloring_nested_tire foundations into separate paper

2026-05-27 00:54:53 -04:00

plantri @ 09745aeb09

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research

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.gitignore

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.gitmodules

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default.tikzstyles

face_monochromatic_pairs: explicit counterexample to Conjecture 5.5

2026-05-25 02:55:35 -04:00

flip_symmetric_census.py

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pyrightconfig.json

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README.md

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requirements.txt

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run.sh

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README.md

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 directory
system_name — optional label for this machine (defaults to hostname -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