didericis
53a676971c
Adds Definition (cut tire) to cut_depth_label.tex:
Given the depth labelling on G'_i, for each d > 0 let H_d be the
subgraph on depth-d edges (with inherited planar embedding). For
each face f of H_d, the cut tire at (d, f) is the subgraph of G'_i
consisting of:
- every edge on the boundary walk of f (all depth d), and
- every edge of G'_i incident to the boundary walk of f with
depth d-1 or d+1.
The depth-d edges form the "face boundary"; the d-1 edges are
"inner spokes" (toward the cut); the d+1 edges are "outer spokes."
This is the dual-side analogue of the tire annular face connector
T'_{f'} (paper.tex Def. 1.16):
face boundary ↔ T'_ann (annular subgraph at depth d)
cut tire ↔ T'_{f'} (annular face connector)
inner/outer spokes ↔ inner/outer spokes of T'_{f'}
Adds experiments/cut_tire.py producing fig_cut_tire.png:
5-panel visualisation of cut tires at depths d = 1, 2, 4, 5, 6 on
G'_1 (V\S half of Holton-McKay #0). Outermost tire at d=1 (face
length 12, 5+4 spokes); innermost at d=6 (face length 12, 7+1).
Note grows from 3 → 5 pages.
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