didericis
d36c2513cc
Previous commit (00229fa) incorrectly extended the empirical
verification of Conjecture 5.26 (strengthening, clauses 1-4) to n=21.
The running test (test_n_21_to_24.py) checks:
- Non-constancy on V(K_b), V(K_c), V(K_b) ∪ V(K_c).
- Deciding-face existence.
These verify Conjecture 5.1 (clauses 1-3) via Corollary 5.4 and via
the Heawood-face-sum route, respectively. They do NOT verify clause
(4) of the strengthening (Conjecture 5.26), which requires
constructing the subdivided graph and checking the new f_n's edge
colouring.
Conjecture 5.26 has been verified at n ≤ 20 (142,812 colourings) only,
via `check_conj_final_scaled.py` (which explicitly constructs the
clause-3 subdivision and checks clause-4). The n=21 results extend
the weaker checks but NOT the strengthening.
Paper fixes:
- Abstract: clarified that strengthened conjecture is at n ≤ 20
(142,812), unstrengthened (clauses 1-3) at n ≤ 21 (535,182).
- Intro paragraph after "we propose": same clarification.
COMMENTARY.md fix:
- Summary table: "Conjecture 5.26 (strengthening)" row reverted
to "142,812 / 142,812 (n ≤ 20)". The other rows (about Heawood-
based checks) remain at 535,182 / 535,182 (n ≤ 21).
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