didericis
50183df6bc
Note records the closed-chain experiment: forward-propagate state
through SR+PDS tire chains with degenerate-inner T_1 and outer-
triangle T_n (m_n=3). All 10 tested chains converge to the same
final state at L_n — exactly the 6 permutations of {1,2,3}.
Introduces the "outer triangle absorption" framing: distinguishes
H1 (chain-dependent: pigeonhole does real work to filter input to
T_n) vs H2 (T_n-only absorption: T_n's σ_U-projection is intrinsically
the 6 permutations regardless of input). Conjecture: H2 (testable by
single-tire computation).
If H2 holds, items 3-4 of the 4CT-via-tire-decomposition outline
become automatic from local data. If H1, the chain-pigeonhole does
structural work and the question is sharper.
Three-panel figure: (A) closed PDS chain (5,6,5,3) with concentric
levels and source apex; (B) outer-face dual constraint requiring
permutation-of-{1,2,3} on outer triangle; (C) state-size trajectory
showing absorption to 6 at the outer step.
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