didericis
ee4233f066
Added section "Could the minimum non-trivial cyclic cut be 8?"
Answer: yes in principle. Birkhoff gives "≥ 6"; nothing in the
condition pins the value to 6. A planar cubic G^* with min
non-facial cyclic edge connectivity = 8 would have:
- No non-facial 6-edge cut.
- No non-facial 7-edge cut.
- Some non-facial 8-edge cut.
By cut-parity lemma: 8-cuts have even sides; 7-cuts have odd
sides.
Heuristic when this happens: link vertices of degree ≥ 6
(rather than icosahedron-tight 5) push second-link length to
≥ 10, eliminating small non-facial separators.
The cut-tire framework adapts: chain DP and T_∂ construction
work for any cut size, with parameter changes. Per-tire half
needs re-examining for larger structures.
Bottom line: min non-trivial cyclic cut is one of {6, 7, 8, 9,
...}; Birkhoff doesn't pin it down. Framework's natural domain
is whatever value it happens to take, with 6 being the simplest.
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"
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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
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./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
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eval "$(path/to/run.sh completion)"
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eval "$(./run.sh completion)"
Building
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latexmk -pdf paper.tex