didericis
9185d626af
Moved from coloring_nested_tire_dual_graphs/ TO coloring_nested_tire_graphs/:
- Proposition (Source-side simple-cycle property) → now 1.7
- Lemma (Tire-component lemma) → now 1.8
- Theorem (Tire treads partition the bounded faces) → now 1.9
- Remark (boundaries-may-be-degenerate) → now 1.10
- Remark (no extra hypotheses needed) → now 1.11
These are foundational structural results about tire-graph
decompositions induced by a level source, not specifically about
the partial tire dual D(T) or coloring. Belongs in the
foundational paper.
Updates:
- Internal \cite[Definition~1.5]{bauerfeld-nested-tires} inside
the moved blocks → local \ref{def:tire-graph}.
- Foundational paper abstract rewritten to highlight the
tire-component lemma and tread partition as the main results.
- Dual paper abstract trimmed: no longer claims the tire-component
lemma as its own contribution.
- Dual paper intro citation list adds bullets for the moved
lemma (\cite[Lemma~1.8]) and theorem (\cite[Theorem~1.9]).
- No external references to the moved items inside the dual paper.
Page counts:
- Foundational: 3 → 7 pages.
- Dual: 9 → 7 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"
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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]
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Setup also compiles the plantri submodule via make.
Running Sage
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./run.sh sage <script.py> [args...]
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./run.sh sage
Linting
./run.sh lint
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Building
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latexmk -pdf paper.tex