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README: refresh papers index

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Replace the stale two-paper list (kempe_style_search_for_smaller_contradiction
and plane_depth_labelling -- neither in the repo) with a table of the
12 papers actually present under papers/, with titles pulled from each
paper.tex.  Also clarify that init_paper creates papers/<name>/ rather
than a top-level directory.

Co-Authored-By: Claude Opus 4.7 <noreply@anthropic.com>
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2026-05-27 23:21:57 -04:00
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# math-research
Personal mathematics research repository by Eric Bauerfeld. Papers are written in AMS-LaTeX using the `amsart` document class.
Personal mathematics research repository by Eric Bauerfeld. Papers are written in AMS-LaTeX using the `amsart` document class and live under `papers/`.
## Papers
### `kempe_style_search_for_smaller_contradiction`
**Humans Suffice: A Novel Proof of the Four Color Theorem**
All papers are at `papers/<name>/paper.tex`. The current set:
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.
| Directory | Title |
|---|---|
| `colored_edge_flip_classes` | Colored Edge Flip Classes |
| `colored_pentagon_contractions` | Colored Pentagon Reductions |
| `coloring_nested_tire_dual_graphs` | Coloring Nested Tire Dual Graphs |
| `coloring_nested_tire_graphs` | Coloring Nested Tire Graphs |
| `even_level_graph_generators` | Even Level Graph Generators: a constructive conjecture stronger than the Four Color Theorem |
| `face_monochromatic_pairs` | Face-Monochromatic Pairs and the Four Colour Theorem |
| `iterated_reduction_in_reduced_dual` | An Iterated Reduction in the Reduced Dual |
| `level_resolutions_of_maximal_planar_graphs` | Level Resolutions of Maximal Planar Graphs |
| `level_switching` | Level Switching |
| `plane_depth` | Plane Depth |
| `plane_depth_sequencing` | Plane Depth Sequencing |
| `plane_diamond_coloring` | Plane Diamond Coloring |
### `plane_depth_labelling`
**Plane Depth Labelling**
Early-stage paper. Title and author information set; content in progress.
The papers form a connected programme around plane triangulations, BFS-level structure, and the Four Colour Theorem. `plane_depth` introduces the level / dual-depth framework that downstream papers build on; `coloring_nested_tire_graphs` develops the tire-tread tree-of-treads decomposition.
## Creating a New Paper
@@ -22,7 +31,7 @@ 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.
This creates `papers/<name>/` (the name is derived from the title, lower-cased, spaces → underscores) containing a `paper.tex` pre-filled with the title and author.
## Setup