didericis
388ab19db9
Rewrite Conjecture 1.20 (universal nesting) with the iso notion fixed
to combinatorial with O preserved: rooted tree iso + plane-outerplanar
iso of O on each tread + child/face correspondence, with B_out
explicitly not required to match (essential for sub-tree embedding).
Factor the technical core out as Conjecture 1.22 (seam realizability):
for every k >= 3, exhibit a triangulated planar disk H_k with
boundary a k-cycle whose BFS-from-boundary tree of treads is iso to a
given T_1. Add Remark 1.23 stating that universal nesting reduces to
seam realizability by excise-and-glue using the existing structural
theorems.
Reworked Remark 1.24 (motivation) keeps the compositional-colourability
and universality bullets, and replaces the old open-questions paragraph
with three concrete subproblems: a candidate apex-removal construction
for the seam, 6-connectivity preservation as the relevant 4CT
subproblem, and a justification of why the weaker iso notion is
necessary.
Add fig_seam_construction.png (and the matplotlib script that generates
it) illustrating the seam construction on a 10-vertex G_1 with
T_1 a chain of length 3; the script asserts BFS-from-boundary in H_5
reproduces ell_{G_1} on V(G_1) \ {S_1}, giving a verified small
instance of the conjecture.
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
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./run.sh setup <sage_python_path> <sage_site_packages> [system_name]
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Linting
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latexmk -pdf paper.tex