didericis
203b005336
NEW NOTE: chain_half_analysis.tex (4 pages). Formulates the chain half of the loose conjecture as a tree DP over the cut tire forest, identifies what's proven vs. open: PROVEN - Tree structure (high-side forest): from cut_tire_tree_structure.tex - S_3-equivariance of the DP: trivial Lemma in this note - Per-tire half for spoke-only cut tires (n ≥ 3): Prop 1.13 OPEN / GAPS DISCOVERED 1. Cut tires are NOT in general spoke-only. H_d can have degree-3 vertices (= branch points), making face boundaries non-simple cycles. Dodecahedron 6-edge cut yields H_1 with one face of length 20 over only 11 distinct vertices. Prop 1.13's count 2^n + 2(-1)^n applies only to spoke-only tires. 2. OUT-only projection loses S_3 orbit info. The per-tire half guarantees a full S_3 orbit on the JOINT (in + out) projection, but restricting to OUT spokes can collapse to |A|=3 (constant tuples). Empirically observed ~20% of the time on test cases. Correct DP must track joint projection (analog of tire_fiber_step2.tex's joint-support tracking). 3. Non-emptiness preservation through the DP is the genuine open piece (Conj. in this note + Strong per-tire extendibility). EMPIRICAL TESTS - chain_dp_test.py: simple cycle DP (assumes spoke-only). - chain_dp_general.py: handles branched faces via brute-force 3-edge-coloring enumeration (cut off at 12 edges/tire for tractability). - chain_dp_debug.py: diagnostic for inspecting H_d face structure. The general test reveals all three gaps above when run on Dodecahedron + HM #0. Cross-cut R_0 ∩ R_1 should be non-empty for both (they are 3-edge-colorable), but the heuristic parent-finding plus OUT-only projection produce false negatives. Status table at end of note summarizes what's needed to close. 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