didericis
7b8a5eb81a
Bypasses the 3^n brute-force iteration in tire_fiber_chords.py by
directly constructing the 2^n proper edge 3-colorings of C_n via a
vectorized binary-branch numpy build. Benchmarked 146× speedup at n=12,
424× at n=15; brings n=18 to 0.1s and n=24 to 6.6s.
Step-2 extension at k=9 (13 pairs) and k=12 (10 pairs): every tested
pair is compatible (23/23, bringing total to 46/46 with the earlier
note). The S_3-orbit observation extends: the smallest tested
intersection at k=12 is again exactly 6 elements forming a single
S_3-orbit of the pattern (1,2,3,2,2,1,3,3,2,3,1,1) — each of T1's four
chord-induced faces receives a permutation of {1,2,3} as its σ-values,
a "Latin-style" assignment.
Note conjectures a structural theorem: every SP-feasible tire's
projection support contains the "Latin-flavoured" subset where each
O-face sees a permutation of {1,2,3}, and this gives a common
substructure that makes chain-pigeonhole succeed.
Caveat: intersection sizes are all multiples of 6, consistent with the
S_3 invariance of both supports.
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