Crouzeix Conjecture

This repository records a research workspace for a candidate proof of Crouzeix's conjecture.

• The candidate proof is written as a standalone LaTeX manuscript.
• Several independent computational and adversarial audits have found no specific mathematical error.
• Formal peer review is still pending.

• AnnMath/the_numerical_range_is_a_2_spectral_set.tex: Annals-formatted submission manuscript.
• AnnMath/the_numerical_range_is_a_2_spectral_set.pdf: compiled submission manuscript.
• AnnMath/aomart.cls: Annals of Mathematics document class used for the submission build.
• Lean/: Lean 4 formalization, verification entry point, and axiom audit.
• LaTeX/crouzeix_conjecture_proof.tex: candidate proof manuscript.
• LaTeX/crouzeix_conjecture_proof.pdf: compiled manuscript.
• LaTeX/main_problem.tex: statement of the problem.
• crouzeix_conjecture_prompt.txt: project provenance and original task specification.

From the AnnMath directory, run:

latexmk -pdf -interaction=nonstopmode -halt-on-error the_numerical_range_is_a_2_spectral_set.tex

From the Lean directory, run:

lake run

This builds the complete library and runs the exported-theorem axiom audit.

OpenAI ChatGPT contributed to proof development, manuscript preparation, and adversarial checking.