AI methodology
The author used Anthropic’s Claude (Claude Opus 5.5 as the main research collaborator, and Claude Fable 5.1 for part of the analysis of Algorithm RSC), OpenAI Codex and GitHub Copilot. These tools materially affected every section of the paper.
Claude proposed and developed ideas in discussion with the author, carried out mathematical derivations and proofs, wrote the code for the experiments, the computer certificates and their checking programs (Appendix F) and the Lean development (Appendix F.9), and drafted and revised the text.
OpenAI Codex was used for independent reviews of the manuscript and the code, and for developing the research-workflow tooling of the project.
GitHub Copilot was used for code completion, reviews of pull requests and commit messages. Pull requests were also reviewed by Claude Haiku 5.5.
The author directed the research, contributed ideas, among them graded closure (Section 8), checked the proofs and the Lean statements, edited the manuscript and extended the literature search. The project started from work of the author from 2020: the W[1]-hardness of MaxLeaf-Extension (Theorem C.2) and the product form of multivariate Monotone Local Search, which were the basis of an Honours thesis (Lu 2020). The author verified the correctness and originality of all content, including references.
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