Writes rigorous mathematical proofs for ML/AI theory. Use when asked to prove a theorem, lemma, proposition, or corollary, fill in missing proof steps, formalize a proof sketch, 补全证明, 写证明, 证明某个命题, or determine whether a claimed proof can actually be completed under the stated assumptions.
Systematically verify mathematical proofs in statistics/ML theory paper appendices. Use when user says "proof check", "check proofs", "verify proofs", "audit paper", "检查证明", "证明验证", or wants to verify correctness of a paper's mathematical proofs.
Generate self-consistent repair plans for mathematical proof issues found by /proofcheck, with literature-backed support. For each problematic assumption, model, proposition, or theorem, proposes fixes that preserve the full dependency chain and searches arXiv, Semantic Scholar, and Google Scholar for new references to support repairs. Use when user says "repair proofs", "fix proof issues", "修复证明", "proof repair", "修正计划", "fix theorem", "repair assumptions", or wants to go from proof audit to actionable repair plan with literature support.
Design a coherent theoretical framework for a new statistics / ML theory research topic, paper-type aware. Three modes — Theory paper (explain phenomena or provide new theoretical tools), Methodology paper (propose a new method with theoretical guarantees), Application paper (apply existing methods to scientific data with assumption verification). Each mode walks a different logical order: the centerpiece of a theory paper is the theorem itself, of a methodology paper the estimator, of an application paper the empirical findings. Mandatory literature anchoring step (recent top-venue papers) identifies the field's theoretical inertia and positioning options BEFORE any phase decision, then constrains every subsequent decision. Produces FRAMEWORK_DESIGN.md + LITERATURE_ANCHOR.md that downstream skills (proof-writer, theory-simulation, proofcheck) consume. Use when user says "design theory framework", "理论框架设计", "新课题怎么开始", "新方向 design", "from scratch theory", "构建理论框架", "start a new topic", or asks for the logical
Systematically assess whether a paper's theoretical results can be strengthened: relax assumptions, sharpen rates, align theory with model and experiments, and benchmark against state-of-the-art literature. Use when user says "sharpen theory", "strengthen results", "relax assumptions", "improve rates", "理论提升", "放宽假设", "优化rate", "theory alignment", "理论对齐", or wants to go beyond proof correctness toward theoretical optimality and practical relevance.
Bridge between theoretical results and Monte Carlo simulation, built to top-stat-journal standards (AoS, JASA, JRSS-B, Biometrika, Bernoulli). Two modes: (1) DESIGN mode — for each theoretical claim, design new simulations that verify rates, coverage, stress-test assumptions, and reveal theory-improvement opportunities; (2) AUDIT mode — when the paper already has simulations, evaluate whether they actually verify the theorems, identify claim-coverage gaps and adequacy flaws, and propose targeted improvements (extend / add / reformat) rather than full redesign. Produces publication-grade figures (no titles, content in caption, color-blind safe) and feeds findings back to refine theory. Use when user says "simulation plan", "Monte Carlo", "验证理论", "审查 simulation", "audit simulation", "模拟实验", "已有 simulation 检查", "stress test theory", "bridge simulation", "rate verification", or wants reproducible stat-journal simulations tied to theorems.