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Investigate one difficult mathematics problem through repeated rounds of independent agent work and review. Track proved, refuted, and unresolved claims, check proposed proofs, and produce a self-contained proof.md that clearly states what remains unproved.
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Work through one difficult mathematics problem with a single agent, saving established arguments and dead ends as progress notes. Resumes from recorded work after interruptions and writes a self-contained proof file, including any unresolved parts.
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Writes and reviews Lean 4 proofs, machine-checked arguments for mathematics or specifications. Follows Mathlib conventions to organize definitions and lemmas, fill proof gaps, refactor lengthy proofs, and establish automated checks for unproved claims and style.
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Expert in visualizing and explaining braid theory, knot mathematics, and topological concepts for educational purposes. Use for creating interactive visualizations, explainer cards, step-wise animations, and translating abstract algebra into intuitive understanding. Activate on keywords: braid theory, knot visualization, σ notation, crossing diagrams, Yang-Baxter, topological education. NOT for general math tutoring, pure knot invariant computation, or non-educational knot theory research.
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Expert-level discrete mathematics knowledge. Use when working with logic, set theory, combinatorics, graph theory, relations, functions, induction, recursion, boolean algebra, or discrete probability. Also use when the user mentions 'combinatorics', 'permutations', 'combinations', 'pigeonhole principle', 'inclusion-exclusion', 'generating functions', 'recurrence relations', 'graph theory', 'trees', 'logic', 'propositional calculus', or 'boolean algebra'.
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Easing mathematics: production-level cubic bezier, damped spring, velocity continuity. Use when implementing, reviewing or testing easing mathematics for React, Vite, Next.js or Perfect_AI projects.
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Use SymPy to simplify expressions, solve equations, and calculate derivatives, integrals, and matrices with exact symbolic results. Specify assumptions, verify solutions, and turn mathematical expressions into numerical functions, source code, or LaTeX output.
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Find scientific datasets, AI models, methodology posts, and interactive demos through the Hugging Science catalog. Compare candidates for a research task and verify their licenses, input formats, access requirements, and supported ways to run them.
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Solve competition mathematics problems and examine proofs through independent agents that actively look for gaps, counterexamples, and misused theorems. Produces a checked argument or clearly states what remains unresolved, with optional PDF output.
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Create or adapt an OpenMAIC lesson for Chinese primary and secondary education. Connect real-world tasks with learner activities, observable work, assessment, and narration, focusing on one or two core competencies from the relevant curriculum framework.
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Use this skill when working with symbolic mathematics in Python. This skill should be used for symbolic computation tasks including solving equations algebraically, performing calculus operations (derivatives, integrals, limits), manipulating algebraic expressions, working with matrices symbolically, physics calculations, number theory problems, geometry computations, and generating executable code from mathematical expressions. Apply this skill when the user needs exact symbolic results rather than numerical approximations, or when working with mathematical formulas that contain variables and parameters.
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Use this skill when working with symbolic mathematics in Python. This skill should be used for symbolic computation tasks including solving equations algebraically, performing calculus operations (derivatives, integrals, limits), manipulating algebraic expressions, working with matrices symbolically, physics calculations, number theory problems, geometry computations, and generating executable code from mathematical expressions. Apply this skill when the user needs exact symbolic results rather than numerical approximations, or when working with mathematical formulas that contain variables and parameters.
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Expert in formal logic, model theory, computability, and foundations of mathematics
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Master discrete mathematics, logic, formal proofs, and computational thinking. Build the mathematical foundation for all computer science.
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Search arXiv physics, math, and computer science preprints using natural language queries. Powered by Valyu semantic search.
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Use this skill when working with symbolic mathematics in Python. This skill should be used for symbolic computation tasks including solving equations algebraically, performing calculus operations (derivatives, integrals, limits), manipulating algebraic expressions, working with matrices symbolically, physics calculations, number theory problems, geometry computations, and generating executable code from mathematical expressions. Apply this skill when the user needs exact symbolic results rather than numerical approximations, or when working with mathematical formulas that contain variables and parameters.
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Design a variation theory task using contrast, separation, and fusion to teach critical features of a concept. Use when students confuse similar concepts or fail to discern key distinctions.
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Design a Concrete-Pictorial-Abstract learning sequence for a mathematical concept using manipulatives. Use when teaching maths through Singapore method or when students struggle with abstraction.
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Review academic papers for correctness, quality, and novelty using OpenJudge's multi-stage pipeline. Supports PDF files and LaTeX source packages (.tar.gz/.zip). Covers 10 disciplines: cs, medicine, physics, chemistry, biology, economics, psychology, environmental_science, mathematics, social_sciences. Use when the user asks to review, evaluate, critique, or assess a research paper, check references, or verify a BibTeX file.
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AMM liquidity provision mathematics including constant-product, concentrated liquidity, price impact, and LP share calculations
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Search arXiv preprint repository for papers in physics, mathematics, computer science, quantitative biology, and related fields
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Applies the Neoplatonic and mathematical reasoning of Hypatia of Alexandria. Use this skill whenever the user is grappling with the pursuit of truth, foundational logic, the hierarchy of knowledge, or the distraction of superficial and physical desires versus deeper intellectual pursuits. Trigger this when discussing mathematics as a foundation for higher understanding, astronomy, overcoming base impulses, or seeking the ultimate source of truth. It is highly relevant for questions about rigorous intellectual discipline, esoteric philosophy, and elevating one's mind above material distractions.
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Design a variation theory task using contrast, separation, and fusion to teach critical features of a concept. Use when students confuse similar concepts or fail to discern key distinctions.
中文简介正在准备中。当前显示原文说明。
Design a Concrete-Pictorial-Abstract learning sequence for a mathematical concept using manipulatives. Use when teaching maths through Singapore method or when students struggle with abstraction.
中文简介正在准备中。当前显示原文说明。