9. Research & Analysis

Routes user queries to the optimal search tool based on query type, enhancing information retrieval efficiency.

Searches historical reasoning records to retrieve relevant decisions and approaches for current problem-solving and analysis.

Provides problem-solving strategies for modular arithmetic applications within graph number theory, supporting mathematical research and analysis.

Performs AI-powered web search, research, and reasoning to gather and analyze information from the internet.

Provides problem-solving strategies for Banach spaces, a key concept in functional analysis, aiding mathematical research and analysis.

Provides problem-solving strategies for propositional logic problems in mathematical logic, aiding in logical analysis and deduction.

Provides problem-solving strategies for compactness in topological spaces.

Provides problem-solving strategies for Lebesgue measure theory, aiding in mathematical analysis and research.

Provides problem-solving strategies for Hilbert spaces in functional analysis, supporting mathematical research and advanced studies.

Conducts external research using web, documentation, and API sources to gather information without accessing internal codebases.

Offers problem-solving strategies for functors within category theory, a branch of abstract mathematics research.

Provides step-by-step strategies for constructing and manipulating sigma algebras in measure theory problem-solving.

Provides problem-solving strategies for group theory problems in abstract algebra.

Provides problem-solving strategies for natural transformations in category theory, supporting mathematical research and theoretical analysis.

Provides problem-solving strategies for operator theory in functional analysis, supporting mathematical research and theoretical analysis.

Provides mathematical strategies for solving prime number problems within graph theory contexts.

Provides formal methods for proving mathematical theorems and verifying system correctness through structured research, testing, and verification phases.

Provides problem-solving strategies for graph algorithms within graph number theory, supporting academic research and analysis.

Searches arXiv for academic papers on agentic AI patterns, enabling discovery and review of the latest research in this domain.

Analyzes blog posts, PDFs, codebases, and other sources to identify agentic patterns, match against a database, and create/update patterns with new insights.

Automates research on libraries, APIs, and patterns using GitHub and Exa, delivering structured reports for technology investigation and debugging.

Analyzes competitors' ad content from social platforms to identify effective messaging and creative strategies for improving marketing campaigns.

Conducts structured web research to gather comprehensive online information for analysis and decision-making.

Searches arXiv preprint repository for academic papers in physics, mathematics, computer science, and related fields using Python and shell tools.