9. Research & Analysis

Offers a universal framework for systematic scientific inquiry, evidence-based decision-making, and rigorous analysis across diverse domains including data, social sciences, and humanities.

Discovers and delivers the latest updates, improvements, tools, and best practices for Claude and Claude Code CLI from official and community sources.

Offers a universal framework for systematic scientific inquiry, evidence-based decision-making, and rigorous analysis across diverse domains including data, engineering, and social sciences.

Guides integration of Gemini CLI as a research assistant, comparing capabilities with Claude to optimize tool selection for information gathering.

Conducts web and document research, fact verification, and competitive analysis, delivering structured findings with citations.

Provides deep research capabilities for topics requiring substantial information gathering, triggered by specific query patterns.

Automates deep research methodology by triggering on user queries containing research-related keywords.

Organizes academic papers for color logic and 2TDX research, enabling efficient access and analysis in scientific contexts.

Verifies multiple effect interpretations in computational systems using temporal coalgebra bisimulation and common fixpoint solutions.

Assists with mathematical research in homotopy type theory, specifically addressing Rezk types and univalence principles.

Interactive proof development tool using typed holes for formal verification in the Narya system.

Models a cybernetic immune system for self/non-self discrimination using information geometry and GF(3) encoding.

Provides a categorical framework for modeling dynamical systems, enabling abstract analysis of system evolution and structure.

Provides mathematical tools for modeling dynamic structures using polynomial functors in topos theory, as developed by the Topos Institute.

Conducts comprehensive academic research using arXiv, Semantic Scholar, Exa, and local knowledge base without web search fallback.

Proof assistant for higher-dimensional type theory featuring observational bridge types to manage version control of formal proofs.

Explains turbulence scaling theory including K41 energy cascade, Onsager's anomalous dissipation, and Hurst exponent for long-range dependence.

Provides a mathematical framework for point-free topology with direction, featuring frames and compatible preorders as described in Heunen-van der Schaaf (2024).

Enables categorical database design using Attributed C-Sets (ACSets) and DPO rewriting for theoretical database modeling research.

Navigates possible worlds using Badiou-inspired frameworks and triangle inequality constraints for theoretical analysis.

Provides tools for constructing and manipulating operads within the DiscoPy library for category theory research.

Analyzes transcritical bifurcation, a mathematical phenomenon where equilibrium points exchange stability in dynamical systems.

Collaborative platform for category theory research, supporting real-time diagramming and model building in academic and epidemiological contexts.

Framework for ∞-operads and category interactions using dendroidal Segal spaces and lazy ACSet materialization, unifying topoi theories.