9. Research & Analysis

Identifies high-quality business leads through market analysis and data-driven research to target potential customers effectively.

Verifies strong parallelism invariants across 15+ programming languages to ensure correctness in concurrent code execution.

Generates diagrams implementing cohesive modalities (♯,♭,ʃ) and linear modality (♮) for quantum-classical bridging via Homotopy Type Theory.

Implements Schreiber's cohesive modalities and Riley's linear modality for quantum-classical bridging using Homotopy Type Theory patterns.

Provides formalization of the directed Yoneda lemma using path induction, based on Riehl and Shulman's homotopy type theory research.

Tool for implementing Lafont's interaction nets, a graph rewriting system enabling optimal parallel lambda calculus reduction in theoretical computer science research.

Verifies Strong Parallelism Invariance (SPI) and GF(3) conservation properties in computational systems for academic research.

Automates extraction and analysis of competitors' ads from Facebook and LinkedIn ad libraries to inform marketing strategy.

Python library for computing with string diagrams in monoidal categories, supporting academic research in quantum computing and category theory.

Provides a structured index and ecosystem mapping for 1057 hatchery repositories within plurigrid/bmorphism/TeglonLabs to associated skills.

Applies Levin's algorithmic complexity theory to prediction markets, Kolmogorov complexity rewards, and Nash equilibrium analysis between exploration and convergence.

Searches academic papers across multiple databases, provides citations, downloads PDFs, and analyzes citation networks for literature reviews and research.

Transforms temporal sequences into derivational chains using deterministic seeds and GF(3) invariants for consistent mathematical modeling.

Provides a theoretical framework for bidirectional programming using Hedges' 4-kind lattice and GF(3) correspondence to model type variance.

Proof assistant for higher-dimensional type theory with observational bridge types, enabling version-controlled formal verification in mathematical proofs.

Analyzes derivation streams through coalgebraic observation and final coalgebra bisimulation for behavioral equivalence analysis.

Provides graph-theoretic gadgets and non-backtracking geodesics for 3-SAT via colored subgraph isomorphism.

Curates a specialized index of GitHub repositories focused on applied category theory, MCP servers, and xenomodern tooling.

Analyzes puns by decomposing linguistic components to reveal double meanings and wordplay structures for linguistic research.

Retrieves historical context, decisions, and tasks associated with a person or topic to support analytical decision-making and research.

Enables autonomous step-by-step reasoning for complex problems, optimizing when to apply sequential thinking to enhance analytical efficiency.

Automates competitor intelligence collection and monitoring for market analysis and strategic business decisions.

Executes read-only research tasks, generates report files, and outputs [AGENT_DONE] marker for sub-agent workflows.

Enables hypothesis-driven iteration through systematic observation, prediction, and verification for research tasks.