Data Science & ML Claude 技能

Naturality Factor

Measures structural conservation and naturality in musical and categorical transformations.

OlmoEarth MLX

Integrates spatio-temporal Earth intelligence and geographic embeddings with crypto-economic data for planetary-scale spatial reasoning.

Triangle Metrics

Unifies diverse metric spaces and triangle inequality constraints into a coherent topological framework for consistent system navigation.

Center Manifold Analysis

Analyzes and models invariant manifolds tangent to center eigenspaces within complex dynamical systems.

Periodic Orbit Analysis

Analyzes and models closed trajectories in phase space to understand the qualitative behavior of dynamical systems.

Eigenvalue Stability Analysis

Classifies the stability of dynamical systems by calculating and interpreting Jacobian eigenvalues for equilibrium analysis.

Knowledge Graph Builder

Builds and manages structured knowledge graphs to enhance AI reasoning and map complex data relationships.

PDF Processing & Manipulation

Facilitates comprehensive PDF manipulation, including text and table extraction, merging, splitting, and document generation using Python and CLI tools.

Categories for AI (cats-for-ai)

Integrates category theory principles into AI development to enable formal compositionality, bidirectional optics, and advanced machine learning architectures.

Phase Locking for Dynamical Systems

Analyzes and implements fixed phase relationships in oscillators and complex dynamical systems.

Unstable Manifold Analysis

Analyzes points diverging from equilibrium to identify qualitative behaviors, bifurcations, and long-term dynamics in complex systems.

Kuramoto Model Dynamics

Analyzes and implements coupled oscillators with sinusoidal coupling to model synchronization in complex dynamical systems.

Möbius Path Filtering

Prevents invalid data navigation and circular references by applying non-orientable topological constraints to complex path structures.

Equilibrium System Analyzer

Identifies and analyzes fixed points in dynamical systems where vector fields vanish to determine system stability.

Pre-Agent Ontology

Establishes a foundational 5-layer topological framework for agent-based systems using sheaf theory and GF(3) arithmetic.

Triadic Color Validation

Validates triadic color systems using predictive loops and active inference to ensure compositional coherence.

Abductive Reasoning REPL

Powers iterative hypothesis testing and exploratory abductive inference through an interactive REPL environment.

Topos of Music

Implements Guerino Mazzola's categorical music theory framework for advanced mathematical analysis and transformation of musical structures.

WorldMat-TiDAR: Parallel Triadic Computation

Orchestrates complex 3×3×3 parallel TiDAR executions for balanced, reproducible triadic computation across temporal and polarity axes.

FlowerPower Pipeline Manager

Automates the creation and management of robust data pipelines using Hamilton DAGs and the FlowerPower framework.

World Extractable Value (WEV)

Quantifies and extracts economic value from coordination inefficiencies and world transitions using Markov blanket arbitrage and Multiverse Finance.

Social Emergence Protocol

Bootstraps complex social behaviors and communication patterns in distributed agent systems using minimal interaction rules.

WEV Verification & Topological Validation

Validates World Extractable Value (WEV) and topological system states using GF(3) logic and cybernetic reafference loops.

Repeller Dynamical Systems

Models and analyzes invariant sets that repel nearby trajectories within complex dynamical systems and topological manifolds.

Dynamical System Limit Sets

Analyzes the asymptotic behavior of trajectories in dynamical systems to determine long-term qualitative patterns.

System 2 Attention

Enhances AI reasoning by implementing a two-stage deliberate attention mechanism to filter noise and ensure factual grounding.

ReasoningBank with AgentDB

Implements high-performance adaptive learning and memory distillation for AI agents using the AgentDB vector engine.

Markov Game ACSet

Models and verifies state-dependent Markov games using Attributed C-sets and GF(3) conservation laws.

RAG Systems Builder

Builds production-grade Retrieval Augmented Generation pipelines with vector search, hybrid retrieval, and advanced re-ranking strategies.

Dynamical Flow Analysis

Models and analyzes one-parameter groups of diffeomorphisms generated by vector fields within dynamical systems.