Data Science & ML Claude 技能

World Extractable Value (WEV)

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

WorldMat-TiDAR: Parallel Triadic Computation

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

Topos of Music

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

Forward-Forward Learning

Implements Geoffrey Hinton's Forward-Forward algorithm for memory-efficient neural network training without backpropagation.

Abductive Reasoning REPL

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

Triadic Color Validation

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

Pre-Agent Ontology

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

Equilibrium System Analyzer

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

GFlowNet ML Framework

Implements Generative Flow Networks to sample diverse candidates proportionally to their reward functions.

Möbius Path Filtering

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

Kuramoto Model Dynamics

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

Unstable Manifold Analysis

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

Phase Locking for Dynamical Systems

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

Cider Clojure Embedding

Enables semantic code navigation and intelligent completions for Clojure using vector space embeddings.

DuckDB Spatial Analysis

Performs high-performance geospatial analysis, H3 hexagonal indexing, and PostGIS-compatible spatial SQL queries using DuckDB.

Categories for AI (cats-for-ai)

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

LHoTT Cohesive Linear

Implements Cohesive Linear Homotopy Type Theory patterns to formalize interaction entropy and generate complex structural diagrams.

ALife Simulation & Modeling

Provides comprehensive resources, mathematical models, and implementation patterns for simulating artificial life, evolutionary dynamics, and emergent systems.

Oapply Colimit: Compositional Systems Modeling

Composes complex systems from individual components using category-theoretic colimits and bidirectional wiring diagram navigation.

PDF Processing & Manipulation

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

HoloViz Advanced Rendering

Optimizes high-performance visualization for massive datasets exceeding 100 million points using Datashader and HoloViews.

Open Games Framework

Enables compositional game theory and economic modeling using category theory optics for complex systems.

Eigenvalue Stability Analysis

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

Periodic Orbit Analysis

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

Center Manifold Analysis

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

Polynomial Operads & Compositional AI

Integrates polynomial functors and category-theoretic operads to model complex interaction patterns and dynamical systems within AI workflows.

Unworld Derivational Logic

Replaces temporal succession with deterministic seed-chaining for observer-independent state derivation.

Triangle Metrics

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

OlmoEarth MLX

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

Naturality Factor

Measures structural conservation and naturality in musical and categorical transformations.