Data Science & ML Claude 技能

Topos Unified

Unifies mathematical topos-theoretic resources, category theory tools, and cognitive modeling frameworks across the filesystem.

Trajectory Analysis

Analyzes and models the paths of solutions through phase space within dynamical systems.

Operad Compose

Facilitates structured generation and composition of complex multi-input operations using colored operads and category theory principles.

Epistemic Arbitrage

Transfers and synthesizes knowledge across domains using propagator-based networks to exploit structural isomorphisms.

Ordered Locale & Triadic Topology

Implements point-free topology and triadic GF(3) logic to manage causal structures and deterministic parallel execution for MCP servers.

Bifurcation Analysis

Detects and analyzes qualitative state transitions in dynamical systems using Hopf bifurcation detection and GF(3) phase portraits.

CatSharp Galois Bridge

Facilitates Galois adjunctions between local agent operations and global cognitive category theory using Mazzola’s mathematical music structures.

Latent-Latency Optimizer

Bridges representation space and execution time to optimize AI model performance through mathematical spectral analysis.

Condensed ANIMA QC

Manages quantum-classical network transitions and state conservation using s-expressions across polyglot computing environments.

Multi-Agent System Consensus

Implements and analyzes agreement protocols within multi-agent dynamical systems using algebraic dynamics and topological principles.

Invariant Set Analysis

Analyzes and identifies sets within dynamical systems that are preserved by the flow of differential equations and manifolds.

Attractor Dynamics

Analyzes invariant sets and long-term trajectory behaviors within dynamical systems to model stable states and system evolution.

Bifurcation Diagram Generator

Generates visual bifurcation diagrams to track stability transitions and behavior changes in dynamical systems.

Pitchfork Dynamics

Analyzes symmetric bifurcations and symmetry-breaking patterns in complex dynamical systems and differential equations.

Fokker-Planck Convergence Analyzer

Verifies that neural network training trajectories have reached theoretical Gibbs equilibrium using Fokker-Planck equations.

Topos Unified

Provides unified access to topos-theoretic resources, mathematical music theory, and categorical database structures for advanced AI reasoning.

Algebraic Graph Rewriting

Transforms structured data and acsets using category-theoretic graph rewriting techniques like DPO, SPO, and SqPO.

GF(3) Task Orchestrator

Routes complex tasks to specialized subagent triads using GF(3) triadic logic to ensure balanced execution and validation.

Kolmogorov-Onsager-Hurst Scaling Analysis

Analyzes time-series data using scaling theory to identify turbulence regimes, persistence, and long-range dependencies.

Curiosity-Driven Learning Agent

Implements intrinsic motivation for AI agents by rewarding compression progress and the discovery of learnable patterns.

Dynamical Systems Stability Analysis

Analyzes the qualitative behavior and robustness of solutions near equilibria in complex dynamical systems.

Möbius Color Duality

Recovers local structural seeds from global color distributions using Möbius inversion and topological duality.

Specter Navigator Gadget

Enables high-performance bidirectional navigation and transformation of complex nested data structures using compiled path expressions and constraint logic.

Constraint Propagator Networks

Implements bidirectional constraint propagation and fixpoint derivation for complex autonomous information networks.

Moth Actias Quantum Synth

Transforms quantum qubit states into expressive musical textures through Bloch sphere sonification and MIDI control.

Datalog Fixpoint Iteration

Implements bottom-up fixpoint iteration for recursive Datalog queries using saturation-based evaluation.

LiveKit Omni-modal Coach

Facilitates real-time, multi-modal continuous coaching and guidance through LiveKit using dynamic modality selection and symbolic expression processing.

Topos Generation

Generates sheaf-theoretic models and forces propositions within topos theory to enable advanced mathematical modeling and logic synthesis.

Geodesic Manifold Calculations

Performs advanced geodesic calculations and Riemannian manifold operations for geospatial navigation and spherical geometry.

Dynamical System Functor

Models and analyzes the categorical structure of dynamical systems to evaluate stability and qualitative behavior.