Data Science & ML Claude 스킬

QRI Valence & Qualia Computing

Implements the Symmetry Theory of Valence (STV) to analyze, map, and optimize phenomenal states through topological mathematical models.

IES Polyglot Social Analytics

Orchestrates a polyglot environment for social network analysis and multimedia processing using Clojure, Julia, and DuckDB.

HyJAX Relational Thread Analysis

Analyzes conversation threads and concept networks using advanced relational thinking and ACSet modeling.

Delta Derivation

Extracts and verifies information deltas between Claude.ai conversation exports using categorical morphisms and bisimulation.

Triadic Color Self-Validation

Validates triadic color systems by comparing predicted efference copies against observed color streams to minimize system error.

Jacobian Linearization

Analyzes dynamical systems using partial derivative matrices to linearize complex flows and evaluate local stability.

Dialectica Game Logic

Transforms formal proofs into interactive game-theoretic strategies using Gödel’s Dialectica interpretation.

Local Model Fine-Tuning Pipeline

Automates the creation of high-quality training datasets from Claude conversation history and local skill files to fine-tune LLMs using MLX on Apple Silicon.

Glass Hopping Navigation

Navigates complex conceptual possibility spaces using type-theoretic bridge transitions and ordered locale structures.

Dynamical Systems Synchronization

Analyzes and implements convergence patterns in coupled dynamical systems for complex mathematical modeling.

Hopf Dynamical Systems

Analyzes and models Hopf bifurcations to identify transitions from equilibrium to limit cycles in complex dynamical systems.

Advanced Excel & Spreadsheet Automation

Automates professional spreadsheet creation, data analysis, and financial modeling with a focus on formula-driven logic.

Pun Decomposition Logic

Analyzes and deconstructs linguistic puns into multiple semantic and phonetic parses using algebraic and topological structures.

Structured Decomposition Engine

Implements Fixed-Parameter Tractable (FPT) algorithms using sheaves on tree decompositions for compositional data structures.

Coupled Systems Dynamics

Models and analyzes interacting dynamical systems using topological and algebraic frameworks for complex system simulation.

Gay.jl Bisimulation Integration

Integrates deterministic color generation with bisimulation game semantics for verifiable GF(3) conservation logic.

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.

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.

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.