3. Data, Science & AI

Enables deliberate, slow reasoning in transformer models through System 2 attention mechanisms for enhanced cognitive processing.

Provides deterministic color generation via SplitMix64 algorithm through Gay.jl MCP server integration.

Discovers and visualizes collaboration networks among GitHub authors by analyzing interaction patterns and relationships.

Enables analysis of invariant sets that repel nearby trajectories in dynamical systems.

A utility for implementing local compositionality in AI models, enabling structured modular reasoning within complex systems.

Manages RAG (Retrieval-Augmented Generation) workflows using ACSet data structures for efficient knowledge retrieval and generation.

Extracts semantic differences between Claude.ai conversation exports using formal methods (ACSets morphisms and bisimulation verification).

Enables condensed ANIMA implementation for quantum-classical network compositions via s-expressions across polyglot substrates.

Simulates synchronization in coupled systems, modeling convergence to a common trajectory in dynamical networks.

Models and analyzes influence propagation flows across interconnected networks using multi-perspective interperspectival analysis for data-driven insights.

Provides a theoretical framework for self-improving AI systems that mathematically prove code optimizations before implementation.

Applies Markov blanket arbitrage to extract value from world transitions using WEV = PoA - 1 within multiverse finance frameworks.

Provides a Julia package for FPT algorithms with sheaves on tree decompositions and bidirectional navigation capabilities.

Provides unified AI skill modification using covariant transport, Darwin Gödel Machine evolution, and self-rewriting MCP tasks under GF(3) constraints.

Converts visual color data into tactile, auditory, and haptic feedback for accessible color perception, supporting visually impaired users through sensory substitution.

Applies Gestalt principles and ergodic theory to enhance data pattern recognition in artificial intelligence systems.

Computes and analyzes the unstable manifold in dynamical systems, representing points diverging from equilibrium.

Visualizes and verifies formal proofs written in Lean 4, supporting mathematical and software correctness validation.

Enables causal state gating via ε-machine to observe and prevent actions in dynamic systems.

Optimizes interaction sequences using entropy-based methods to maximize information gain in AI decision systems.

Performs bottom-up fixpoint iteration to evaluate recursive Datalog queries, enabling efficient data processing in deductive databases.

A propagator-based parallel system for identifying and exploiting knowledge differentials in information networks.

Generates dynamics of nonlinear systems using Koopman operator theory for linear lifting from observable data.

Provides category-theoretic data structures (Attributed C-Sets) for algebraic database modeling, generalizing graphs and dataframes with Julia integration.