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Hook Development Rules

Friendly onboarding when users ask about capabilities

Formal theorem proving with research, testing, and verification phases

Parallel Agent Type Contracts

System health check (MOT) for skills, agents, hooks, and memory

Search Mathlib for lemmas by type signature pattern

Problem-solving with Rudin's Real and Complex Analysis textbook

Full 5-layer analysis of a specific function. Use when debugging or deeply understanding code.

Problem-solving strategies for groups in abstract algebra

Problem-solving strategies for second order odes in odes pdes

Write reliable prompts for Agentica/REPL agents that avoid LLM instruction ambiguity

Guide for integrating Agentica SDK with Claude Code CLI proxy

Unit-aware computation with Pint - convert units, dimensional analysis, unit arithmetic

TDD workflow for migrations - orchestrate agents, zero main context growth

Problem-solving strategies for source coding in information theory

Interactive workspace discovery - learn what tools, workflows, agents, and hooks are available

Problem-solving strategies for compactness in topology

Routes problems to appropriate mathematical frameworks using expert heuristics

AI-powered web search, research, and reasoning via Perplexity