
Guide to the math cognitive stack - what tools exist and when to use each
Friendly onboarding when users ask about capabilities
Meta-skill workflow orchestrator for bug investigation and resolution. Routes to debug, implement, test, and commit based on scope.
Validation agent that validates plan tech choices against current best practices
Agentica server + Claude proxy setup - architecture, startup sequence, debugging
Fast codebase search via WarpGrep (20x faster than grep)
Async REPL Protocol
Background Agent Pings
A complete skill for E2E testing
Create or update continuity ledger for state preservation across clears
Create handoff document for transferring work to another session
Semantic memory retrieval that queries stored learnings from past sessions
Resume work from handoff document with context analysis and validation
Systematic hook debugging workflow. Use when hooks aren't firing, producing wrong output, or behaving unexpectedly.
Git Commit Rules
Graceful Degradation with Helpful Messages
Complete Maestro hooks reference - input/output schemas, registration, testing patterns
Problem-solving strategies for fields in abstract algebra
Problem-solving strategies for limits colimits in category theory
Problem-solving strategies for residues in complex analysis
Problem-solving strategies for graph algorithms in graph number theory
Problem-solving strategies for vector spaces in linear algebra
Problem-solving strategies for lebesgue measure in measure theory
Research-to-implement pipeline chaining 5 MCP tools with graceful degradation
Create git commits with user approval and no Claude attribution
Implementation agent that executes a single task and creates handoff on completion
Comprehensive code review workflow - parallel specialized reviews → synthesis
Parallel Agent Orchestration
Observe Before Editing
Analyze Maestro sessions via Braintrust
Maestro CLI commands, flags, headless mode, and automation patterns
Use RepoPrompt CLI for token-efficient codebase exploration
External research workflow for docs, web, APIs - NOT codebase exploration
Search Tool Hierarchy
Skill Development Rules
Hook Development Rules
Guide for integrating Agentica SDK with Maestro CLI proxy
Reference guide for Agentica multi-agent infrastructure APIs
Problem-solving strategies for analytic functions in complex analysis
Braintrust tracing for Maestro - hook architecture, sub-agent correlation, debugging
Problem-solving strategies for categories functors in category theory
Problem-solving strategies for compactness in topology
Completion Check: Verify Infrastructure Is Wired
Problem-solving strategies for constrained optimization in optimization
Problem-solving strategies for continuity in real analysis
Problem-solving strategies for convex optimization in optimization
Generate comprehensive PR descriptions following repository templates
Environment Triage
Meta-skill for internal codebase exploration at varying depths (quick/deep/architecture)
Problem-solving strategies for first order odes in odes pdes
Interactive workspace discovery - learn what tools, workflows, agents, and hooks are available
Implement technical plans from thoughts/shared/plans with verification
Index at Creation Time
Problem-solving strategies for integration theory in measure theory
Semantic search across codebase using LEANN vector index
LLM Tuning Patterns
Develops mathematical understanding through examples, visualization, and analogy
Routes problems to appropriate mathematical frameworks using expert heuristics
Metacognitive check-ins during problem solving - detects when to pivot or persist
Deterministic router for math cognitive stack - maps user intent to exact CLI commands
MCP Script Rules
Unified math capabilities - computation, solving, and explanation. I route to the right tool.
Migration workflow - research → analyze → plan → implement → review
Fast file editing via Morph Apply API (10,500 tokens/sec, 98% accuracy)
Search library documentation and code examples via Nia
Never Use TaskOutput
Analyze brownfield codebase and create initial continuity ledger
OPC Architecture Understanding
Problem-solving strategies for open sets in topology
Unit-aware computation with Pint - convert units, dimensional analysis, unit arithmetic
Problem-solving strategies for prime numbers in graph number theory
Formal theorem proving with research, testing, and verification phases
Code quality checks, formatting, and metrics via qlty CLI
Release preparation workflow - security audit → E2E tests → review → changelog → docs
Problem-solving strategies for root finding in numerical methods
Router-First Architecture
Problem-solving with Rudin's Real and Complex Analysis textbook
Search Tool Hierarchy
Security audit workflow - vulnerability scan → verification
Problem-solving strategies for sigma algebras in measure theory
Create and use Maestro slash commands - quick prompts, bash execution, file references
Problem-solving strategies for source coding in information theory
Create and configure Maestro sub-agents with custom prompts, tools, and models
Token-efficient code analysis via 5-layer stack (AST, Call Graph, CFG, DFG, PDG). 82% savings (balanced mode) with semantic completeness.
Goal-based workflow orchestration - routes tasks to specialist agents based on user goals
Show users how Maestro works - the opinionated setup with hooks, memory, and coordination
Problem-solving strategies for limits in real analysis
Maps questions to the optimal LeIndex command
Test-driven development workflow with philosophy guide - plan → write tests → implement → validate
Store a learning, pattern, or decision in the memory system for future recall
Problem-solving strategies for natural transformations in category theory
Maestro spec-driven development for Amp CLI. Load this skill when invoking Maestro commands so workflows stay aligned with LeIndex and the Rust TUI.
Parallel Agent Type Contracts
QLTY During Development
Check reference SDK implementations using btca ask
Problem-solving strategies for predicate logic in mathematical logic
Problem-solving strategies for proof theory in mathematical logic
Agent Orchestration Rules
Agentic Workflow Pattern
Write reliable prompts for Agentica/REPL agents that avoid LLM instruction ambiguity
Build Python agents with Agentica SDK - @agentic decorator, spawn(), persistence, MCP integration
Full 5-layer analysis of a specific function for debugging or deep understanding
Get a token-efficient overview of any project using the TLDR stack
Transform session learnings into permanent capabilities (skills, rules, agents). Use when asked to "improve setup", "learn from sessions", "compound learnings", or "what patterns should become skills".
Search past reasoning for relevant decisions and approaches
Explicit Identity Across Boundaries
Idempotent Redundancy
Problem-solving strategies for groups in abstract algebra
Problem-solving strategies for rings in abstract algebra
Problem-solving strategies for contour integrals in complex analysis
Problem-solving strategies for banach spaces in functional analysis
Problem-solving strategies for hilbert spaces in functional analysis
Problem-solving strategies for operator theory in functional analysis
Problem-solving strategies for channel capacity in information theory
Problem-solving strategies for entropy in information theory
Problem-solving strategies for matrices in linear algebra
Problem-solving strategies for propositional logic in mathematical logic
Problem-solving strategies for interpolation in numerical methods
Problem-solving strategies for numerical integration in numerical methods
Problem-solving strategies for second order odes in odes pdes
Problem-solving strategies for boundary value problems in odes pdes
Problem-solving strategies for convergence in real analysis
Problem-solving strategies for gradient methods in optimization
Problem-solving strategies for connectedness in topology
Computational geometry with Shapely - create geometries, boolean operations, measurements, predicates
Debug issues by investigating logs, database state, and git history
Implement technical plans from thoughts/shared/plans with verification
Code refactoring workflow - analyze → plan → implement → review → validate
Comprehensive testing workflow - unit tests ∥ integration tests → E2E tests
Identify failure modes before they occur using structured risk analysis
Scrape web pages and extract content via Firecrawl MCP
Search GitHub code, repositories, issues, and PRs via MCP
Research agent for external documentation, best practices, and library APIs via MCP tools
Document codebase as-is with thoughts directory for historical context
Choose the right search tool for each query type
Meta-skill for creating and managing Maestro skills
Upgrade any skill to v5 Hybrid format using decision theory + modal logic
Wiring Verification
System health check (MOT) for skills, agents, hooks, and memory
AST-based code search and refactoring via ast-grep MCP
Problem-solving strategies for modular arithmetic in graph number theory
Problem-solving strategies for eigenvalues in linear algebra
Agent Context Isolation
Spawn Agentica multi-agent patterns
Search Mathlib for lemmas by type signature pattern
No Polling for Background Agents
Planning agent that creates implementation plans and handoffs from conversation context
Deep interview process to transform vague ideas into detailed specs. Works for technical and non-technical users.
Modular Code Organization
Analyze repository structure, patterns, conventions, and documentation for understanding a new codebase
AI-powered web search, research, and reasoning via Perplexity