Ai agentic evolving

Skill r-irbe/proof-skills/skills/ai-agentic-evolving

APM-installable agent skills for Lean 4 and Mathlib4 — proof tactics, math domains, review and research workflows, generic tooling.

Install

npx -y skills add r-irbe/proof-skills --skill ai-agentic-evolving

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USE FOR: Agentic AI systems, multi-agent coordination, evolving agents, agent lifecycle management, emergent behavior, and trust dynamics in autonomous systems. Use for reasoning about agent architectures, communication protocols, coalition formation, reputation systems, and the mathematical foundations of agentic safety and multi-agent trust formalization. DO NOT USE FOR: formal verification of those AI systems (use @lean-ai-formalization); high-stakes / verifiable AI mode (use @ai-high-stakes-verifiable); causal/deontic reasoning (use @ai-causal-deontic). TRIGGERS: agentic AI, multi-agent, evolving agent, agent lifecycle, emergent behavior, trust dynamics, autonomous system.

SKILL.md

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Agentic & Evolving AI Systems

Mathematical and architectural foundations for autonomous agents, multi-agent systems, evolving capabilities, and formally verified trust/safety dynamics.

Routing

USE FOR: Agentic AI systems, multi-agent coordination, evolving agents, agent lifecycle management, emergent behavior, and trust dynamics in autonomous systems. Use for reasoning about agent architectures, communication protocols, coalition formation, reputation systems, and the mathematical foundations of agentic safety and multi-agent trust formalization.
DO NOT USE FOR: formal verification of those AI systems (use @lean-ai-formalization); high-stakes / verifiable AI mode (use @ai-high-stakes-verifiable); causal/deontic reasoning (use @ai-causal-deontic).
TRIGGERS: agentic AI, multi-agent, evolving agent, agent lifecycle, emergent behavior, trust dynamics, autonomous system.

Workflow

Frame the system: how many agents, what each agent optimises for, what coordination signal exists, and which lifecycle phase (spawn / coordinate / evolve / retire) the question is about.
Pick the matching theoretical lens from the body — emergence, multi-agent game theory, mechanism design, evolutionary dynamics, or trust dynamics.
Run the reasoning at the methodological level; do not attempt formal proofs here. Belief floor 0.90 before publishing.
Hand off: to @lean-ai-formalization if a property needs Lean proof, to @ai-high-stakes-verifiable if the agents are safety-critical, to @lean-zettelkasten for the durable note.

Recovery & STOP

STOP if the question is about formal AI verification rather than agentic dynamics — hand to @lean-ai-formalization.
STOP if the system collapses to single-agent — switch to whichever non-agentic AI skill matches (e.g., @ai-symbolic-neuro for KR, @ai-commonsense-reasoning for reasoning).
STOP if emergence analysis would require empirical simulation rather than methodological reasoning — escalate to @research-council.

Handoffs

Predecessors: agent:gateway, skill:lean-research.
Successors: skill:lean-ai-formalization, skill:ai-high-stakes-verifiable, skill:lean-zettelkasten.

Detailed reference

Full content for ai-agentic-evolving lives in references/ai-agentic-evolving-handbook.md. Load that file when the skill is convened; the SKILL.md only carries the dispatch contract and the parts index.

Section	Topic
Part 1	Agent Architectures
Part 2	Multi-Agent Coordination
Part 3	Evolving Agents
Part 4	Safety in Agentic Systems
Part 5	Reputation & Trust Systems
Part 6	Connection to Project Lean Modules
Part 7	Research Frontiers