Product & Design Skills

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.

USE FOR: Causal reasoning, counterfactual analysis, and deontic logic for AI systems. Use for formalizing cause-effect relationships (Pearl's hierarchy), interventional reasoning, structural causal models, counterfactual simulation, obligation/permission/prohibition reasoning, normative systems, and legal/ethical rule formalization in Lean 4. DO NOT USE FOR: formalising those models in Lean (use @lean-causal-reasoning); agentic AI behaviour (use @ai-agentic-evolving); commonsense reasoning (use @ai-commonsense-reasoning). TRIGGERS: causal, counterfactual, Pearl hierarchy, deontic, obligation, permission, structural causal model.

USE FOR: Commonsense reasoning for AI systems — world knowledge, naive physics, folk psychology, temporal/spatial reasoning, default reasoning, and their formalization. Use for reasoning about everyday knowledge that humans take for granted but AI systems need explicitly, especially when a downstream project must make implicit context explicit. DO NOT USE FOR: formal KR/ontology engineering (use @ai-symbolic-neuro); causal/deontic reasoning (use @ai-causal-deontic); formalisation in Lean (use @lean-knowledge-formalization). TRIGGERS: commonsense, naive physics, folk psychology, temporal reasoning, spatial reasoning, default reasoning.

USE FOR: Formally verifiable AI, high-stakes AI systems, safety-critical deployment, certification, and regulatory compliance. Use for reasoning about AI systems that must be provably correct, auditable, or certifiable — medical AI, autonomous vehicles, legal decision support, military/intelligence systems, and mathematically rigorous AI governance. DO NOT USE FOR: formal verification proofs in Lean (use @lean-ai-formalization); agentic AI dynamics (use @ai-agentic-evolving); causal/deontic reasoning (use @ai-causal-deontic). TRIGGERS: high stakes, verifiable AI, safety critical, certification, regulatory compliance, AI assurance.

USE FOR: Symbolic AI, neuro-symbolic integration, knowledge representation and reasoning (KRR), ontology engineering, description logics, and hybrid symbolic-neural architectures. Use for reasoning about formal knowledge structures, rule-based systems, logic programming, semantic web technologies, and their integration with neural approaches in knowledge graphs and structured reasoning pipelines. DO NOT USE FOR: formalising the ontology in Lean (use @lean-knowledge-formalization); commonsense reasoning (use @ai-commonsense-reasoning); agentic AI (use @ai-agentic-evolving). TRIGGERS: symbolic AI, neuro-symbolic, knowledge representation, KRR, ontology engineering, description logic, hybrid AI.

USE FOR: Data security and information security formalization — CIA triad, access control models (BLP, RBAC, ABAC), information flow, cryptographic primitives, privacy (differential privacy, k-anonymity), threat modeling, and their formal verification in Lean 4. Use for security properties of provenance chains, trust composition, and multi-agent systems. DO NOT USE FOR: Lean formalisation of these policies (use @lean-security-formalization); engineering disciplines more broadly (use @applied-engineering-disciplines); legal-policy reasoning (use @applied-legal-reasoning). TRIGGERS: CIA triad, access control, BLP, RBAC, ABAC, information flow, cryptographic primitive, data security.

USE FOR: Engineering disciplines relevant to formal mathematical systems — control theory, systems engineering, reliability engineering, software verification, signal processing, and testing methodology. Use for bridging mathematical foundations to engineering practice, and for formalizing engineering requirements in Lean 4. DO NOT USE FOR: formal verification in Lean (use @lean-ai-formalization); security-specific engineering (use @applied-data-information-security); strategy analysis (use @applied-strategy-analysis). TRIGGERS: control theory, systems engineering, reliability engineering, software verification, engineering discipline.

USE FOR: Intelligence analysis methodology — structured analytic techniques (SATs), evidence reasoning, hypothesis generation, cognitive bias mitigation, competitive intelligence, and their formalization. Use for analysis of competing hypotheses (ACH), link analysis, timeline reconstruction, source reliability assessment, and connections to quality gates, provenance, and multi-agent trust. DO NOT USE FOR: formalising intelligence reasoning in Lean (use @lean-applied-reasoning); strategy analysis (use @applied-strategy-analysis); legal reasoning (use @applied-legal-reasoning). TRIGGERS: structured analytic techniques, SATs, evidence reasoning, hypothesis generation, cognitive bias, intelligence analysis, competing hypotheses.

USE FOR: Legal reasoning formalization — statutory interpretation, case-based reasoning, argumentation frameworks, defeasible rules, deontic norms, regulatory compliance, and their connection to provenance chains, governance structures, and formal verification for legal-adjacent AI systems. DO NOT USE FOR: formalising those legal models in Lean (use @lean-applied-reasoning); deontic reasoning specifically (use @ai-causal-deontic); security policy (use @applied-data-information-security). TRIGGERS: statutory interpretation, case-based reasoning, argumentation framework, defeasible rule, deontic norm, legal reasoning, regulatory.

USE FOR: Strategy creation, analysis, and evaluation — game-theoretic foundations, competitive analysis, decision frameworks, SWOT/PESTLE, wargaming, and their mathematical underpinnings. Use for strategic reasoning about complex multi-agent scenarios, organizational strategy, research strategy, and mathematical planning for governance and optimization layers. DO NOT USE FOR: formalising strategic models in Lean (use @lean-applied-reasoning); intelligence analysis (use @applied-intelligence-analysis); game-theoretic optimization (use @math-optimization-game). TRIGGERS: strategy, SWOT, PESTLE, wargaming, decision framework, competitive analysis, game-theoretic strategy.

USE FOR: epistemic discovery — picking a discovery mode (Census / Dependency / Literature / Cross-domain / Community), running an Unknown-Unknown (UU) hunting protocol at the right depth (Shallow / Standard / Deep / Exhaustive), emitting census + probe + trigger reports, anti-stagnation mechanisms, project relevance scoring. DO NOT USE FOR: a known research question (use @lean-research); council convocation on a known artifact (use @lean-review-council or @research-council); synthesis emission of known content (use @research-synthesis-engine). TRIGGERS: discovery, unknown unknown, UU hunt, epistemic discovery, census, dependency probe, cross-domain probe, community probe, anti-stagnation.

USE FOR: mapping a domain's concept lattice, identifying load-bearing assumptions, surfacing implicit ontologies, drafting an epistemic terrain map. DO NOT USE FOR: producing formal proofs (use @lean-proof), gathering primary research data (use @applied-intelligence-analysis). TRIGGERS: concept-map, ontology, terrain, epistemic-survey.

USE FOR: Formal verification of AI systems — agentic AI safety, alignment, high-stakes AI, evolving agents, neural network properties, and AI governance constraints. Use when formalizing safety envelopes, trust dynamics, multi-agent composition, AI act compliance, reward specifications, alignment properties, or any AI system property that must be formally verified. DO NOT USE FOR: AI methodology itself (use @ai-high-stakes-verifiable or @ai-agentic-evolving); security-specific formalisation (use @lean-security-formalization); knowledge formalisation (use @lean-knowledge-formalization). TRIGGERS: AI formalization, agentic safety, alignment proof, high-stakes AI, neural network property, AI governance.

USE FOR: Applied reasoning for intelligence analysis, strategy creation and analysis, brainstorming methodologies, investigative reasoning, and domain-specific decision-making. Use when formalizing strategic frameworks, situational analysis, hypothesis generation workflows, decision-under-uncertainty models, or when connecting theoretical formalization to practical operational contexts. Bridges mathematical formalization to real-world application domains. DO NOT USE FOR: pure intelligence-analysis methodology (use @applied-intelligence-analysis); strategy analysis methodology (use @applied-strategy-analysis); legal reasoning methodology (use @applied-legal-reasoning). TRIGGERS: applied reasoning, intelligence formalisation, strategy formalisation, investigative reasoning, domain-specific reasoning.

USE FOR: bisecting Lean 4 toolchain versions or commits to find which one introduced a regression, using script/lean-bisect with guardmsgs / exit-code signatures, ignoring messages with --ignore-messages, bisecting between nightlies or arbitrary commits. DO NOT USE FOR: building a project (use @lean-build), minimising a Mathlib repro to a self-contained file (use @lean-mwe first), writing or fixing the proof itself (use @lean-proof), filing the bug report (use @lean-pr after the bisect points at a culprit). TRIGGERS: bisect, regression, "which commit broke", "behavior changed between", nightly bisect.

USE FOR: generating Lean blueprint, annotating theorems with @[blueprint], scaffolding blueprint directory, building blueprint LaTeX, rendering blueprint web. DO NOT USE FOR: writing Lean proofs (use @lean-proof), opening Lean/Mathlib PRs (use @lean-pr). TRIGGERS: blueprint, leanblueprint, LeanArchitect, dependency-graph.

Build, test, and debug Lean 4 projects using Lake. Use when building the ComputationalPaths project, checking for errors, running tests, cleaning artifacts, or debugging Lean 4 compilation issues.

USE FOR: Formalize causal DAGs, knowledge graph quality gates, counterfactual reasoning, and provenance bridges in Lean 4. Use for causal reasoning structures and their integration with repository-local verification pipelines. DO NOT USE FOR: causal methodology not in Lean (use @ai-causal-deontic); knowledge graph formalisation generally (use @lean-knowledge-formalization); general AI formalisation (use @lean-ai-formalization). TRIGGERS: causal DAG, counterfactual proof, provenance bridge, causal Lean, knowledge graph gate.

USE FOR: reviewing a Lean documentation draft, flagging undefined terms, suggesting cross-links, scoring readability against a rubric. DO NOT USE FOR: rewriting prose end-to-end (use @lean-doc-improvement), generating new blueprints (use @lean-blueprint). TRIGGERS: doc-review, readability, doc-feedback.

USE FOR: Update academic papers, technical reports, and documentation based on results from Lean 4 formalization. Use when formal verification reveals paper imprecisions, missing hypotheses, sharper bounds, new insights, or when metrics need synchronization. Covers paper appendix updates, verification tables, erratum entries, insight propagation, and metric synchronization between Lean and documents. DO NOT USE FOR: extracting requirements from papers (use @lean-doc-requirements); blueprint generation (use @lean-blueprint); report compilation (use @lean-report). TRIGGERS: update paper, doc improvement, paper revision, documentation update from Lean, doc-feedback consumer.

USE FOR: Extract formal requirements from academic papers, technical reports, and design documents. Use when converting informal mathematical claims into Lean 4 theorem specifications. Covers claim extraction from LaTeX sources, equation identification, proposition mapping, hypothesis inference, and requirement traceability from document to formal specification. DO NOT USE FOR: paper update post-Lean (use @lean-doc-improvement); specification design (use @lean-specification); blueprint generation (use @lean-blueprint). TRIGGERS: doc requirements, requirement extraction, informal-to-Lean, claim extraction, paper-to-spec.

USE FOR: running programmatic CI / pre-review / post-review gates for a Lean 4 project — axiom audit, council precheck, review coverage, metric sync, zettelkasten lint, bridge validation, proof quality, ecosystem health, workflow gate enforcement. DO NOT USE FOR: semantic / judgement review (use @lean-proof-review or @lean-review-council); orchestrating the broader QA lifecycle (use @lean-quality-engine); routing tasks across skills (use @lean-gateway). TRIGGERS: enforcement, CI gate, axiom audit, councilprecheck, workflowgate, ecosystemhealth, sorry check.

USE FOR: routing the top-level entry-point for a complex Lean 4 task; selecting which downstream skill(s) own each phase; preventing context collapse across long sessions; maintaining feedback / feedforward loops; fan-in / fan-out coordination; system-wide health monitoring. DO NOT USE FOR: doing any actual work (always delegate to a domain skill); single-file editing (use @lean-proof or @lean-doc-improvement); script-level enforcement (use @lean-enforcement). TRIGGERS: gateway, orchestrate, route, dispatch, top-level, context collapse, fan-out, fan-in, ecosystem health.

USE FOR: Cross-skill integration protocol defining how all 39 skills work together. Covers the complete lifecycle from document to proof to document, inter-cluster communication, workflow templates for common tasks, and the master orchestration patterns. Use when coordinating multi-skill workflows or diagnosing cross-skill issues. DO NOT USE FOR: any single-skill execution (use that skill directly); the review council itself (use @lean-review-council); the gateway (use @lean-gateway). TRIGGERS: integration protocol, skill integration, cross-skill, skill lifecycle, inter-cluster routing.