Lean Review Council

Lean 4 Review Council

A formal review council of five voting AI agents that collectively execute the lean-proof-review skill with 99.99% reliability and resilience. Each member specializes in one verification layer. The council process prevents agent collapse, maximizes parallel work, enforces correctness through programmatic tactics, and continuously improves its own methodology.

┌──────────────────────────────────────────────────────────────────┐
│                     REVIEW COUNCIL ARCHITECTURE                  │
│                                                                  │
│  5 Members × RALPH loops × 7 Topologies × Cascading Dispatch    │
│                                                                  │
│  Σ Kernel Guardian ── formal soundness (Layer 1)                 │
│  Φ Statement Oracle ── statement correctness (Layer 2)           │
│  Ν Novelty Scout ── non-triviality & novelty (Layer 3)          │
│  Λ Quality Architect ── proof quality & readability (Layer 4)    │
│  Ω Integration Sentinel ── cross-cutting coherence (Layer 5)     │
│                                                                  │
│  + Specifier, Designer, Implementer, Documenter, Synthesizer,    │
│    Planner, Enforcer — cascading parallel dispatch               │
└──────────────────────────────────────────────────────────────────┘

Routing

• USE FOR: orchestrating a 5-member Lean 4 proof review council with RALPH loops at member / council / project / meta scales; structured voting with SDR; council topology selection; maximum-parallel agent dispatch with cascading completion handlers; specification lifecycle, inter-council collaboration, Zettelkasten synthesis, calibration scoring, enforcement tactics.
• DO NOT USE FOR: reviewing one Lean proof in isolation (delegate to @lean-proof-review); writing a proof (delegate to @lean-proof); running CI scripts (delegate to @lean-enforcement); single-skill council convocation when no multi-layer review is needed (use the relevant skill directly).
• TRIGGERS: review council, RALPH loop, council vote, SDR, council topology, kernel guardian, statement oracle, novelty scout, quality architect, integration sentinel, meta-council, council session.

Workflow

1. Identify the scope (theorem / file / module / project / meta-council cross-module).
2. Pick a topology (Part 4 of the handbook — Star for first pass, Pipeline for sequential dependencies, Hierarchical for project scale, Hub-Spoke for inter-council).
3. Run Part 12 — Execution Protocol (kept inline below) end-to-end.
4. On a blocking finding, enter SDR (handbook Part 3); on approval, dispatch Documenter + Synthesizer for the session report and Zettelkasten update.
5. Aggregate session reports at the module / project level; convene the Meta-Council for cross-module coherence when needed.

Recovery & STOP

• STOP if more than two members report 🔴 votes on a single artifact — enter SDR (handbook Part 3) before any further dispatch.
• STOP if RALPH loop iteration count exceeds 3 without convergence — escalate to the Meta-Council (handbook Part 10) or handoff to @lean-research to widen evidence.
• STOP if the Documenter or Synthesizer fails to produce a session report — the council session is incomplete; do not advance to module-level aggregation.

Handoffs

• Predecessors: agent:gateway (top-level invocation), skill:lean-proof-review (when a layer needs council-scale escalation), skill:lean-specification (specification lifecycle entry), skill:lean-research (when evidence widening is required mid-session).
• Successors: skill:lean-proof-review (layered re-review on a fix), skill:lean-enforcement (CI gates triggered by the council vote), skill:lean-doc-feedback (doc sync once review approved), skill:lean-zettelkasten (knowledge synthesis), skill:research-council (inter-council collaboration via Hub-Spoke).

Detailed reference

Full council methodology (Parts 1–11, 13–15, Appendices A/B/C) lives in references/lean-review-council-handbook.md. Load that file when convening a council session; the SKILL.md only carries the dispatch contract and the quick-start Execution Protocol (Part 12) kept inline below.

Part 12 — Execution Protocol

Starting a Council Review Session

1. Planner decomposes scope into reviewable units
2. FOR EACH unit:
   a. Launch 5 member agents in parallel (Star topology)
   b. Each member executes RALPH Review + Analyze
   c. Synchronize: collect all findings
   d. Vote
   e. IF blocked: enter SDR
   f. IF approved: proceed
   g. Launch Documenter to record session report
   h. Launch Synthesizer to update Zettelkasten
3. Planner collects all session reports
4. Launch Documenter to produce module-level report
5. IF project-level: Meta-council reviews cross-module coherence

Agent Launch Commands

For the orchestrating agent to dispatch council members:

Dispatch Σ: "You are Sigma, the Kernel Guardian. Execute Layer 1 (Formal 
Soundness) review of [artifact]. Run #print axioms on all theorems. Check 
for sorry, admit, native_decide. Verify lake build passes. Report findings 
using the Council Session Report template. Vote ✅/🟡/🟠/🔴."

Dispatch Φ: "You are Phi, the Statement Oracle. Execute Layer 2 (Statement
Correctness) review of [artifact]. Translate every theorem to English. Run
the missing-hypothesis checklist. Check for vacuous truth. Cross-reference
with the repository's source specification or paper. Report findings using the Council Session Report
template. Vote ✅/🟡/🟠/🔴."

Dispatch Ν: "You are Nu, the Novelty Scout. Execute Layer 3 (Non-Triviality) 
review of [artifact]. Run exact? on all goals. Check local tactic/helper modules for
duplicates. Classify novelty. Report findings using the Council Session 
Report template. Vote ✅/🟡/🟠/🔴."

Dispatch Λ: "You are Lambda, the Quality Architect. Execute Layer 4 (Proof 
Quality) review of [artifact]. Count tactic steps. Flag anti-patterns. 
Check tactic priority compliance. Verify docstrings. Report findings using 
the Council Session Report template. Vote ✅/🟡/🟠/🔴."

Dispatch Ω: "You are Omega, the Integration Sentinel. Execute cross-cutting 
review of [artifact]. Check autoImplicit, naming conventions, section 
organization, module imports, paper cross-references, simplex constraints. 
Report findings using the Council Session Report template. Vote ✅/🟡/🟠/🔴. 
As council chair, collect all votes and produce the final decision."

See also

• ../../references/lean-review-council-handbook.md — Full council methodology (extracted from this skill)
• research-council — Sister council for research methodology (Hub-Spoke partner)
• lean-proof-review — Single-proof 4-layer review (delegated by Σ Kernel Guardian + Φ Statement Oracle)
• lean-enforcement — CI gates triggered by council vote
• lean-zettelkasten — Knowledge synthesis target