# RUNBOOK-A: Formal Theory Lane — Von Neumann Algebra Factor Type Classification

## Topic
- **Slug:** `von-neumann-algebra-factor-type-classification-proof`
- **Mode:** `formal_derivation` (mapped from `formal_theory`)
- **Front door command:**
  ```
  python -c "from knowledge_hub.aitp_service import AITPService; AITPService().new_topic(
    topic='Von Neumann Algebra Factor Type Classification Proof',
    question='Prove that every finite-dimensional von Neumann algebra factor is Type I (isomorphic to M_n(C)).',
    mode='formal_theory',
    human_request='Classify finite-dimensional factors and produce one promotable bounded result.'
  )"
  ```

## Bootstrap Result
- **Conformance audit:** 27/27 checks pass
- **Resume stage:** L3 (candidate_shaping)
- **Research mode:** formal_derivation
- **Next action:** L0 source expansion (register Jones 1983 sources)
- **Runtime root:** `research/knowledge-hub/runtime/topics/von-neumann-algebra-factor-type-classification-proof/`

## Promotion Path
1. Register source (Jones 1983 arXiv or reference)
2. Advance L1 → L3 derivation of Type I classification
3. Create candidate with bounded proof
4. Run `audit_formal_theory` → verify readiness
5. `request_promotion` → `approve_promotion` → `promote_candidate`

## Evidence Location
- `.planning/phases/170-positive-promotion-proof-lane/evidence/lane-a/`
