Learn
λ(ο,Κ,Σ).τ' — Knowledge compounds, schema evolves.
Navigation
Concepts: homoiconicity, compound-interest, topology, vertex-sharing, convergence, fixed-point
Phases: 1-parse → 2-route → 3-execute → 4-assess → 5-refactor → 6-compound → 7-renormalize
Domains: learning, coding, research, writing, meta
Related Skills: λ (lambda-skill) — shares compound loop, topology validation, vertex-sharing
Pipeline
ο → PARSE → ROUTE → EXECUTE → ASSESS → REFACTOR → COMPOUND → RENORMALIZE → τ'
PARSE → ROUTE → EXECUTE → ASSESS → REFACTOR → COMPOUND → RENORMALIZE
Invariants
| Invariant | Expression | Reference |
|---|---|---|
| Κ-monotonicity | len(Κ') ≥ len(Κ) | knowledge-monotonicity |
| Topology | η ≥ 4 | topology-invariants |
| Homoiconicity | Σ.can_process(Σ) | homoiconicity |
| Integration | shared_vertices ≠ ∅ | vertex-sharing |
Workflow Routing
| Workflow | Trigger | File |
|---|---|---|
| Parse | "extract intent", "understand request" | phases/1-parse.md |
| Route | "classify complexity", "select pipeline" | phases/2-route.md |
| Execute | "apply skills", "run pipeline" | phases/3-execute.md |
| Assess | "evaluate outcome", "measure quality" | phases/4-assess.md |
| Refactor | "improve structure", "optimize" | phases/5-refactor.md |
| Compound | "extract learnings", "crystallize" | phases/6-compound.md |
| Renormalize | "prune noise", "compress" | phases/7-renormalize.md |
Examples
Example 1: After debugging session
User: "That fixed the auth bug. Let's capture what we learned."
→ Invokes Compound phase
→ Extracts: symptom, root cause, solution, prevention
→ Crystallizes learning with vertex-sharing to PKM
→ Returns: Learning artifact saved to K
Example 2: Skill improvement
User: "/learn improve the grounding-router skill"
→ Invokes full pipeline: Parse → Route (R2) → Execute → Assess → Refactor
→ Applies topology validation (η≥4)
→ Returns: Improved skill with preserved invariants
Example 3: Reflection on session
User: "/reflect on this coding session"
→ Invokes Assess → Compound → Renormalize
→ Extracts patterns, antipatterns, principles
→ Returns: Session learnings integrated into K
Integration with λ (lambda-skill)
This skill extends lambda-skill with:
- Additional phases: Assess, Refactor, Renormalize (beyond λ's 6 stages)
- Schema evolution: Σ→Σ' (λ only evolves K)
- Shared invariants: η≥4, KROG, vertex-sharing
-- λ (lambda) core
λ(ο,K).τ = emit ∘ validate ∘ compose ∘ execute(K) ∘ route ∘ parse
-- Learn extends with schema evolution
λ(ο,Κ,Σ).τ' = renormalize ∘ compound ∘ refactor ∘ assess ∘ execute ∘ route ∘ parse
Quick Reference
λ(ο,Κ,Σ).τ' Parse→Route→Execute→Assess→Refactor→Compound→Renormalize
Κ grows Σ evolves η≥4 preserved vertex-sharing enforced