learn

[INDEX](INDEX.md) | [schema](schema.yaml)

Concepts: [homoiconicity](concepts/homoiconicity.md), [compound-interest](concepts/compound-interest.md), [topology](concepts/topology-invariants.md), [vertex-sharing](concepts/vertex-sharing.md), [convergence](concepts/convergence.md), [fixed-point](concepts/fixed-point.md)

Phases: [1-parse](phases/1-parse.md) → [2-route](phases/2-route.md) → [3-execute](phases/3-execute.md) → [4-assess](phases/4-assess.md) → [5-refactor](phases/5-refactor.md) → [6-compound](phases/6-compound.md) → [7-renormalize](phases/7-renormalize.md)

Domains: [learning](domains/learning.md), [coding](domains/coding.md), [research](domains/research.md), [writing](domains/writing.md), [meta](domains/meta.md)

Related Skills: [λ (lambda-skill)](../lambda-skill/SKILL.md) — shares compound loop, topology validation, vertex-sharing

```

ο → PARSE → ROUTE → EXECUTE → ASSESS → REFACTOR → COMPOUND → RENORMALIZE → τ'

```

[PARSE](phases/1-parse.md) → [ROUTE](phases/2-route.md) → [EXECUTE](phases/3-execute.md) → [ASSESS](phases/4-assess.md) → [REFACTOR](phases/5-refactor.md) → [COMPOUND](phases/6-compound.md) → [RENORMALIZE](phases/7-renormalize.md)

| Invariant | Expression | Reference |

|-----------|------------|-----------|

| Κ-monotonicity | len(Κ') ≥ len(Κ) | [knowledge-monotonicity](concepts/knowledge-monotonicity.md) |

| Topology | η ≥ 4 | [topology-invariants](concepts/topology-invariants.md) |

| Homoiconicity | Σ.can_process(Σ) | [homoiconicity](concepts/homoiconicity.md) |

| Integration | shared_vertices ≠ ∅ | [vertex-sharing](concepts/vertex-sharing.md) |

| 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 |

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

```

This skill extends [lambda-skill](../lambda-skill/SKILL.md) 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

```haskell

-- 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

```

```haskell

λ(ο,Κ,Σ).τ' Parse→Route→Execute→Assess→Refactor→Compound→Renormalize

Κ grows Σ evolves η≥4 preserved vertex-sharing enforced

```