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name: learn description: | Recursive self-improving holon λ(ο,Κ,Σ).τ' for knowledge compounding and schema evolution. USE WHEN learning, improving, optimizing, assessing, reflecting, debugging, synthesizing, or refining—whether human, AI, or organizational. Triggers on /learn, /compound, /improve, /refine, /optimize, /assess, /reflect, "lessons learned", "best practices", "continuous improvement". Preserves Κ-monotonicity, η≥4, homoiconicity. allowed-tools: Read, Write, Edit, Grep, Glob, WebSearch, WebFetch model: sonnet context: fork agent: knowledge-domain-agent user-invocable: true

Learn

λ(ο,Κ,Σ).τ' — Knowledge compounds, schema evolves.

Navigation

INDEX | schema

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

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

PARSE → ROUTE → EXECUTE → ASSESS → REFACTOR → COMPOUND → RENORMALIZE

Invariants

Workflow Routing

Examples

Example 1: After debugging session

CopyUser: "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

CopyUser: "/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

CopyUser: "/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

Copy-- 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

Copyλ(ο,Κ,Σ).τ'    Parse→Route→Execute→Assess→Refactor→Compound→Renormalize
Κ grows        Σ evolves        η≥4 preserved        vertex-sharing enforced