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

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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

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