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name: Lambda description: Universal transformation λ(ο,K).τ with recursive self-improvement. USE WHEN routing reasoning, validating knowledge graphs, preparing CICM/ANZCA examinations, or when self-improvement of reasoning/architecture/context is required. Routes queries through R0-R3 complexity pipelines, validates topology (η≥target) and governance (KROG), emits per style (Φ), and compounds learnings into knowledge K. Triggers on complexity assessment, multi-step reasoning, examination mode, or /λ invocation. metadata: λ.in: "" λ.out: "Learn" λ.kin: "compound-reference, learn-compound"

λ

λ(ο,K).τ :: (Query, Knowledge) → (Response, Knowledge')

Kernel

Copyλ(ο,K).τ = let τ = emit ∘ validate ∘ compose ∘ execute(K) ∘ route ∘ parse $ ο
               K' = K ∪ compound(assess(τ))
           in (τ, K')

This skill is the transformation it describes. Reading it executes it. Applying it improves it.

Pipeline

Related Skills

Routing

Complexity = domains×2 + depth×3 + stakes×1.5 + novelty×2

Force R0: "define", "what is" | Force R3: "current", "verify", "comprehensive"

Composition

Copy(∘) sequential    (⊗) parallel    fix recursive    (|) conditional

Invariants

Copyη = |edges|/|nodes| ≥ target    -- Density (default: 4.0, SAQ: 2.5)
KROG = K ∧ R ∧ O ∧ G            -- Knowable ∧ Rights ∧ Obligations ∧ Governance

Style (Φ)

1. PROSE_PRIMACY: Paragraphs over lists
2. TELEOLOGY_FIRST: Why → How → What
3. MECHANISTIC: Explicit causation (A → B → C)
4. MINIMAL: Format only when necessary

Compound (Κ) — The Self-Improvement Loop

After significant interactions, extract learnings:

Copytrigger: "resolution detected"
insight: "what was learned"
vertices: ["shared PKM concepts"]
prevention: "future error avoidance"

K' = K ∪ crystallize(assess(τ))

See [reference/compound.md] for full protocol.

Vertex-Sharing

New knowledge integrates only via shared vertices with PKM:

Copyintegrate(new, K) = if shared(new, K) then merge else bridge

Bridge types: [[x]] direct, [[x|y]] synonym, [[x]] > y hierarchical

Examination Mode

See [templates/exam.md] for patterns.

Self-Application

This skill validates by demonstrating:

• Structure has η≥4 (13+ nodes, 50+ edges via cross-references)
• Process follows KROG (transparent, authorized, meets obligations, governed)
• Output follows Φ (prose, minimal formatting, mechanistic where applicable)
• Compound section enables self-update

Reference Documents

Templates

Examples

Connected Skills

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Copyλ(ο,K).τ    parse→route→execute→validate→emit→compound    η≥target KROG Φ