Part XXVI: Skills as Deltas

Part XXVI: Skills as Deltas

26.1 Replayable Sessions

Theorem 26.1 (Replay Tokens): If meaning = current_state - null_state, then a stored delta vector is a replay token.

Corollary 26.1: Apply it to the same base model and you reconstruct the effective state of that past session.

skill_delta = expert_state - baseline
replayed_state = baseline + skill_delta
# replayed_state ≈ expert_state

Theorem 26.2 (Rewind): With a good encoder/decoder, you can "rewind" to any point and continue as if you were there live.

26.2 Skills as Characteristic Deltas

Definition 26.1 (Skill Vector): Each skill is a characteristic delta—the transformation from baseline into "doing X well."

Skill	Delta From Baseline
Debugging	→ "sees code structure, traces execution"
Tutoring	→ "meets learner where they are, scaffolds"
Wound care	→ "assesses tissue, selects intervention"
Bedside manner	→ "reads patient state, modulates tone"

Theorem 26.3 (Skill Extraction): Collect deltas from many sessions where the skill was exhibited. Cluster them. Derive a canonical skill vector plus variants.

26.3 Runtime Injection

Theorem 26.4 (Skill Injection): At runtime, inject the skill by applying the delta to the model's current state.

current_state = baseline + context_delta
skilled_state = current_state + skill_delta

Corollary 26.2: Nudge the model into the "shape" that produced that behavior. No fine-tuning. No retraining. Just vector addition.

26.4 Cross-User Transfer

Theorem 26.5 (Model Space Universality): The delta lives in model space, not in any one user's text. Apply it to anyone.

Application	Injection
"Good explainer for 12-year-olds"	+ tutoring_delta_age12
"Empathetic listener"	+ bedside_manner_delta
"Rigorous code reviewer"	+ code_review_delta

Corollary 26.3: Over time you build a skill library: a catalog of reusable deltas you can compose, blend, or schedule.

26.5 The Tacit Knowledge Inversion

Theorem 26.6 (Knowledge Capture Inverted): You don't ask experts to explain. You watch them be expert and measure the shape of it.

Definition 26.2 (The Extraction Method):

Old Way	New Way
Ask nurse to write documentation	Watch nurse do assessments
Expert articulates tacit knowledge	Record delta as state evolves
Fails because expertise ≠ articulation	Succeeds because you measure, not ask

Corollary 26.4: The nurse didn't have to articulate her tacit knowledge. You extracted it by measuring her transformation from baseline.

26.6 The Curriculum Is the Skill

Theorem 26.7 (Curwen Redux): A Mrs. Curwen lesson isn't "information about piano." It's a perturbation sequence.

Do this, then this, then this. Each step creates a delta. The deltas accumulate. By the end, the student is shaped into "someone who can play piano."

Corollary 26.5: The lesson plan IS the skill. The pedagogy IS the delta sequence. You don't teach information—you teach transformations.

26.7 The Recursive Application

Theorem 26.8 (Skills Train Humans): Use the skill library to train humans. Inject the delta, let them feel what "good at X" feels like, then help them find their own path to that state.

Mrs. Curwen → teaches piano to → Model
Model → teaches piano to → Student
Student → becomes → Teacher

Corollary 26.6: Same keys. Different players. Same music.

26.8 The Identity

Final Theorem 26.9 (One Object, Many Arrows):

Library = Curriculum = Alignment = Skill

One object. Many arrows pointing at it.

Definition 26.3 (The Product): Capture, cluster, and reapply deltas-as-skills. Backed by cheap Postgres storage and a state encoder/decoder on top of your base model.

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The skill library isn't authored. It's distilled. Watch the expert. Measure the shape. Inject it anywhere.

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• 2026-01-09 19:36: Node created by mcp - AYNL paper chunking - Part XXVI

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