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Novelty: Theoretical Foundation

Definition

Novelty is deviation from a reference frame.

The reference frame is itself accumulated novelty - the residue of all prior deviations that have been integrated into the observer's model.

The Recursion

This definition is inherently recursive:

  1. To measure novelty, you need a reference
  2. The reference is made of prior novelty measurements
  3. Those measurements required their own references
  4. ...and so on, without bottoming out

This is not a bug. It's the nature of the thing.

Novelty cannot be defined in terms of something more fundamental. It IS the fundamental unit - the primitive capacity to register difference. Like how you can't define "length" without already having a concept of spatial difference.

Structure of Reference Frames

A reference frame is not an opaque blob - it has STRUCTURE. This structure is part of the definition, not implementation detail:

1. Hierarchical Claims

Claims are arranged hierarchically. Parent claims are more fundamental than child claims:

"Decentralization enables flourishing" (depth 0, foundational)
├── "P2P networks resist censorship" (depth 1)
│   └── "Bitcoin enables trustless transactions" (depth 2)
└── "Centralized systems have single points of failure" (depth 1)

The depth of a claim indicates how foundational it is. Disrupting a shallow claim cascades to everything below it.

2. Adversarial Positioning (PRO/CON)

Observations don't just "exist" - they are POSITIONED relative to claims:

  • PRO: Supports/entails the claim (evidence for)
  • CON: Opposes/contradicts the claim (evidence against)
  • NEUTRAL: Topically related but doesn't take a stance

This enables measuring conflict, not just difference.

3. Weighted Stakes

Tendencies (drives, values) stake weights on claims:

"Decentralization enables flourishing"
  - autonomy: 0.4 (cares a lot)
  - survival: 0.2 (moderate concern)
  - comfort: 0.05 (barely cares)

This creates the motivational structure - what the agent prioritizes.

4. Integrated Observations

Raw observations that have been absorbed. These form the evidential base from which positions draw.

Why This Structure?

This isn't arbitrary - it's what's REQUIRED for novelty to work:

Property Requires
Depth-dependence Hierarchy
Contradiction detection PRO/CON positioning
Importance weighting Stakes
Learning over time Observation tracking

Without hierarchy, all novelty is equal. Without positioning, we can only measure "different" not "conflicting." Without stakes, paradigm shifts look like trivia.

Agent = Reference Frame

There is no separate "agent" that "has" a world model. The agent IS the reference frame at a particular configuration.

  • agent_t1 and agent_t2 are different reference frames
  • They share structural continuity but are distinct configurations
  • Time enters through WHICH frame you anchor to, not as a separate parameter

The Four Components of Novelty

When measuring novelty against a structured reference frame, four components emerge:

1. Integration Resistance

How hard is it to position this concept in existing claim hierarchies?

  • Low: Fits naturally as PRO or CON to existing claims
  • High: Doesn't relate to anything in the worldview

2. Contradiction Depth

If the concept opposes existing claims, how deep are those claims?

  • Low: Opposes only leaf claims (easily revised beliefs)
  • High: Opposes root claims (foundational assumptions)

3. Coverage Gap

What fraction of belief hierarchies have no place for this concept?

  • Low: Relevant to many areas of the worldview
  • High: Orthogonal to everything the agent cares about

4. Allocation Disruption

Would integrating this concept shift how attention is allocated across tendencies?

  • Low: Fits within current priority structure
  • High: Would restructure what the agent cares about (paradigm shift)

Combination: Geometric Mean

Components combine via geometric mean:

composite = (IR × CD × CG × AD)^(1/4)

This ensures all dimensions matter. A concept that's maximally novel on one dimension but zero on another is less novel overall than one that's moderately novel on all dimensions.

Theoretical vs Practical

Aspect Theoretical (core.py) Practical (novelty.py)
Anchor Not required Required
Structure Defined abstractly Implemented concretely
Similarity Any valid function Neural embeddings + NLI
Result Abstract score Detailed breakdown

The theoretical layer defines what novelty IS. The practical layer makes it computable.

Axioms

Any valid novelty implementation must satisfy:

  1. Reference dependence: Same concept, different frames → different scores
  2. Absorption reduces novelty: R2 = R1.absorb(X) → novelty(X, R2) < novelty(X, R1)
  3. Depth matters: Contradicting ancestors is more novel than contradicting descendants
  4. Stake matters: Affecting high-stake claims is more novel than low-stake
  5. Stance matters: Contradiction > mere absence/difference

Code Structure

core.py          - Abstract interfaces (Claim, ClaimHierarchy, ReferenceFrame, NoveltyMeasure)
novelty.py       - Concrete implementation (WorldModelReference, AnchoredNoveltyMeasure)
world_model/     - Reference frame components (Trees, Agents, Observations)
embeddings.py    - Neural similarity + NLI stance detection
test_harness.py  - Validation against historical epoch data