§ 1 Definition

What is a world model?

Eighty years after Craik proposed that the brain carries "small-scale models" of external reality, the term world model remains formally undefined. The field has been building prediction engines and calling them world models. Prediction is three of ten ingredients.

StateIngredients 1–3

ChangeIngredient 5

ConstraintIngredient 6

TimeIngredient 4

Recursion is how we compute the change. Observation, Uncertainty, Purpose, and Memory define the geometry of evolution.

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§ 2 The ten ingredients

Ten irreducible requirements for a world to be modelable.

State + Change + Constraint + Time

StateWhat persists

01Distinctions

Boundary between this and not-this.

Not recursive — a single operation.

02Entities

Things that persist across distinctions.

Recursive — entities contain entities.

03Relations

Connective tissue between entities.

Recursive — relations create relations.

TimeAxis of evolution

04Time

Directional ordering. The arrow matters.

Not recursive — the axis for recursion.

ChangeRules of motion

05Transition Logic

Rules of change — themselves subject to change.

Second-order recursive.

ConstraintLimits of motion

06Constraints

What cannot happen. Constitutive limits, not guardrails.

Recursive — constraints tighten and loosen.

Geometry of evolutionFrom whom, with what knowing, toward what end

07Observation

A model from somewhere, for someone, with limits.

Recursive — each observation refines the limits.

08Uncertainty

What the model does not know, represented structurally.

Recursive — uncertainty resolves and re-emerges.

09Purpose

Teleology. Distance between actual and intended.

Recursive — purpose itself evolves.

10Memory

Retained, queryable, accessible history.

Recursive — every transition accretes.

§ 3 Completeness assessment

Six leading definitions, evaluated against the same ten ingredients.

The field reliably covers Distinctions, Time, and Transition Logic. Constraints, Purpose, Memory, Uncertainty, and Relational Structure are absent or partial in every existing definition.

Ingredient	Craik1943 · Mental model	Ha / Schmidhuber2018 · V + M + C	LeCun2022 · JEPA	DreamZero2026 · World action model	Meta VLWM2025 · Vision-language	Consensus2025–26 · Represent + predict + act
01Distinctions	impl.Implicit — the model distinguishes aspects of reality	●VAE learns to distinguish features in latent space	●JEPA learns to separate relevant from irrelevant	●Visual scene decomposition	●Multimodal scene understanding	impl.Subsumed under "represent"
02Entities	impl.Implicit — external reality contains things	◐Latent codes, but no persistent identity across episodes	◐Representations without persistent named identity	◐Object reps, but identity is frame-level	◐Referenced in language, no persistent formal identity	impl.Subsumed under "represent"
03Relations	impl.Not formalized	○Latent space is flat; no relational structure	○Embedding space — flat, not relational	◐Spatial relations implicit in visual scene	◐Language captures some relational structure	impl.Subsumed under "represent"
04Time	●Future situations before they arise	●RNN models temporal sequence	●Hierarchical JEPA predicts across timescales	●Temporal prediction through video sequences	●Multi-step planning across temporal horizon	impl.Subsumed under "predict"
05Transition Logic	●Core — try out various alternatives	●M predicts state transitions in latent space	●Core state-transition prediction	●Physics learned from video — strong transition prediction	●Four-component prediction at each step	●Core of "predict future states"
06Constraints	○No concept of what is prohibited	○No concept of prohibited states or invariants	◐Cost Module encodes preferences, not constitutive limits	○Physics is statistical, not invariant	◐Task-specific penalties or guard-rails — acknowledged but unspecified	○
07Observation	◐Acknowledges limited senses in surrounding text	●V is explicitly a partial observer	●Explicitly partial; JEPA designed around partiality	●Camera-perspective partial observation	●Vision-language input is inherently partial	○Model assumed to observe correctly
08Uncertainty	○Model treated as veridical	◐MDN outputs mixture-density distributions	●Latent variable z represents what cannot be predicted from context	○Generates visual futures without confidence	○Not formally represented	○
09Purpose	◐Conclude which is the best — goal presupposed, not formalized	○Reward is external environment signal	◐Cost Module — designer-specified, not constitutive	○Intent arrives as flat imperative sentences	◐Goal description present; task-level, not constitutive	○"Enable action" — action toward what?
10Memory	○Present-tense; no accumulated history	◐RNN hidden state decays; not queryable or persistent	◐Short-Term Memory Module — working memory only	○No persistent history; each episode independent	○No history beyond current planning episode	○Prediction is forward-looking; history not required
Completeness	4/10	5/10	7/10	5/10	6/10	2/10

● Explicit◐ Partialimpl. Implicit○ Absent

§ 4 Three mechanisms of model creation

“Model” is not a synonym for “trained artifact.”

Models come into existence through three mechanisms. Each produces properties the others lack. A complete world model requires all three — the field has built one leg of a three-legged stool.

M1Episodic

Training

Discover statistical structure from data.

Expose a parameterized function to data, optimize against a loss function, update parameters. The model discovers structure from the statistical properties of the data.

Produces: Statistical capability — distributional patterns, correlations, stylistic conventions, factual associations, reasoning patterns present in the training data.
Cannot: Structure not present in the data. What is prohibited as distinct from what is unlikely. Persistent identity across episodes.
Analogy: Learning a language by immersion.

Ingredient coverage4.5 / 10

01 Distinctions
● Yes02 Entities
◐ Partial03 Relations
◐ Partial04 Time
● Yes05 Transition Logic
● Yes06 Constraints
○ No07 Observation
◐ Partial08 Uncertainty
○ No09 Purpose
○ No10 Memory
○ No

M2Architectural

Constitution

Specify the grammar directly.

Specify the primitives, invariants, rules of composition. The model's architecture is given based on domain expertise — declared, not discovered.

Produces: Structural guarantees — authority chains, constitutive constraints, epistemic status tracking, constitutive purpose. Structure that holds because it was specified to hold.
Cannot: Content. Constitution builds the container; it does not populate it.
Analogy: Writing the grammar book.

Ingredient coverage9.5 / 10

01 Distinctions
● Yes02 Entities
● Yes03 Relations
● Yes04 Time
● Yes05 Transition Logic
● Yes06 Constraints
● Yes07 Observation
● Yes08 Uncertainty
● Yes09 Purpose
● Yes10 Memory
◐ Partial

M3Continuous

Accretion

Fill through governed operational capture.

Every decision, every state transformation, every boundary crossing deposits another layer of organizational truth. The model gets richer through accumulation of governed records.

Produces: Organizational truth — the accumulated record of what actually happened, who decided, under what authority, with what evidence, against what constraints.
Cannot: Structure. Accretion fills the container but does not build it.
Analogy: Accumulating a library in that language.

Ingredient coverage8 / 10

01 Distinctions
◐ Partial02 Entities
● Yes03 Relations
● Yes04 Time
● Yes05 Transition Logic
◐ Partial06 Constraints
◐ Partial07 Observation
● Yes08 Uncertainty
● Yes09 Purpose
◐ Partial10 Memory
● Yes

—	Training	Constitution	Accretion
Timescale	Episodic (train, deploy)	Rare (architectural events)	Continuous (operational tempo)
Produces	Statistical capability	Structural guarantee	Operational content
Cannot produce	Structural guarantees	Operational content	Statistical capability
Evolves by	Retraining on new data	Amending the specification	Accumulating through use
Error mode	Learns the wrong patterns	Specifies the wrong structure	Captures garbage if ungoverned

§ 5 Implication

The gap is not in the definitions. It is in the mechanism.

The field has built one leg of a three-legged stool. Training has produced extraordinary prediction engines. The systematic underinvestment in constitution and accretion explains why those engines cannot govern action, track epistemic status, or accumulate organizational memory. These are not capability gaps that more training will close.

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