The World Model Definition

Eighty years after Kenneth Craik proposed that the brain carries "small-scale models" of external reality, the term "world model" remains formally undefined. The AI research community uses it to describe everything from variational autoencoders to trillion-parameter architectures dreaming robotic futures, but no authoritative definition specifies what a world model must contain to be complete. The absence has consequences. Without a formal definition, the field cannot distinguish a world model from a prediction engine. It cannot assess completeness. It cannot identify what is missing from a given approach or determine whether two approaches are solving the same problem at different scales.

The result is a landscape of partial implementations, each called a "world model," each covering a different subset of the actual requirements, and none able to explain why its outputs cannot be governed, audited, or trusted in operational contexts. The founding-period research of GrytLabs Research Institute encountered this absence not as a theoretical curiosity but as an engineering constraint: the structural gap identified in TR-A-001 and the architectural necessity argued in TR-A-002 both appeal to a formal definition of what a world model must contain. That definition did not exist in the literature. This report supplies it.

This report makes three contributions. First, a formal definition: ten ingredients that any world model must satisfy, each justified by what becomes impossible without it. Second, a completeness assessment: six leading definitions evaluated against the ten-ingredient standard, establishing that all are incomplete in the same structural pattern. Third, a mechanism taxonomy: three complementary processes — Training, Constitution, and Accretion — by which model ingredients come into existence, establishing that the completeness gap in definitions traces to a mechanism gap in the field's practice.

The thesis would be weakened if: (1) a prior definition were identified that specifies the ten ingredients at comparable formality — meaning the originality claim (WMI-P03) is overstated; (2) an existing definition were shown to be complete against the ten-ingredient standard — meaning the completeness gap does not exist; or (3) training alone were demonstrated to produce constitutive constraints, carried purpose, or attributable memory — meaning the mechanism taxonomy is unnecessary.

The field has been building prediction engines and calling them world models. Prediction is three of ten ingredients.

A world model is the minimum representation that makes a world modelable. It requires ten ingredients: Distinctions (the capacity to differentiate), Entities (things that persist through change), Relations (connective structure between entities), Time (directional ordering), Transition Logic (rules of change, themselves subject to change), Constraints (constitutive limits on what can occur), Observation (structural acknowledgment of partiality), Uncertainty (structural representation of what is unknown), Purpose (the directional bias that makes action evaluable), and Memory (accumulated, accessible history). The compact formula organizes them: State (Distinctions + Entities + Relations) + Change (Transition Logic) + Constraint + Time. Recursion computes the change. Observation, Uncertainty, Purpose, and Memory define the geometry of evolution — from whose perspective the model operates, what it knows it does not know, what it is trying to achieve, and what it has learned from the past.

Six leading definitions are assessed against this standard. Craik (1943) scores 4/10 — the philosophical foundation, but a definition of prediction, not of a world model. Ha & Schmidhuber (2018) score 5/10 — the first computationally realized world model, strong on observation and temporal prediction, but the dream has no rules about what is permissible. LeCun (2022) scores 7/10 — the most complete existing definition, with explicit Memory, Uncertainty, and a Cost Module approaching Purpose, but Constraints remain soft (preferences, not invariants) and Purpose remains designer-injected. DreamZero (2026) scores 5/10 — impressive physical prediction from video, but no governance structure whatsoever. Meta FAIR VLWM (2026) scores 6/10 — notable for acknowledging the constraints gap explicitly ("task-specific penalties or guard-rails" as unspecified inputs) without being able to fill it. The consensus view scores 2/10 — represent, predict, act — Craik's 1943 definition with neural networks attached.

The pattern across all six: Transition Logic (prediction) is universally present. Time and Distinctions are universally present or implied. Constraints, Purpose, and Memory are universally absent or inadequate. The pattern is not random. It maps to a mechanism gap: the field recognizes only one way to build a model — Training — and Training discovers statistical structure from data. Constraints are not statistical regularities. Purpose is not a pattern in data. Memory is not compressed weights. The missing ingredients are missing because the mechanism that could produce them is not recognized.

Three mechanisms are required. Training discovers statistical structure from data — it reliably produces Distinctions, Time, and Transition Logic, partially produces Entities, Relations, and Observation, and cannot produce Constraints, Purpose, Uncertainty (in the epistemic-status sense), or Memory. Constitution specifies structural grammar directly from domain expertise — it produces nine of ten ingredients, including the four Training cannot, but cannot populate Memory with actual operational content. Accretion accumulates governed operational records continuously — it uniquely provides Memory and enriches every other ingredient through operational experience.

The three mechanisms are complementary, not competing. Training provides the intelligence layer. Constitution provides the governance layer. Accretion provides the memory layer. A complete world model requires all three. The field has invested in one. The completeness gap in definitions is a mechanism gap in practice, and the mechanism gap explains why capable systems cannot govern: they are built from one mechanism that cannot produce what governance requires.