Toward verifiable causal world models: discovering, validating, and intervening on governing laws from data

A model of a system earns the name world model only if it can be trusted: its laws must be the true governing laws, not curves that happen to fit the data, and its predictions must hold where the data does not reach. We build interpretable world models from data — closed-form governing laws and dynamics — and make trust the organizing principle rather than an afterthought. The system, SparkOrigin, discovers a law and then accepts it only if it stays numerically equivalent to the data-generating process both inside the observed range and beyond it. On the Feynman equations, this extrapolation-equivalence test overturns 3 of the 22 apparent recoveries that a goodness-of-fit criterion accepts. The validated laws are the world model's content: across astronomy, biology, linguistics, economics, and ecology, SparkOrigin recovers known laws that survive held-out, noise, and cross-magnitude tests, reconstructing the outer planets' periods from the five innermost planets alone to within 0.1%. The world model also acts. On a synthetic dynamical system, where the counterfactual is known exactly, SparkOrigin recovers the governing equations and predicts the effect of an intervention to within numerical error — a validated causal prediction. On a real predator–prey record it recovers the dominant dynamics, predicts a held-out cycle better than a persistence baseline, and identifies the correct causal directions; absent a real counterfactual we report direction, not a validated magnitude, and we are explicit that this is a step toward causal world models rather than one achieved on real data. SparkOrigin runs fully offline and deterministically, reporting a standard error and significance for every coefficient; under a single shared ruler it comes within one problem of an open-source state-of-the-art system on recovery rate (19 of 45 versus PySR's 20). The bottleneck in machine discovery is not fit but trust; we give a cheap, general way to measure it and a world model built around it. Scope. The causal/intervention result is validated only on a synthetic system with a known counterfactual; on real data we report predictive accuracy and correct causal direction, not a validated causal magnitude. The recovery rate — 19 of 45 on the cached Feynman development set, falling to about 16% on a never-cached held-out set — is below specialised symbolic regressors such as AI-Feynman, and we report both figures; the contribution is the trust / extrapolation-equivalence layer, not raw recovery rate. We do not claim a validated causal world model on real data. Versions. This version revises earlier versions of this record, whose framing over-stated some claims; the scoping is now built into the paper itself. Earlier versions remain in the version history. A separate methodological study, "Ranking Is Not Certification" (DOI 10.5281/zenodo.20653570), examines the limits of trust / uncertainty signals as cross-problem acceptance gates.