Why Does the Future Branch? Identifiable Closure Tests for Stochastic Physical World Models

Many high-stakes decisions depend on forecasts made before outcomes are known. In this future prediction setting, the central challenge is that public evidence evolves over time, while the main supervision signal arrives only after resolution: the realized outcome mainly assesses final correctness, offering only coarse guidance on what to track, what to verify, and which judgments to leave uncertain along the way. Our key observation is that revisiting the same unresolved question over time creates informative temporal contrasts across evolving evidence and repeated forecasts, exposing what earlier attempts missed before resolution and yielding a diagnostic signal we call the pre-resolution signal. We instantiate this idea in Milkyway, a future prediction agent with a persistent future prediction harness, an editable external state that stores reusable procedural guidance across revisits to the same unresolved question. As the same unresolved question is revisited, Milkyway extracts pre-resolution signals from evolving evidence and repeated forecasts, uses them to update the harness, and improves later forecasts on that question before resolution. After resolution, the realized outcome serves as a post-resolution check of provisional updates. On the FutureX and FutureWorld benchmarks, Milkyway achieves strong performance against competitive baselines, and a mechanism study suggests that the gains stem from harness evolution driven by pre-resolution signals rather than repeated prediction alone.

A common assumption holds that enough observational and interventional data, given to a strong enough predictor, suffices. We report a failure mode that contradicts it. Across hundreds of structural causal models, on identified quantities a strong predictor and a Bayesian baseline both succeed, but on unidentified quantities (the couplings between counterfactual worlds) the predictor collapses to a point, on 28% of models to one no valid model can produce, while the truth is an admissible interval more data never narrows. The gap is structural: prediction cannot represent uncertainty over counterfactual couplings. We cast a world model as a single positive semidefinite coupling kernel K(T,T') over admissible worlds, whose diagonal is the ordinary posterior (what a predictor recovers) and whose off-diagonal is the cross-world coupling it cannot, which every counterfactual reads. The paper is the theory of that off-diagonal. It is real: two states with identical posteriors differ on a cross-world query, and the off-diagonal is the coupling that fixes counterfactuals. It can be bounded: positive semidefiniteness is partial-identifying information the marginals lack, and enforcing it bounds counterfactuals in polynomial time where the exact response-type program is intractable. Logical structure sharpens it: ontology axioms tighten the bound by up to a third, propagating to couplings they never touch. It can be acquired: targeted scars, constraints learned from encountered infeasibilities, close the gap several times faster than untargeted ones. Its full reconstruction is approximate counting of the admissible worlds, tractable below the Sly-Sun threshold and inapproximable above; we do not claim to beat the worst case.

JEPA world models commonly predict the next latent state with one regressor. Under stochastic transitions, squared and cosine regression return the conditional mean and its normalized direction, respectively: a single compromise that may match no valid successor. MoP-JEPA instead uses $K$ hard-assigned heads and a context-only router to produce a finite candidate set in one pass. On held-out OGBench transitions, graph search with single-output predictors succeeds on $0.02$--$0.09$ of queries, whereas MoP-JEPA reaches $0.85$. To distinguish useful successors from indiscriminate coverage, we also measure verified-route success (\emph{realroute}), which checks after graph construction whether the proposal contains a path of real transitions. MoP-JEPA leads this same-protocol metric on all three mazes; an MDN attains high raw coverage but predicts many nonexistent edges.