World Models for Active Measurement: Revealing Static Hidden Worlds and Planning What to Measure Next

World models support planning by predicting how candidate actions affect future states and observations. In active measurement, the hidden physical state is effectively static on the decision timescale; actions instead reveal evidence that updates the agent's belief. We study this setting in the Earth's subsurface, where indirect surface surveys must be combined with sparse, costly drillholes. Our subsurface world model reconstructs three-dimensional mineral composition, porosity, and copper from heterogeneous exploration histories, then uses simulated measurement outcomes to learn which drillhole to acquire next. Across 400 synthetic diagnostic worlds, Cu-mass intersection-over-union (IoU) increases from 0.071 without drilling to 0.308 after 20 holes; shuffling measured values among fixed drill locations reduces it to 0.028, showing that the reader uses measurement content. With the reader frozen, a five-member action-ranking ensemble improves five-hole reconstruction on 1,536 held-out worlds. Its mean Cu-mass IoU gain on a common region outside all policies' drilling neighborhoods is 0.0564, compared with 0.0464 for predicted-copper targeting and 0.0276 for random selection. The advantage over all four baselines survives multiplicity correction and is corroborated on a region fixed before drilling. Benefits are strongest for the copper-mass objective used to train the ranker. These results demonstrate a route from hidden-world inference to learned sequential measurement and motivate transfer to field settings as the next step.