Children expertly construct mental models under uncertainty despite limited world knowledge. Which computational principles make this possible? We study this question in an interactive physical Box Task in which participants infer a latent cause through interaction with a stochastic and partially observed environment. The Box Task was originally designed to study children's puzzle-solving qualitatively. We contribute a computational analysis of behavior that formalizes the cognitive process by which children generate new hypotheses and respond to environmental uncertainty as inference unfolds. Our modeling framework is based on Bayesian particle-based inference, which maintains a small set of working hypotheses and continually generates new ones. We give two complementary implementations of hypothesis representations within this framework: (1) as constraints on evidence, and (2) as executable programs evaluated against evidence. Using the constraint-based formulation, we show that the model needs to account both for subjective reliability of evidence and online hypothesis generation to explain key signatures of children's behavior. Using the programmatic formulation, we show that hypotheses may take the form of partial compositional rules to guide information gathering when evidence interpretation is hard. The programmatic hypotheses are implemented using LLM-based program synthesis, evaluated across three prompt variants and several LLM backends, demonstrating robustness of our approach. Together, these results extend current models of children's inference to account for subjective reliability of evidence and open-ended hypothesis spaces, and provide a computational analysis of the form generated hypotheses may take in practice.

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