SHELDON: Reasoning through Dual Search over Hypotheses and Observation Spaces

Test-time scaling has enabled large language models to solve increasingly complex reasoning, discovery, and optimization tasks, but existing approaches often suffer from fixed search strategies, or hypothesis-centric reasoning that under-explores informative evidence. Inspired by the hypothetico-deductive method (Hempel, 1945) and dual-space models of scientific discovery, we introduce SHELDON, a scientific reasoning harness that jointly models hypothesis and observation spaces. By treating observations as first-class objects, SHELDON can identify gaps in its current understanding, uncover new hypotheses, and design investigations that better distinguish among alternatives. Across diagnosis, abstract reasoning, and optimization benchmarks, SHELDON outperforms prior state-of-the-art methods by upto 26.7 points. Moreover, on system root cause analysis tasks, SHELDON discovers 29.8% points more ground-truth causes and investigates 34.4% points more discovered causes than other baselines, demonstrating that joint hypothesis-observation search leads to broader and more effective scientific reasoning at test time.