LLM-based scientific exploration agents need feedback signals that decide which experimental outcomes should guide future search. Recent systems use Bayesian surprise, rewarding results that change an LLM’s belief. This can create a noisy-TV failure mode: unstable artifacts, leakage, proxy effects, or gaps in the model’s prior may appear more valuable than reliable mechanisms. We introduce Reducible Information Gain (ReIG), a validation-aware discovery method. ReIG keeps LLMs for hypothesis proposal and interpretation, and uses evidence that remains stable under resampling and null calibration as the search feedback. ReIG then reports final candidates along separate axes of reliability, novelty, and non-triviality. Across Rep-60, Stress-72, and faceted report evaluations, ReIG consistently improves discovery quality under matched search policies. Under MCTS, ReIG-MCTS improves ValidDisc@10 from 0.57 to 1.55 over Surprise-MCTS, raises reward AUROC from 0.44 to 0.83, and reduces false flags on no-signal tasks from 3.8 to 0.38 at budget 20. Ablations, same-candidate reranking, and the semantic audit show that the gains come from guiding exploration with validated, reusable evidence and keeping reliability, novelty, and non-triviality as distinct criteria.