Beyond Action Entropy: Quotient-Space Exploration for Biological Hypotheses in Genome-Scale Metabolic Model Repair

Agentic biological discovery requires exploring alternative scientific hypotheses under indirect functional feedback. We study genome-scale metabolic model (GEM) repair, where multiple reaction edits explain the same phenotypes and apparently distinct edits can implement the same biological mechanism. This many-to-one structure makes output-space diversity an unreliable proxy for scientific-hypothesis diversity. We introduce QuotientPO, which collapses redundant repair realizations into canonical repair cores and optimizes exploration directly over the resulting quotient space. To make quotient exploration informative under finite rollouts, we derive a kernelized R\'enyi estimator that resolves graded crowding among distinct repair cores beyond coarse exact-match counts. On 2,212 held-out GEMs, QuotientPO improves Success@32 from 17.93\% to 20.10\% (+12.1\% relative) while consistently increasing distinct successful-core discovery under the same sampling budget. QuotientPO provides a specialized exploration component for agentic biological discovery, generating diverse, verifier-validated hypotheses.