Replanning Precision for Pareto Identification with Accumulated Evidence

How should existing measurements guide the next experiment in Pareto set identification? We distinguish the remaining cost of completing a sufficient certificate from the information needed to exclude incorrect answers. A three-candidate construction reverses their preferred history allocation: concentration completes a rectangular certificate, while balanced history requires less additional Gaussian information cost. We explain this reversal through convexity and symmetry: averaging histories over an information-preserving symmetry cannot increase residual information cost, whereas alternative certificate routes can favor concentration. For fixed routes, we establish complementary bottlenecks and a suffix identity under which frozen progress scores tie across required actions. We implement certificate and information replanning with primal–dual allocation bounds and an anytime-valid Gaussian stopping rule. Across 1,068 synthetic trajectories, certificate replanning has lower observed mean cost on two targeted historical suites; an information planner's initial gain disappears on fresh seeds, and native PSIPS uses fewer capped measurements on cold-start suites. The results separate history value, certificate geometry, and sequential execution as distinct design problems.