DATABASE-GROUNDED CLARIFICATION THROUGH ORDERED PROGRAM-WORLD EXPLORATION

Interactive Text-to-SQL systems must do more than generate executable queries: they must identify underspecified user intent, determine which information can be obtained from the database environment, and decide what to ask the user under a limited interaction budget. Existing tool-augmented agents largely leave these decisions to free-form reasoning, which can lead to redundant questions, low-value exploration, and unsupported assumptions that silently alter the resulting SQL. We introduce DB-COPE, an inference-time framework that represents uncertain intent as explicit SQL decisions and instantiates grounded alternatives as complete program worlds. Structural validation checks that a claimed interpretive difference changes the SQL; unresolved, result-changing choices are clarified and the answers are carried forward in a canonical state for initial and follow-up queries. On the 600-task BIRD-INTERACT Full set, DB-COPE raises DeepSeek v4-Flash Phase 1 success from 16.17% to 23.50% and end-to-end Phase 2 success from 7.67% to 13.17%. DB-COPE likewise improves both phases by nine percentage points with GPT-5.6 Terra. On PRACTIQ, it reaches 82.48% nine-way accuracy, showing that the same representation transfers to static user-request classification. This result suggests that explicit SQL-decision representations can support program-grounded clarification by distinguishing user-request status.