Certified Against Which Oracle? Execution Labels Set the Reported Risk of Conformal Abstention for Text-to-SQL

Abstract

A conformal abstention certificate for text-to-SQL is only as truthful as the correctness labels it is calibrated on. The uncertainty pipelines that read confidence off execution consistency take those labels from the single database a benchmark ships, an oracle known to be lenient. We run a preregistered intervention on Spider-Realistic, swapping that database for the benchmark's distilled multi-instance test suite. Across four SQL-specialist checkpoints and two split schemes, the swap raises the certificate's held-out risk 2.73 to 10.23 points above the risk its own labels report. Neither oracle reports the risk experts assign. Under blinded labels from two SQL experts, a certificate calibrated at a nominal 0.10 carries 20.0 and 17.2 points of risk on two checkpoints. The stricter oracle errs in both directions: most of the answers it rejects are not judged wrong, and some of those it accepts are. An AI-assigned census of what it rejects finds a semantic error in a quarter to a third of them, depending on the population. It attributes most of the rest to underspecified questions, synthetic instances or suspected reference-query defects, a flag supported by a preregistered blinded expert audit. The oracle also decides how a confidence score is judged. Every execution-consistency score looks better under the labels of the oracle that built its clusters, in 16 of 16 combinations. Under expert labels, building such a score on suite clusters instead of shipped-database clusters raises its area under the ROC curve (AUROC) by 6.96 points on one checkpoint and 1.53 on the other. On the second, the expert interval excludes the 8.3 points the suite labels report. A certificate should be reported with both oracles, and an oracle-relative difference read as semantic risk only after the benchmark is audited. A consistency score should be evaluated under an oracle that did not build it.