Identifying Recursive Self-Improvement: Five Gates for Synthetic-Data Training

A score gain over a trained baseline does not by itself identify recursive self-improvement: the comparator may have degraded, received different exposure, or been evaluated through a defective or contaminated pipeline. We formalize this distinction as a claim-conditional identification contract: every claimed effect must name its estimand, the contrast that estimates it, the factors held fixed, and the integrity checks that make that contrast interpretable. The contract yields five necessary gates — untouched-base comparison, exposure matching, verifier validation, controller activation, and decontamination — whose relevance depends on the claim being made. We apply it to DataEvolve, a protocol-frozen, three-round generator-verifier-trainer study on a sealed 2,070-item logic benchmark. The full loop exceeds the strongest declared trained baseline by 10.26 percentage points, yet remains 4.12 points below its untouched starting model: the observed gain is real, but its self-improvement interpretation is not identified. A nominal 14.55-point verifier contrast is likewise confounded; under corrected and matched conditions, verified and unverified arms score 0.6680 and 0.6681. Rebuilding a positive control with instance-disjoint data reduces it from 0.6834 to 0.6678, near the 0.6671 base. An audit-derived mixture pattern is directionally consistent across exploratory seeds, but a pre-specified fresh-holdout replication gains only 0.7 points, below its two-point minimal effect. The five-gate contract turns performance differences into auditable scientific claims and provides a concrete reporting standard for recursive training.