Improvement by Inheritance: Measuring Recursive Self-Improvement in Coding Agents

Self-improving coding agents are usually judged by the best agent retained during search. But a lineage can get better without getting better at self-improvement: a good edit to the improver can be selected once and then inherited unchanged. We distinguish an improver's child quality, how good the task agents it writes are, from its successor quality, how good the improvers it writes are. A lineage comparison mostly measures inheritance when the improver rarely edits itself; we formalize this decomposition and introduce nested replay, which crosses candidate improvers on common starting states and scores the improvers they produce on one common evaluation bank. On the released Hyperagents history, the selected self-edit raises child quality from 0.48 to 0.86 on common states but does not detectably raise successor quality: the next generation's gain matches the gain in child quality almost exactly (0.29 against 0.30), because the edited improver almost never edits itself. The assay is sensitive: a modifier built to act on evidence about the improvement procedure yields a clear gain in successor quality under the same design. Controlled experiments trace the gain in child quality to evidence routing: the edit sends the improver to evaluation results it otherwise ignores, and helps only when those results carry information the task lacks. Claims of recursive self-improvement need measurement at the recursive order they claim.