We study a self‑improving agent that can enlarge its computational repertoire without any reward, judge model, or answer key, yet still guarantee exact answers. The system consists of a frozen model that runs two nested loops over a compact, exact domain‑specific language (DSL). The inner loop only accepts an answer when two independently written expressions agree on every record, providing self‑consistency. The outer loop searches for missing capabilities in the DSL, writes a new operator for each gap, and admits it only if a second independent implementation produces the same result and the outcome respects a conservation law—no ground‑truth required. Empirically, the inner loop roughly triples the set of answerable questions, while the outer loop self‑extends on disjoint starting sets, inventing operators outside the initial closure; a control without induction answers none of the new questions. The admission rule rejects all 138 buggy operator variants under an independent reference, even those authored by a different model family, whereas naïve admit‑if‑it‑runs, self‑consistency, or compression signals would accept most of them. Unmodified, the same mechanism scales to two unrelated schemas—business ledger and clinical encounter—expanding their answerable sets by more than tenfold and nearly twentyfold. The loop also transfers across model families: with additional proposers the gate remains sound and each family self‑extends comparably, with induction yield reflecting each family’s DSL fluency.
Review