First-order concept synthesis asks a system to infer one formula that classifies labeled objects consistently across several finite relational structures. Every candidate can be evaluated exactly, but quantified first-order formulas form a vast search space, and LLM outputs are often semantically promising without being fully correct. We introduce Hypothesis Frontier, a verifier-guided neurosymbolic framework that evaluates each LLM formula on every training object, retains the strongest verified hypothesis across rounds, and uses its remaining errors to guide subsequent generation. Symbolic processing repairs invalid formulas while remaining anchored to the LLM-generated hypothesis, and simplifies train-valid formulas without changing any training prediction. Under matched models, problem sets, and LLM-round budgets, Hypothesis Frontier solves substantially more problems than repeated original-prompt generation. After the final formulas are selected, exact simplification shortens many train-valid formulas while preserving every training prediction. Exact symbolic reasoning therefore helps both to solve more induction problems and to compress many of the resulting formulas.
Agent skills are portable packages of instructions and resources an agent consults at deployment. Self-evolving them fails in two ways today. First, skills evolved from scratch underperform human-curated ones and, on a weak model, using no skill at all. Second, an evolution-time pass records one lucky trajectory that a fresh stochastic agent often fails to reproduce at deployment. We present reSolve, a per-task, oracle-in-the-loop framework built on three components. It decouples interactive solving from a self-contained deliverable that is independently re-executed in a fresh container, a protocol we call solve-and-reproduce. It enhances the sparse reward signal with a surrogate verifier that cannot access hidden tests or reference answers. It then runs verifier-guided beam search over a solution-construction graph. Within a fixed harness, a cheap model self-evolves skills that reach $74.9\%$ mean-of-3, $+14.8$ points over the $60.1\%$ human-curated baseline, exceeding the strongest official curated-skill result ($67.3\%$, GPT-5.5/OpenHands). We also report observed failure cases and domain-level results, including performance on the 14 Natural Science tasks, to clarify when the approach does and does not help.