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As the time horizons of sequential decision-making tasks grow, keeping full interaction histories in model context becomes increasingly costly. Recent work reduces context lengths by instead conditioning decision-making agents on recursively updated natural-language summaries, which are concise and interpretable. However, they underperform agents with access to the full context, suggesting that they fail to generate sufficient summaries. To address this we propose ABBEL, a recursive summarization framework that isolates and directly supervises each summary's information contents in the form of explicit natural-language belief states. First, we analyze the belief states generated by frontier models under ABBEL across five domains, and verify that performance is often degraded due to omitting or incorrectly updating information. We also discover settings where models use memory inefficiently by retaining extraneous information. We target these limitations by fine-tuning with two RL-based methods: belief grading, which reduces update errors by rewarding belief generations based on their information content, and peak belief penalties, which encourage compressing the beliefs with the greatest memory footprints. We demonstrate that these methods significantly reduce the performance gap with full context models, and enable ABBEL to outperform prior memory agent work by 40% while using 67% of the memory. Our code is available at https://github.com/jakob-bjorner/optimal-explorer-dev

Core systems like key-value stores have historically taken years to build, and are designed to be general so as to amortize cost across deployments, paying a significant performance cost. We argue that LLM-based coding agents now make a different approach tractable: Just-in-Time Systems, in which the entire system is synthesized from scratch, specialized to the environment, workload, and required system properties. We present a JIT system synthesis pipeline, Jitskit, and explore its effectiveness in synthesizing key-value stores from spec cards that span different YCSB workloads, deployment constraints (e.g., compute resources), and system properties (e.g., consistency and durability). Jitskit iteratively refines a system implementation to match the specification against an evolving evaluation test suite. The resulting synthesized systems are performant, beating comparable state-of-the-art systems on 18 of 18 specs tried, by up to 4.6x over the best off-the-shelf baseline on the most favorable spec. Naively running Claude Code either reward-hacks or underperforms Jitskit by up to 5.4x. We discuss the challenges we overcame in building Jitskit and our key takeaways.

AI agents increasingly excel at generating, testing, and refining code. However, they fall short on tasks requiring formal guarantees of full coverage that testing alone cannot provide. Distributed systems are a prime example: properties such as consistency between reads and writes must hold under every possible interleaving of events. Mechanized formal verification can guarantee such correctness, but typically demands months to years of expert effort. As evidence, even SOTA coding agents (Codex with GPT-5.4 and Claude Code with Opus 4.6) succeed on only 2/7 distributed key-value-store specifications. In this paper, we present the first effective approach to addressing this gap, Inductive Deductive Synthesis (IDS), which jointly and incrementally synthesizes implementation and proof, and learns from failed attempts to systematically try promising strategies. Built as an agentic LLM system, IDS achieves 7/7 in about 6.8 hours and $106 per spec on average, roughly 200x faster than expert effort and 17% cheaper than SOTA agents. IDS further incorporates performance feedback into the same loop, yielding implementations up to 3x faster than published verified systems.