Claim-Centered Research Records for AI-Assisted Theoretical Research

AI systems are beginning to contribute directly to theoretical research. Existing projects also release artifacts alongside their final papers, including reasoning walkthroughs, prompts, executable verifiers, and formal proof certificates. These releases improve provenance and reproducibility but are typically run-centered: their materials are organized around the interactions that produced them. As a result, future researchers and agents may struggle to identify routes that have already failed, and reviewers may struggle to locate the materials supporting a particular claim. We therefore present a claim-centered research record organized as a problem-specific AND/OR DAG. Each claim has a stable node that records its dependencies, evidence, review status, failed routes, and links to supporting materials. We study two complementary cases in quantum query complexity: small-alphabet $k$-Sum produced new upper and lower bounds, whereas minimal-alphabet Set Equality produced a weaker unconditional witness and four explicit obligations toward the intended bound. Maintaining the record used roughly 5\% of each project's total API-equivalent model cost, excluding human labor. Including shared evidence, the complete claim-centered packages were 89.8\% smaller for B4 and 4.8\% smaller for L2. In a one-shot audit of two frozen states, claim- and run-centered packages recovered the same target findings under each of three models, while the claim-centered packages used fewer requests and lower API-equivalent cost. This one-shot pilot therefore supports an end-to-end package-level efficiency result in the audited states.