A Claim-Centered Publication Framework for Efficient Auditing of AI-Assisted Theoretical Research

AI systems are beginning to contribute directly to theoretical research and have already produced exciting mathematical results. As these systems generate new mathematical results at an increasing pace, a growing challenge is how to review these results efficiently. Existing projects release supporting artifacts organized around research runs rather than individual claims, which can make it difficult for reviewers to locate and assess the evidence supporting individual claims. We therefore propose a claim-centered publication framework designed to improve audit efficiency in AI-assisted theoretical research. Under this framework, a problem-specific AND/OR proof DAG serves as a research record maintained throughout the project and shared alongside the final paper. Each claim is represented by a node that records its dependencies, evidence, and review status and links directly to its supporting materials. Failed claims and proof routes are explicitly retained rather than discarded. We study two complementary cases in quantum query complexity and find that, in each, maintaining this record accounted for roughly 5% of the project’s total API-equivalent model cost. In our preliminary audit, the research-record condition used 20.9% fewer total tokens on average than the run-centered condition. The positive case, small-alphabet $k$-Sum, yielded an $\Omega (\sqrt{N}{q}^{1/6})$ lower bound for $2$-Sum over odd cyclic alphabets of size $5\le q\le 2N-3$, reducing the alphabet condition required by the previously used large-alphabet construction from $q\ge N^2$ to $q=\Theta (N)$. The negative case, minimal-alphabet Set Equality, did not produce the desired explicit optimal-order adversary witness, but yielded an $\Omega (n^{1/6})$ witness and reduced the remaining explicit $\Omega (n^{1/3})$ construction to four unresolved proof obligations, conditional on a separately recorded supporting layer. Together, the two cases illustrate how the proposed framework can support efficient claim-level auditing through a research record that preserves intermediate results, failed routes, and unresolved questions for future research.