ProofTrace examines how mathematical proofs are organized rather than relying only on the language used to present them. The preprint compares five groups containing 8,281 papers, including human work reworded by a model and proofs reconstructed by models. Dependency graphs distinguish these interventions, although differences between groups do not establish mathematical correctness or provide a conclusive origin judgment for an individual paper.
ProofTrace is a framework for studying the organization of mathematical proofs through the results they depend on. Its directed graphs connect theorems, lemmas, intermediate steps and external results. The extraction process uses a language model and retains supporting passages. From these graphs the researchers calculate 342 features, keeping measures of writing style in a separate analysis. The preprint compares 8,281 papers divided into five cohorts.[1]
The cohorts distinguish historical human work, disclosed artificial intelligence contributions, model-originated manuscripts, reconstructed proofs and reworded human papers. For controlled comparisons, seven hundred human papers supply problems and targets for proof reconstruction, while six hundred twenty-five texts receive wording changes alone. The authors find that reworded papers broadly keep the original proof organization, whereas model-reconstructed proofs have different structural patterns.[1]
Analyses include controls for subject area, manuscript length and graph size. Even so, cohort selection and different production procedures affect interpretation: the disclosure group is self-selected and historical papers come from another period. The measured property is proof presentation, with errors also possible in graph extraction. Group differences provide no conclusive judgment about an individual author’s use of a model or the correctness of a proof.[1]
