Effect of fine-grained formalization on mathematical drafting

Determine whether working with machine-checked mathematical components at a fine level of granularity changes the drafting of statistical and mathematical arguments by enabling verified assembly, immediate detection of incorrect steps, and faster exploration.

Background

The paper argues that proof assistants require every hypothesis and proof step to be made explicit, while tactics and formal libraries provide reusable verified components. In discussing this potential benefit, the authors move beyond observations from the case studies and state a conjecture about how such a workflow may affect the process of drafting arguments.

The claim remains unresolved in the paper: no empirical comparison of drafting speed, error rates, or exploratory productivity is presented. It is included because the authors explicitly label the proposed effect a conjecture.

References

We conjecture that working at this granularity changes drafting itself: arguments are assembled from verified components, a wrong turn is detected at the step where it occurs, and exploration accelerates because the environment never has to be re-audited by hand.

— Statistical Theory in the Age of Machine-Assisted Mathematics: Rethinking How Theory Is Made and Taught  (2609.04481 - Coretto, 3 Sep 2026) in Section 2, “Proof Assistants for the Theoretical Statistician”