Asymptotic complexity of the static audit fold

Determine the asymptotic source of the superlinear running time of Tacet's static audit fold and derive an asymptotically efficient implementation whose complexity is characterized for large claim families.

Background

The runtime appendix measures the static checker on plans ranging up to 10,000 claims and observes that the fold grows somewhat faster than linearly. An earlier quadratic duplicate-label scan had already been replaced by a constant-time set check, but the remaining superlinear behavior was not explained. The authors explicitly identify naming this term as still open, making complexity characterization and optimization an unresolved implementation problem.

References

naming the fold's super-linear term is still open (an earlier $O(n2)$ duplicate-label scan is now an $O(1)$ set check, which shrank but did not remove it).

— Tacet: A Language and Type System for Automatic Statistical Validity Accounting  (2608.27451 - Abuah, 27 Aug 2026) in Appendix, Section “Checker Runtime”