I was involved in one such pair:

- Van den Berg, Garner, *Types are weak $\omega$-groupoids*, https://arxiv.org/abs/0812.0298

- Lumsdaine, *Weak $\omega$-categories from intensional type theory*, https://arxiv.org/abs/0812.0409

(different calendar dates in UTC, but within 12 hours of each other, and the same day in the time zone where the latter was submitted)

These have the same main result: constructing a weak $\omega$-category structure on the terms of a type and its iterated identity types in Martin-Löf type theory.

As in several other answers, the timing is not a coincidence: we’d become aware of the overlapping result while we were both writing up the papers, so we acknowledged each other’s work and co-ordinated the posting.