[jshprentz]

That X-Files episode may have been inspired by "Time Shards" [1] by Gregory Benford, a short story first published in 1979.

TLDR: Too late to be included in the bi-millenium vault, a Smithsonian researcher discovers an audio recording accidentally inscribed on a c. 1280 pot by a pointy tool cutting a decorative spiral. After listening to the banal conversation recorded on the pot, the researcher wonders about the contents of the vault to be opened in a thousand years: “What makes you think we’ve done any better?”

[1] https://www.lightspeedmagazine.com/fiction/time-shards/

[dcminter]

As so often, Daedalus (David E H Jones) got there first with one of his semi-humorous articles in New Scientist in 1969 - one of those collected in "The Inventions of Daedalus" in 1982.