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Where can I read about the testing that goes into these claims?
I'm far from an expert, but anything on standards JIS X6257 / ISO 18630 would probably be a good start. It's an open standard for 100+ year discs.
Otherwise probably best to look into accelerated aging studies. For technology that's less that 100 yrs old to claim 100 or 1000 is a bit uncertain but accelerated aging is probably the closest to a best guess. I recall skimming over a third party lab saying Verbatim gold foil archival DVDs were estimated to last 30-120 years depending on storage methods and luck, but never saved the link.