[I have seen this topic being discussed on Reddit and I found it interesting enough to post the results here. So trust me on this one.]
There are two scenarios:
1. The means to read the data is magically preserved over the 10,000 years, so only the storage medium must last the duration.
2. The means to read must be preserved through conventional means alongside the data.
So what are the options? Let’s use our creativity with these answers.
Using Bytes laser-engraved in diamonds, sent out to space onto an almost everlasting, precisely calculated orbit around Earth, Moon, both or simply around the Sun itself. Or maybe send it to a big stable asteroid in the asteroid belt, that should also last quite some time yet.
The probability of a disastrous cosmic event is less than a fatal nuke war on Earth or bigger earthquakes or simple human stealing (don't store it at home).
The use of Sapphire disks with platinum coating. Though it may be over kill for a your mere 10,000 years
https://www.theverge.com/2012/7/13/3157081/andra-sapphire-disc-data-million-years
A cave wall seems like a pretty solid choice. As we know.
As a mental health therapist I have to say turn it from data into intergenerational trauma. It’s guaranteed to survive each generation, although creating a religion comes close, right? Or make cultural songs passed on verbally to carry information forward over thousands of years.
Gold plates like Voyager. Or perhaps DNA inside the population of a living organism, however, given enough time the useless genetic data you are passing on will be abandoned, the same way mitochondria abandoned the majority of their entire genome to specialize life inside animal cells.
A metal or stone plate fully embedded in glass. Digital? Not possible with any current tech.
I would use the most durable media ever used by humanity: the Clay tablet. Some of them have endured for 4200 years so far, which is how we know we shouldn't buy copper from Ea-nasir.
The Long Now Foundation did this with their Rosetta project: https://rosettaproject.org/ Etchings on a nickel plate.