Hm. Yet to be proven that any digital storage will last anywhere close to that long. At best it will be a continually active process of refreshing the archive and converting the data to whatever storage media and formats are currently in use.
That's not a problem. The problem is in the analog mediums (paper) that will always disintegrate over time. Digital media will not lose fidelity over time at all. In 10,000 years, as long as the backups were maintained, the data will be as good as the day it was made.
If the backups aren't maintained, the data will be instantly, totally, and irreversibly lost. The maintenance on paper involves not leaving it in the rain or setting it on fire; both failure modes shared with digital.
This is only partially true: with online storage, it's relatively easy to make bit-for-bit identical copies even if the physical storage medium changes over the years because there's always an overlap period when a technology falls out of favor.
Where it gets expensive is when you neglect to do that and then 50 years from now someone is pulling a Zip disk or LTO tape out of a box and wondering how to read it.
In contrast, analog formats will always lose quality as you copy it so you have a strong incentive to make copies which will last as long as possible. If you get the right material it might be transferable in the future with no work – e.g. high-quality photographic prints on archival-quality stock – or you might end up needing to build exotic equipment which can do things like optically scan records to reconstruct an audio waveform (http://irene.lbl.gov) or deal with media which has disintegrated (https://www.nedcc.org/audio-preservation/irene-blog/2014/08/...). One look through e.g. http://britishlibrary.typepad.co.uk/collectioncare/index.htm... should be enough to see limited a time period “no extra work” is valid for.
The common theme for both formats is that it's critical to maintain the ability to read and make copies. Once something falls out of common usage the cost to rebuild that capacity go up dramatically because you're no longer enjoying mainstream economies of scale and the work will increasingly require skilled technicians using bespoke tools.
This can be particularly bad with digital formats if the use of DRM means that few/no people are legally allowed to create tools during the period where many of the original creators are still available for consultation.
Paying the rent on a building takes extra work. Keeping the roof in good repair so it doesn't leak takes extra work. Maintaining an atmosphere of 14% oxygen takes extra work. Just because we call it maintaining existing stuff instead of making new stuff doesn't mean it's not needed work.
Digital storage probably won't last that long, but if you store it right and keep rotating media (possibly upgrading to better ones as they become available) then the data itself can last as long as someone is putting time into caring for it.
