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This long-term data storage will last 14 billion years
(www.theregister.com)
This is a most excellent place for technology news and articles.
Beyond that, the sun has about 5 billion years before we might not be able to starlift it back to a "younger" state, so The Earth and Venus may not exist at all if we don't get our asses in gear for sustainable intragalactic life in the next century or so.
I am failing to connect the two time scales you mention.
The storage device can't outlast the Sun.
there is some chance that earth may be ejected from the orbit into the space when the time comes, in which case this device could theoretically survive, but its users definitely won't.