One can prove selected data existed at certain point in tim…
One can prove selected data existed at certain point in time, if data's hash is saved into bitcoin's transaction and then stored locally with corresponding merkle tree path.
Existence can be proven offline even if all miners pruned that block long ago.
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So you can prove it, but your can’t access it online?
You can store the original data wherever you want. There are cheaper options that blockchain itself. Blockchain offers immutable timestamping. And the best part, even if blocks get pruned, you still have proof.
Check chapter 3 in WP
And chapter 7