I've checked that this concept is a few years old and it seems interesting. In a quick search, I couldn't find any information about the use of this service. Do you know if this service has been adopted, or if there are any sources about this?
this service has been adopted,
What do you mean by that? You use it to record your documents and done. What other better proof of existence you know that is better than the Bitcoin blockchain?
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I'd be interested to know if it's possible to find out the number of records. The documents are not stored on the blockchain, correct?
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No, on the blockchain you only store a bunch of text data (OP_RETURN) that prove the existence of a document (wherever is stored) in a certain point in time.
You do not need to store the document on the blockchain, that's insane.
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They use a unique header DOCPROOF, which you can look for on chain
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