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[danielW]

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[amaclin1]

I.e. If I wanted to re-implement this myself what would I need to do?

I think you should hire Peter Todd or ask him what to do.  

but still dont know how open timestamps actually works.

Hmmmm...
Have a look to https://app.originstamp.org/home
Let us call it "close timestamps" contrary to "open timestamps"
I think it is not very hard to compare these two projects and understand the technique.
If no, you must give up and switch to something else.

[haltingprobability]

I'm guessing that they create an unspendable output with an OP_RETURN which allows you to embed arbitrary data in a transaction. So, they can aggregate a bunch of individual hashes into a single hash, then submit a Bitcoin transaction to an unspendable output with OP_RETURN that contains the literal bytes of the aggregated hash. So, for the cost of about 70-80 bytes or so (assuming compressed signatures), you can embed an unbounded number of hashes into a Bitcoin block, thus timestamping all of those hashes with that block.