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I think you are probably right since there is only one mention of "reputation" in the Steem whitepaper https://steem.io/SteemWhitePaper.pdf and it is not about the reputation we are talking about. I suppose that SMT using sites could still look at reputation on Steem or elsewhere - if they can positively correlate two identities across the networks.

Also came across this post that explains the logarithmic calculation of reputation and that is stored on the blockchain: https://steemit.com/steemit/@digitalnotvir/how-reputation-scores-are-calculated-the-details-explained-with-simple-math

I take that to confirm what I said, that any external app could query your reputation if it can confirm your id - presumably via something you sign with one of your keys that would verify your id.

This brings up a further issue that needs clarification. Do sites that operate SMTs require their users to have a steem user id (that could be used to login to steemit, for example) - or not. I imagine that such a username/id would be required, but I haven't seen anything about mechanisms for perhaps autocreating the names for people who are members of your site, but not of steem/steemit.

Additionally, there is the question of whether posts to your site will be visible in Steemit or not - which is something else I haven't seen mentioned anywhere that I have looked yet.