Eric Rescorla @rtfm.com · Dec 15

Finally, when you go to the Web server, it proves that it's certificate matches the summary. What this means technically is that it gives you a Merkle inclusion proof that goes back to the root.

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Eric Rescorla · Dec 15

The post has more detail, but the idea behind the proof is to show that there is a path from your certificate back to the root of the true, thus demonstrating that the tree was computed over your certificate.