Consulting the registry…
Every seal enters an append-only registry. Here you can check two things yourself, without trusting anything we say: that a specific seal is inside, and that we haven't rewritten anything we had already published.
Three values that summarise the whole registry: how many seals it holds, the fingerprint you get by combining all of them, and when we signed it. If we changed a single old seal tomorrow, this fingerprint could not come out the same.
The current head has just been saved in your browser. Come back another day and this check will run against it on its own.
All three verdicts are computed in your browser: you are not trusting the server to say «valid», you are recomputing the hashes yourself. Asking for the proofs does need a connection. What it does not need is trusting whoever sends them.
Proves that a seal is in the published tree. The root is recomputed from its leaf using a path of a few hashes; if the result matches the signed root, the seal was there. It reveals nothing about the content: the leaf only binds the commitment to a time.
Proves that today's tree contains yesterday's, with no rewrites or deletions. It only proves anything if the old head is one you hold yourself: if the registry supplies it, a registry that had rewritten its history would send a matching fabrication and the check would come out green while proving nothing. That's why your browser stores the head from each visit and compares against your own.
The tree is not something we invented: it is the same structure, RFC 6962, used to watch that nobody issues HTTPS certificates in secret. That matters because the proofs you see here are of a kind already audited worldwide, not a homemade format only we know how to check.
Heads are signed with our key, but they are not yet anchored outside the system. Until they are, whoever holds that private key could rewrite history and sign it again; the consistency proof only protects you if you archived an earlier head. External anchoring with a qualified timestamp is the missing piece.