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That will let you verify that your vote is counted, but is there any way to verify that additional votes are not manufactured?

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To start you'd want voters to register first I think, so you can't just invent people, at least not without being able to infiltrate the systems that manage birth certificates, tax records, and social-security ids.

That raises the question of how do you avoid double-voting or voting for people who didn't vote. I think there's technical solutions to both.

Even if there is registration, that only helps if I can verify that the entire chain only includes registered people. So how can I verify everyone who voted is registered, without also knowing which vote is from which person?

Maybe have a separate record for "this person voted" and another record for "1 vote for X", with encrypted references back and forth? Then you could at least verify that there are an equal number of both records, that all the identities are valid and only used up to once, and tabulate the final results. It would still be possible for someone who didn't vote to have a false vote logged, but that is a more narrow attack.

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