I send two transactions to the same recipient. The two sets of mixins used to generate the transactions would each include my public address. Is the recipient then able to reasonably infer that my address is that of the true sender?

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Your public address will never appear on the blockchain. What you're spending is amounts sent to one-time destinations so they're unlinked. Not only that, but each one-time addres will be "mixed" with a few others. With this, there's no way to link the two payments together. To the recipient, they will seem unrelated unless you tell him yourself they're coming from you.

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