If tomatoes are a fruit, is ketchup a jam?

If tomatoes are a fruit, is ketchup a jam? Botanically, a tomato is a fruit. Jam is fruit cooked down with sugar, and ketchup is tomatoes cooked down with sugar and vinegar. So the logic holds up. But in 1893 the US Supreme Court ruled tomatoes are vegetables for tax purposes, because that's how people eat them. Is ketchup a condiment or a jam?

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