What is the mechanism of aldol condensation between two diketo-compounds with sodium bicarbonate?


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> In particular, what is the mechanism of aldol condensation of dimethyl-1,3-acetonedicarboxylate and 2,3-butanedione with sodium bicarbonate?
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I'm trying to work out the mechanism of this aldol condensation using aqueous sodium bicarbonate as a base. I came up with this following mechanism:


[![My mechanism for the reaction](https://i.stack.imgur.com/mNwWu.jpg)](https://i.stack.imgur.com/mNwWu.jpg)


However, I showed this to a Ph.D. student and they said that because the solution is aqueous the bicarbonate would form carbonic acid, a very weak acid which would be unstable and decompose to $\ce{CO2}$ and $\ce{H2O}$. I know this reaction can occur with this base but now I don't know how the mechanism works if it isn't in the way outlined below. Can anyone help with this?


