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The DAO automatically converts any HIVE sent to it into HBD. It's done instantly, not via the slow trickle that applies to the "ninjamine" fund. Same thing happens when the DAO is set as beneficiary and receives HP.

Nope, it has always been sending to the DAO, never has involved burning: https://peakd.com/hbd/@smooth/request-for-comments-hbd-stabilization-dhf-proposal

Maybe you are thinking of burnpost?