incorrect. outputs and fees cannot exceed inputs. they dont need to be the same. fees are suggested by the tx maker, but its up to the block producer to accept all available fees offered or burn some.

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Your statement does not invalidate mine. The fee of a transaction is always the remainder of all inputs - all outputs. Therefore the sum of all outputs and the fee is always equal to the sum of the inputs.

A miner choosing to claim less reward than permitted when they mine a block is irrelevant to the point I'm making here.

It's a nice fun factoid, but doesn't make my statement incorrect.