How to pause the source task to not send output to downstream?

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I choose to update its partitions with a new rescale id when synchronization. By doing that, it will not send output outside since we will not update the child input gates during synchronization.

Therefore, when updating key mappings, I will not update the partition on the source task but just update its children's input gates. Then the source task will resume sending output immediately, not any other operation to resume it.