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Are pool provided merkle branches trustable?

I'm a beginner is this field. Can someone explain to me how mining pool provided merkle branches are valid?Normally, when we make the root, it starts from top to bottom, a single change in order can lead to a different hash.

But in pools miner get merkle branches, with coinbasetx left for the miner to tweak.Is this process correct?Usually coinbasetx should be calculated first, shouldn't this lead to different root, or may be I'm wrong, can someone explain?


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