If timed right, dismounting a horse while it is stepping up a block can launch the player to launch at least 20 blocks into the air. I was unable to catch a time where the launch was greater that 20 blocks, but dying to it is how I spotted it.
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Can confirm. Interestingly, while both the original report and the second method described in the comment give roughly the same vertical momentum, the version where you mount/dismount quickly seems to give much more horizontal momentum (or at least it did when I tested it). Also, I don’t think you need to be holding a spear for this method to work.
Can confirm, it also occurs if you quickly dismount after mounting a horse with a spear