Really cool idea to make the jump an untrusted mechanic... I had a hard time at first for figuring it out but eventually I did complete it! :)
I think it would be even better if the jump(or not) mechanic aplied for when the player is standing still, because once you learn that you can trust jumping when you're not moving it's really easy to complete.
Overall I had a lot of fun, it's always nice to play some classic platformer game :)))
It could use some music and sfx tho...