Something I can say about the world doesn't completely determine everything else I can say about the same green strand, but something that exists in the world does completely determine what else exists along the same blue line.

That seems true. The core reductionist tenet seems to be that you don't need the thing that exists explained/observed on every level of abstraction, but rather that you could deduce everything else about the object given only the most fundamental description. This seems to imply that there is some element of direction even in the blue arrow, since one model follows from another.

It's not clear to me why it would be an error within reductionism to say that the higher levels of abstraction approximates the lower ones or something like that. Maybe I should read up on reductionism somewhere outside LW, can you recommend any specific articles that argues for directionless blue arrows?