Ok, I’m with you. I didn’t realize before that + meant concatenation.
So you’re essentially relying on 3 steps which each individually don’t make the diagram worse, and composing them to show that moving a new higher-fee chunk to the front while leaving internal ordering the same, makes the overal thing not worse.
Those 3 steps are:
- If a \geq b, then a + c \geq b + c. That seems reasonable, though I do want to think through what happens when c gets chunked together with some suffix of a or b (but not both).
- Two chunks can be swapped if the second one has higher feerate than the (highest chunk feerate in) the first. That’s probably true under some conditions, but it’s not entirely clear to me what those conditions are. Does this also hold when both/either isn’t really a chunk (in the sense of being chunked togeter) but consists of multiple?
- Reordering and splitting a chunk is fine. If it’s really a chunk, then this is obviously the case - it’s just reordering transactions within a chunk which at worst has no effect on the diagram - but is it obvious here that c_{j+1} is actually a single chunk, when considered in the linearization presented there?
In short, I think we need some theorems that relate diagram quality with transformations/reorderings of the linearization, even when those modify chunk bounaries.