Right. I’ve added a paragraph to elaborate on why that is.

Chunks, as defined here, are sets; they don’t have an internal ordering. I’ve gone back and forth in my thinking whether sets or sequences are better. The advantage of sets is that at the chunking level, you don’t need to care about distinct intra-chunk linearization orderings. The disadvantage is that converting back from chunkings to linearizations isn’t as natural.

Let me think a bit more about that.

Done.

Fixed.

Agreed, done.

I’ve formalized this a bit more, selecting the ordering before the function definition.

Consider the following cluster:

```
graph BT
T0["B: 7"] --> T1;
T1["A: 1"];
T2["D: 5"] --> T3;
T3["C: 3"];
T4["E: 1"] --> T0;
T4 --> T2;
```

- The linearization [ACDBE] has chunking [ACDB,E]
- The linearization [ABCDE] has chunking [AB,CD,E]

As defined so far, both linearizations are equivalent (because their diagram coincides), and optimal. Yet still, chunk ACDB contains two disconnected components. The point of this theorem is showing that in an optimal linearization, chunks are still not necessarily connected, but this is only possible if the connected components all have the same feerate (4 in this example).

What I want to get to here, but haven’t really fleshed out, is a stronger notion of optimality than defined so far, which also requires all chunks to be connected - and that every graph has such a very-optimal linearization too.

Actually, now that you bring it up, I realize that’s not as strong as we’d want yet. Even with requiring connected chunks, it’s still possible that optimal chunkings contain chunks with equal-feerate subsets, so I guess very-optimality should instead be “optimal diagram, and chunks cannot contain topologically-valid strict subsets with equal feerate as the chunk itself” or so?