I assume you are defining it on a graph so that you can have a chunking across multiple clusters, but
it seems to me that this definition would only require that the topology is valid at the chunk borders and would not require the transactions to be topological within the chunks. I think it would be correct if you said “every prefix of the chunking is topological” instead of “every prefix of chunks is topological”.

Would it perhaps be sufficient that a feerate diagram has exactly one “convex hull” for a geometric proof? E.g. if we draw all transactions separately in the feerate diagram instead of their chunks, could we use the approach you use in the gathering theorem to show that all possible subgroupings will always be below the convex hull?

Should this perhaps be restricted to topologically valid reorderings?

This should be “in chunk j of L”.

Maybe “all remaining transactions of Safter the first j chunks of L” would be clearer.

“choose an arbitrary but consistent way/approach/method/criteria/something to order them”?

Linebreak missing before the Proof.

I find that phrasing a bit confusing. What do you mean with “have connected components whose feerate is all the same”? I assume you are referring to the optimal linearization consisting only of chunks that cannot be split further by reordering, i.e. that any valid reordering would not lead to a different chunking, but the “have connected components whose feerate is all the same” makes me think that you are postulating that there are two chunks with the same feerate.