Cluster mempool definitions & theory

The discussion revolves around the strategy of managing transaction chunks in blockchain technology, specifically concerning their size and order based on fee rates. It is debated whether it is fundamentally better to prioritize smaller transaction chunks over larger ones when they offer equal fee rates. While one implementation favors smaller sizes for such transactions to prevent merging, this preference is acknowledged as an arbitrary decision rather than one grounded in objective reasoning.

There is a proposition to maintain the current preorder on linearizations rather than altering it. This approach suggests that the definition of an "optimal linearization" should include a condition where no chunk can contain subsets with higher or equal fee rates. By doing so, the integrity of transaction prioritization based on fee rates is preserved without necessarily favoring smaller-sized chunks.

Furthermore, there's an introduction to the concept of "perfect linearization," which may be regarded as a more stringent criterion compared to the optimal one. The idea here is to create a hierarchy of properties that can be defined and proven incrementally, possibly providing a clearer framework for understanding and implementing transaction chunk management. This tiered approach allows for a distinction between perfect and optimal linearizations, offering different levels of adherence to fee rate-based prioritization.