Cluster mempool definitions & theory

This theorem facilitates the movement of a specific segment or "chunk" of transactions denoted as $p$ to the forefront of the optimal transaction list, $L_{opt}$. After moving this chunk to the beginning, it's essential to rearrange the transactions within this segment to mirror their original sequence in the list $L$. This step is permissible and vital as the transactions within the chunk inherently form a sequential block, allowing for such reordering without violating any predefined constraints or rules governing transaction sequencing. This approach contributes significantly to optimizing the overall transaction processing strategy by leveraging the inherent order and structure within the chunk, thus enhancing efficiency and effectiveness in achieving the desired transactional arrangement.