The core of the issue seems to be the desire to compare two different sequences of transactions, identified as $\epsilon_n + \delta_j$ and $\gamma_j + \zeta_j$, which consist of the same transactions but are ordered differently. This comparison is not straightforward due to the potential for the sets of transactions to have arbitrary groupings.

To address this challenge, the author proposes a mathematical equation, $\epsilon_n + \delta_j \ge \gamma_j + \zeta_j$, as a way to formalize the comparison between the two orderings. The goal is to demonstrate that rearranging the transactions in certain ways does not degrade the overall ordering, with a focus on achieving a greater or equal value through these rearrangements. To simplify the process, the strategy includes setting $j=n$ to eliminate $\zeta_j$ from the equation, thus simplifying the comparison.

The approach involves several steps, beginning with the base case where $j=0$ and both $\delta_0$ and $\gamma_0$ are empty sets, making $\epsilon_n = \zeta_0$ by construction. The proceeding steps involve inductive reasoning, showing how adding a new transaction $d_{j+1}$ to the sequence can maintain or improve the comparison value. These steps are meticulously outlined using algebraic expressions to detail the process of moving transactions around without making the overall set worse off.

Each step in the process is aimed at demonstrating the feasibility of reordering chunks of transactions in a way that either maintains or improves their original ordering, based on certain assumptions about the transactions themselves (e.g., feerate considerations). Although the author acknowledges the complexity of formalizing these steps fully, they suggest that the underlying logic appears sound.

The discussion encapsulates a technical exploration into optimizing transaction orderings, leveraging mathematical formulations to argue the viability of specific rearrangements. Despite the admitted challenges in fully formalizing this approach, the email reflects a substantive attempt to tackle a nuanced problem within the realm of diagram comparison, underscoring the intricate balance between theoretical mathematics and practical application in optimizing transaction sequences.