Merging incomparable linearizations

The email addresses a correction concerning mathematical notations used within a specific context, clarifying that "$P_1 \le R_1$" should be the correct assumption rather than what was previously mentioned. Additionally, it notes a modification in the notation from "$M_{PI}$" to "$M$," explaining that the original "PI" in "$M_{PI}$" stood for "prefix-intersection." This change was made during the editing process to simplify or correct the notation used in the discussion.