When will the U.S. Supreme Court stop having a conservative majority?

Conservatives currently have a 6-3 majority. A majority is defined as a ratio of at least 5-4 conservative-liberal justices on the bench (or the minimum majority ratio if the total number of justices changes). If the number of justice stays the same (9), conservatives would need to have 4 or less justices to lose their majority. The conservative/liberal distinction is normally well established. In doubt, conservatives are those that are nominated by a Republican administration; liberals by a Democratic administration. That is, absent unequivocal public recognition of a justice as conservative or liberal, its appointment by a conservative or liberal administration will be treated as dispositive. Let us fix the meaning of ‘conservative’ to refer to right-of-center justices while they serve their appointment. Thus, if the cultural meaning of ‘conservative’ changes, the terms of the question can be revised to stay true to its intended meaning (i.e. when will SCOTUS lose its right-wing majority?). It doesn’t matter if the GOP/Democratic party valence changes, the relevant distinction is conservative (right) vs. liberal (left) as they have been understood in the US throughout much of the 20th century and all of the 21st century so far. If a justice is appointed by an Independent president, they do not count toward the majority unless they identify as conservative or are clearly considered as conservative by legal experts. So-called 'swing' justices (e.g. Kennedy; sometimes, Roberts) inherit the affiliation of their appointing administration. This question resolves as soon as the majority changes (when conservatives no longer have a majority). If the court ceases to exist as a recognizable institution (under this or a different name but performing the same function in the legal system) before the majority changes, this question resolves to 'After 2070 (or never)'. For any other option to resolve YES, the court has to exist and its majority has to be non-conservative. Suppose the United States or the court ceases to exist in their current recognizable form. In that case, I expect this fact to be both widely recognized and sufficient to meet the condition for resolving the last option. I will have retired long before this market can resolve. I have tried to make the resolution as unambiguous as possible so that any moderator can do it. Please suggest any amendments or clarifications that could help.