Time-travel explained: It's a Time Bubble, not multiple timelines

There is no possible way to explain the time travel logic in this show if you stick to the most common fictional time travel trope: multiple timelines. There just is no way to reconcile what was the original timeline, remember the first time travel we saw, the ML was the one who saved himself and then he got lost in time, and we learned later that he started visiting the FL in-between, YET the characters also said they had 1st and new memories.

The only way to reconcile it are by the following:

• Option 1: Real-world mathematics. Everything that should happen already happened. However, it can not explain the new memories and the final time travel.
• Option 2: The Bubble theory. Details below.

In the Bubble theory, the idea is that the time period between two time travel points (origin and destination) are in constant flux, or is fluid, until the very issue that started the loop is resolved. Thus, from destination time (night of high treason) to 2020 (or was it 2021?), that entire period is in a Time Bubble. All possible cause and effect are happening simultaneously.

• E01: ML saved himself. But this version did not show himself to FL's past, other than to give her the flowers and broke-up with her (in what we know as the 'present')
• Second time-travel in the show: He practically repeated everything. HOWEVER, this time when he was lost in time, he started to show up in FL's past and even gave her tips.
• Third time-travel: His plan was a success.

From the Villain's perspective:

• His first and only time travel was when he got himself killed by his past self. This did not happen in the ML's first attempt (reference: E01).
• Villain 2.0 is now equipped with extra knowledge and did not repeat the mistake of Villain 1.0 (i.e. he did not travel back to the past; he knew it's fruitless, he knew his past self won't listen).

When the loop was finally resolved—the flute not getting halved—the Time Bubble started to collapse. The only ones who were protected from the changes were the ML, his bodyguard, and the FL, because they were "in the world between worlds" (that's what the trope is called). When the time bubble finally collapsed, only three people retained their memories while the rest of reality reformed based on what was more balanced and wouldn't repeat the loop.

This is why there was no grandfather paradox. Reality adjusted that the traitors died, how they died is of no consequence, reality simply accepted it. From that point (night of high treason) to the 'present', it finally settled into a single balanced "history".

The end.

There's no need for a supernatural cause. The flute is simply the enabler, it is the humans who still make decisions.

For example, in one of their reality hopping, the ML met the middle-aged FL-world's version of Kang. The flute did not forced them to be at the right place, at the right time. The flute simply enabled them to be in the past of the FL's reality. It was all up to the humans after they stepped into that reality. It was them who decided to be on that place at that time, which caused Kang to see the ML and get distracted, thus, saving him from that car crash.

The flute is powerless to change anything. In the rare times it intervened, like freeing the FL from captivity, probably used up its more of its power.

Yes, the flute also chose to keep their memories. There's no issue with that, after all, the "world between worlds" is its domain. The flute could've chosen to delete their memories before tossing them back to their own worlds.

In the end, there still was no supernatural or magical power involved in time travel. It's simply a case of a Time Bubble. Once the very thing that started the loop was resolved, the Time Bubble collapsed.

Think of it this way. If time-travel in E01 did not happen, there won't be a Time Bubble at all. The Villain probably is controlling both worlds. Or, the two worlds permanently froze because the time freeze reached 773774848839299 millenia before it unfreeze again.

Whatever happened before E01, the ML and Villain happened to enter the portals at the same time, but only the ML went to the past, the Villain in that version had no clue.

Because of that first time-travel, the Time Bubble formed. Now there's a chance to fix things. The flute simply have to play its cards right without depleting its power.

 Knight:

thank you for your time to giving answer. you are smart to notice park, i didn't pay attention to it. i think i have got it now, it was that their consciousness merged with their newer version, so no extra body, and they had memories of both the versions. Thank you again ☺️

My pleasure. And it's a good thing you asked, I didn't realize at first why they had to mention about having both memories of their "first encounter". Good authors always leave clues, no scene or dialogues are wasted. When you asked, it was when it clicked! That scene about double memories, it was to explain the ending they planned without having to write another episode.

Thank you as well for asking it.