Wait a minute! If you say that Marle's erasure from history is due to their being no such thing as TTI, then we have a big problem on our hands. If TTI does not exist, in which case Marle's disappearance functions correctly, then Crono and Lucca do not come back in time because they would never meet her, and then we have the Grandfather Paradox continually running in circles. If TTI does not exist, then Marle's actions in the past will not take place originally, then they will, then they won't, etc. It's a neverending loop at that point. The entire game and a bunch of mini-areas are all GPs. Marle's is one, stopping Lavos is another. These are the two main TTIs in my opinion. I still hold regard that it's a matter of probabilities.
I'm working on researching to come up with a full on explanation that adds to TTI and TB but accounts for Marle's paradox at the same time. I have mentioned it a few times, the Theory of Probabilities. I know people don't like taking certain blocks of text literally, but let's look at this quote by Belthasar on Serge's predicament:
Serge... This world is not
the world you grew up in.
10 years ago, something
happened that put your very
soul teetering on the
balancing scales of fate...
with a fifty-fifty chance
of life or death!
This is when your future
was split in twain.
I stated quite a while ago the following:
Crono's appearance at Death Peak is not assured, as it requires, according to Gaspar, a certain amount of effort to be put into retrieving Crono for him to actually be retrieved. If it were an assured event, then all the rest of the group would have to do is just sit there and wait for him to show up. But this goes back to the Free Will theory, that inaction produces no action, and that until the group actually performs an action, the resulting chain of events does not yet occur. Until Marle and whoever the player picks to join her travel into the pocket dimension during that frozen second, and until they decide and will themselves to exchange Crono and the clone, Crono is not assured to appear at Death Peak.
Perhaps this lends credence to not necessarily a single event being the point of timeline alteration, but rather a checklist. Like, in order for Crono to appear once again, the following must occur: 1) The Time Egg is used at Death Peak; 2) A clone of Crono must be present; 3) The clone must be shifted into Crono's position and Crono be removed from where he was at; and 4) Crono must be removed from the pocket dimension. So it's a chain of events, and if all four of those do not take place, then the theoretical #5) Crono appears at Death Peak, cannot occur.
Quote
Marle Paradox
Leene is supposed to be saved at Time X, this is what the Entity recalls. Leene is, however, not saved at Time X - ultimately forcing her doom. We see, in game, that Yakra is moments away from killing Queen Leene in the Cathedral when we find them. It was, perhaps, not possible for Frog to save the Queen alone in time. Though Crono and Lucca intervene to make saving the Queen possible, this is only after the ultimate result has been witnessed: Marle ceases to exist.
When the three of them save Queen Leene, they create a new Time X within the Dreamline where Marle's family line is restored, therefore Marle's previous actions are recalled by the Entity, placing her exactly where she was first forgotten.
While I would initially reference my theory that a 50%-50% of something happening (50% of the time Leene is saved, 50% of the time she is killed, in this example) allows a timeline to stay in a sort of Limbo (which if you read my latest post on my discussion on whether the universe was split or duplicated in Chrono Cross, I state the theory could explain both Belthasar's statement that the 50-50 probability of Serge's life or death and the reasoning for the universe splitting and Another World not being shifted to the DBT due to the uncertainty), perhaps a modified version could be applied here. Notice how I stated that 50% of the time Leene is saved/killed, not Marle. Say whichever has the higher percentage of probability is what occurs. The moment one of the two options breaks 50%, it becomes the event in the current timeline.
Since Lucca arrived pretty much right after Marle "disappeared", we can safely assume that Lucca had gained TTI by this time. So, we have Crono and Lucca both with TTI. Let's say they decide to just sit around. Well, then Frog is left to go after Yakra by himself. Continuing on, let's assume that Frog makes his way through the cathedral until he reaches Yakra's room. Any idea of who is going to win in a Frog vs. Yakra match? Probably Yakra. Okay, so probability here is that while Frog's intervention delayed the Queen's death, it didn't prevent it. Then we can add in Crono and Lucca, and boom, the chances rise. For an example (and don't quote me on these being actual percentages, since we don't know), here's some example values to illustrate.
Remember, the Percentage theory (gotta think of a better name for it) states that until a choice rises about 50%, the timeline is in Limbo.
1. Timeline at start of game: Leene is kidnapped, but soldiers find her and defeat Yakra. Leene's survival rate: 100%. Leene survives and Marle exists.
2. Timeline after Marle time-travels: Leene is kidnapped. Marle has not yet chosen to interact with the citizens of the Kingdom of Guardia in 600, so the soldiers still find Leene and defeat Yakra. Leene's survival rate: 100%. Leene survives and Marle exists.
3. Timeline after Marle time-travels and Crono time-travels: Leene is kidnapped. Marle may not have chosen to interact with the citizens of the Kingdom of Guardia yet (this would allow for Lucca to travel back still), so the soldiers still find Leene and defeat Yakra. Leene's survival rate: 100%. Leene survives and Marle exists.
4. Timeline after all three have time traveled: Leene is kidnapped. While the soldiers are out looking for Marle in different groups, one small contingent finds Marle while the rest are looking in the Cathedral for Leene. When word is heard that "Leene" (Marle) is found, the search is called off moments before finding Yakra and the real queen. Crono is just now approaching the castle, and Lucca has appeared in the past, thereby giving her the TTI she needs to still be there.
At this point, we get to a slight discussion of how the Probability Theory (there, better name) takes effect. We have three possible outcomes at this point: a) Yakra kills the Queen; b) Yakra fights Frog and kills the Queen; c) Yakra fights Frog, Crono, and Lucca, and doesn't kill the Queen. At this point, until any action is made, there is a 66% chance (since until an action is made all probable outcomes have the same probability) that the Queen will die. So, the Queen dies since that probability is a 2 in 3 chance she'll die. However, becomes the timeline doesn't know which of the two timelines where she dies to utilize (where Yakra kills the Queen and then the one where Yakra fights Frog and then kills the Queen), the timeline is still in Limbo, which unfortunately has the side effect of removing Marle from the "timeline" (partially because she would no longer exist, but also because the timeline is in such a state of limbo that she's not shunted to the DBT).
5. The final timeline: Leene is kidnapped. While the soldiers are out looking for Marle in different groups, one small contingent finds Marle while the rest are looking in the Cathedral for Leene. When word is heard that "Leene" (Marle) is found, the search is called off moments before finding Yakra and the real queen. Crono watches as Marle is shunted into a state of Timeline Limbo due to the Probability Theory, and he and Lucca go off and help Frog defeat Yakra. Upon defeating Yakra, he can no longer kill Leene, and the one remaining timeline, where Leene is saved, takes precedence and the timeline realigns itself with the events of that outcome (which now has a 100% chance of happening). Leene's survival is now at 100% once more, and Leene is alive and Marle is returned from her Timeline Limbo state, as the probability she exists in this timeline is 100% again.
The Theory of Probabilities would function along the lines of timelines altering based on a "majority wins" rule with regards to probabilities. In my discussion above, Marle's disappearance occurs prior to Leene's death. This is the true plot hole, not Marle's disappearance. Since inaction causes no action, and just because it's a certainty that Leene is going to be killed, there is no reason for Marle to disappear when she did. If Leene were to be killed, at that point we'd have the paradoxical problem we continually refer to as the MP. And that point only.
Serge had a 50-50 chance of death or survival. The time line split due to it, even Belthasar makes this statement. However, Kid has the pendant with her, so that makes the time line split in conjunction with the 50-50 survival rate. I mention that, because in CT, if you apply the percentages rule to that Keystone, and apply it to the Marle Paradox, we are left wondering why the timeline doesn't split. I know you are probably saying "but the pendant was there". Not entirely. If we say that Kid's actions with resulted in the 50-50 chance of Serge's survival while she was wearing the pendant, then Marle's actions without wearing the pendant account for the difference. However, the pendant was present (in Crono's inventory) when Marle was about to be shunted, so perhaps it acted as a counter measure. However, because it wasn't charged (Kid's pendant is barely what, 16 years after the events at the Ocean Palace while Marle's is 13,000 years old), it was only able to keep the timelines in a state of overlap for the moment, instead of splitting them apart (which I would deem is more stable).
And as far as using a clone to swap out Crono doesn't mean anything bad on TTI. How else are you suggesting Crono be maneuvered out? Conservation of Energy is the key here. By placing the Crono clone in for Crono, we have a slightly more balance CoE, the whole thing stating that energy can be neither created nor destroyed. We are replacing one form of energy (Crono) with another (Crono clone). There's no TTI involved.