This theory is still not complete. This is the second major edit - the purpose of reediting this time is to increase clarity while keeping explanations to the point, so forgive me if keypoints do not flow well into eachother.
The DreamlineThe Dreamline is the view of the adventure from the perspective of the Entity. It is the Entity's subjective interpretation of events while "revisiting" and "predicting" them in an effort to save itself from it's eventual death due to Lavos in 1999AD.
It works like a timeline, but in order of memories
recalled/predictions made, rather than chronological order:
Normal timeline :
------------------------------------------------------------------
65milBC 12000BC 600AD 1000AD 1999AD 2300AD EoT
Dreamline (segment) :
------------------------------------------------------------------
1000AD 600AD 1000AD 2300AD EoT 1000AD EoT 600AD EoT ...
As such, causality is treated very differently, for example:
"Person A" conceives "Child B" at Time X.
Time travellers from X+1000 disrupt this by convincing A, currently at Time X-10, to come back with them. It turns out that one of the time travellers is a descendant of A. They hang around for a bit and then A returns to her own time at X-9.
Causality on a normal timeline would make this troublesome. If Time X never produces B, how can the time traveller from X+1000 still exist?
TTI seems like it would save the time traveller from vanishing, but we see in the game that Marle vanishes when Queen Leene remains kidnapped, so obviously TTI cannot function this way.
Normal Timeline:
---P1--P3--------------------------P2---------------
X-10 X-9 X X+1000
Here we have the 3 important positions "A" holds. A reaches P2 before A can experience Time X, and is therefore meeting with her descendant before it is even sure that he can ever be born. Marle is not spared, so why should he be spared?
The Dreamline avoids all of these nasty little complications, watch:
Dreamline:
P1-------P2-----P3
X-10 X+1000 X-9
Now take the above and "unfold" it over the normal, chronological timeline:
Normal Timeline (after dream) :
P1 P3 P2
(----)(--)------------------------(--)------
X-10 X-9 X X+1000
This is (or was) the Ayla Paradox. Now let's look at the Marle Paradox, where again she has ancestor-descendant issues, yet we have the opposite result this time.
Marle Paradox:
Time X is the point of no return. The period in which it is no longer possible for Frog to save Leene on his own. After Chrono witnesses Marle vanish, he and Lucca aid Frog, creating a new Time X and helping the Entity recall Marle once again.
Normal Timeline:
-------P2-------P3----------------------------P1-P4---------
600AD Time X 601AD 1000AD
Dreamline:
--P1-------P2-------P3--------P4------------------------------------
1000AD 600AD Time X 1000AD
Normal Timeline (after dream) :
P2 P3 P1 P4
(---------)-----------------------------(---)----(---)
600AD TX 1000AD ""
Notice the key difference from the Ayla example, Time X is within the scope of the Dreamline. So let's go over this:
Critical Moment Time X within Dreamline, Marle's ancestral chain is broken, so the Entity forgets her where she stands, to Crono's dismay.
Critical Moment Time X outside Dreamline, Marle's ancestral chain is preserved, so the Entity recalls her, despite the apparent break in physical causality.
I will edit this post again soon to re-include the "Crono, Clone and the Time Egg" and "Doan Paradox" sections.
I am posting this here and replacing the original post. I will clean it up even further after feedback or just later on.