I'm pretty sure it's canon that Crono and co defeat Lavos via the Black Omen in 12,000BC.
Anything else and you have conflicting evidence.
You have conflicting evidence any way you look at it. Defeating Lavos in 12,000 B.C. does not prevent him from emerging in 1999 A.D. to ruin the world. This is because he has already emerged from his PD (=time-traveled) in 1999 A.D. (Crono can only travel to the ruined future, which means that Lavos "time-traveled" to 1999 A.D. before Crono time-travels to 2300 A.D., 12000 B.C., or anywhen else.) The only solution is to revise one of the site's theory, because there's something wrong somewhere.
For instance, should Lavos be defeated in 1,999AD, firstly that means the humans would detect a distrubance, and Lavos' rising.
This one argument is inconclusive. The statement in Chronopolis allows for a fairly large amount of interpretation. The ghost says that...
On some time lines, Lavos
appeared on the surface of
the planet in the year 1999
and brought the world to
ruins.
The sentence is:
"On some time lines, Lavos appeared on the surface of the planet in the year 1999
and brought the world to ruins."
There are two statements here, "A" and "B" (they're separated by the "and"). The ghost then says that the Apocalypse was prevented in his timeline; basically that "B" was negated. However, he says nothing about "A". We don't know if Lavos appeared on the surface in his timeline or if he didn't appear at all. And we don't know what happened after the final battle in CT; perhaps Lavos's shell exploded in the Core's crazy time-warping effect and left no corpse on the field (or was sucked and fell directly in the DBT...).
Chronopolis may have sensed a disturbance and known about a mysterious hole in the ground; Lavos may have emerged and been defeated before a photo or recording of him could be made; we don't know. The only thing that Chronopolis definitely didn't get is the destruction of the world, the "Apocalypse". And a potential disturbance or a hole don't constitute useful information for them, even if they have them.
Secondly, it'd mean Zeal would be fact because of the ruined Black Omen and the people who saw it in 600AD +.
Inconclusive too. You can beat the Black Omen in 12000 B.C. and retreat after defeating Lavos's first form, then face Lavos again using the Epoch or the 1999 A.D. bucket.
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Anyway, I've attached two two-dimensional timelines to this post. The regular timeline is on the y axis. The Time Error line, which corresponds to the order of each change to the timeline by the time-travelers, is on the x axis. Read each diagram horizontally so as to not get confused.
Let's consider the first diagram, which corresponds to the "Compendium's canon", with Lavos in a Pocket Dimension, etc. Remember that Pocket Dimensions run on the Time Error axis rather than the regular timeline. Thus, on the diagram, Lavos's Pocket Dimension only exists between point A (his arrival on the planet) and point D (his dissolving of the PD in 1999 A.D. and emerging). Let's summarize the problem.
Facts:
- Lavos appears in 12000 B.C. after the Black Omen is beaten (point I on my diagram).
- If the party defeated Lavos's shell earlier in the game, Lavos will be without shell (well, without "head" more precisely) there.
Issue:
- According to the Pocket Dimension theory and the Time Error principle, Lavos shouldn't even be able to appear in 12000 B.C. after the Black Omen, since his Pocket Dimension has already been dissolved at point D. He also never appeared at that date in the original timeline (no Black Omen back then).
Flawed solution (in case you're wondering):
- Perhaps Lavos simply never dissolved his PD? He wouldn't have exited it in 1999 A.D. and continued to live within it on Death Peak. This doesn't work, because even if Lavos didn't exit his PD at point D, his Destruction Rain would still have exited it, and thus the Rain would still appear in 1999 A.D. at point J, destroying the world.
It's complicated, so let's consider the second diagram, which corresponds to what the game should be if we discard the Pocket Dimension theory. Lavos would be a normal inhabitant of the timeline and the Apocalypse a normal event of history rather than the result of him entering the timeline from somewhere else (a Pocket Dimension). Surprisingly, the diagram is heavily simplified in this scenario (I kept the same letters for consistency).
In this no-PD scenario, the only issue is how Lavos loses his head in 12000 B.C. after the Black Omen if you had destroyed it in 1999 A.D. (this unique issue was the reason the PD theory was imagined initially). Well, a possible solution is that this 12000 B.C. Lavos is the 1999 A.D. one time-traveling to the past. This solution was already mentioned in this thread, but it's really less farfetched and more simple with the PD theory taken out. Seeing how Lavos can time-warp people and his Core can create weird time-warping vortex effects, Lavos can probably time-travel himself. This would even explain why the Ocean Palace Lavos always has its head regardless of what you do to him in 1999 A.D. (the OP Lavos would simply be the past version of the 1999 A.D. one).
We can leave it this way: Lavos is defeated in 12000 B.C. No paradox, no unresolvable issue. It works, I think.
As for what to do with the Armageddon-Branch theory, we'll discuss that in another thread because there's probably too much stuff here already (I hope this post made sense).
EDIT: Actually, the "flawed" solution can work if we say that exiting a Pocket Dimension doesn't grant Time Traveler's Immunity (alpha's suggestion of existing both "in and out of time"), and that Lavos created his PD at point B (
like V_Translanka once suggested). Thus his defeat in the PD would prevent the Apocalypse, but not the Fall of Zeal which was caused by a non-PD Lavos. Thoughts?
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