According to the
Dead Sea / Sea of Eden FAQ Refutation article, Arris Dome belongs to Guardia and if Porre rises, then Guardia will fall, Arris Dome won't exist and so Crono & co will never find out about Lavos, so it will live to destroy the planet. This will in few words lead to the creation of the Dead Sea in the Home World. This means, that the Home World Lavos still exists, Crono & co did nothing. In Another World, Crono & co defeated Lavos. In short...
Home World:
Porre rises
Guardia falls
Arris Dome isn't built
Crono & co don't know about Lavos
Lavos destroys the planet
Dead Sea becomes a timeline graveyard
Another World:
Porre doesn't rise
Guardia still exists
Arris Dome is built
Crono & co find out about Lavos
Lavos is defeated
The Sea of Eden remains what it is
Now, I may be wrong, but there is not reason to believe that Arris Dome was belongs to Guardia. It can belong to Porre (or to Guardia which belongs to Porre). If such thing happens, then Arris Dome exists in the Home World, so... So what? I can't imagine what happens here... What do you think?