With the end of the Chaos Timeline story, Hellfilth comes in question.
I've been noting most of the Chaos Timeline appearances, the appearances have been linked with the Broken Gear as it allows it's user get there via portals.
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Vergil: Count Thunder
CT Vergil uses it first in his side story, after traversing the Memory Corridor and then arriving in the following unique areas and eventually reoccurring areas, Edge of Darkness, Ruins of Agony, Chaos Plaza and Twilight Altar.
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Dante: Destined Executioner
Lily then has possession of the Broken Gear in part 2 of the Dante's Destined Executioner story, using it in the Unknown Ground area to traverse through the same places CT Vergil went after getting to the Chaos Timeline, the areas Dante and Lily go through is the Edge of Darkness and Ruins of Agony.
Part 3 of the Destined Executioner has Vergil suddenly ambushed and taken by Hellfilth after Dante and Vergil's fight, this occurs at the Clock Tower area.
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V: Charismatic Ally
V uses the Broken Gear to track down Nightmares and other stuff...he travels to the Twilight Altar to fight Nightmare Phantom, the scan for this is in the Theories section at the bottom of the post.
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Dante: Blazing Tempest
Dante travelling with Lily who is still in possession of the Broken Gear, in the Blazing Tempest side story, starts him off in the Ruins of Agony, Dante goes to a few other locations and finally at the
Twilight Altar (for the 2nd time the player gets to this area in PoC) where Lily states they're in a rift between worlds, where the rules of time and space are different.
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Part 2 of the Blazing Tempest side story Lily and Dante form a plan to get another demon artefact, Lily states they need energy, the energy they collect is Chaos energy from defeating demons in the Ruins of Agony.
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Part 3, Dante and Lily arrive in the Nightmare space, the area they're in is called the Nightmare Shore, as they traverse ahead they get to an area familiar to Coop boss players, Hellfilth's boss arena which has an area name of the Nightmare Balcony (the Hellfilth boss fight doesn't name any of the areas, so only now we are getting the names for these areas). Lily mentions that this realm has a master, and said master doesn't want to meet Dante and Lily.
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Random theories I was thinking of whilst playing through..
With our prior knowledge of Hellfilth through her description in the strategy guide, we know she is the source of all Nightmares, and the Nightmare space she has control over is her domain.
I'm going to say the Edge of Darkness, Ruins of Agony, Chaos Plaza and Twilight Altar areas are within the Chaos Timeline, with other areas being part of it too, but I can't be definite on the others, so they won't be used in the Theories.
Theory 1
In part 3 of Blazing Tempest, Lily and Dante stop traversing the Chaos Timeline and end up using the Broken Gear to travel to Hellfilth's Nightmare world/realm/space, which is completely separate from the Chaos Timeline.
Theory 2
The Chaos Timeline is Hellfilth's realm/domain.
Reasoning- In part 2 of Blazing Tempest, the Ruins of Agony and Twilight Altar areas have the mission objective of explore the mysterious space, when you reach part 3 of BT, this mission objective changes to Nightmare space meaning that the Chaos Timeline CT Vergil, CA V got to is the Nightmare Space.
Counter- The mysterious space can still mean the Chaos Timeline as the Nightmare space is only revealed after Dante/Lily get to the Nightmare Shore/Balcony.
Reasoning- Hellfilth is able to traverse the Chaos Timeline freely like when she randomly appeared in the Clock Tower without being in possession of the Broken Gear, which shouldn't be possibly without the Broken Gear unless she in fact is the master of the Chaos Timeline.
Counter- This could be explained that in her strategy guide description, she is stated to wander beyond time and space and could just be moving through timelines/realms/whatever due to her power.
Random baseless reasoning - Taking into consideration her vast magnitude of power, being the source of all Nightmares and the embodiment of fear, her having nightmare versions of Demon lords such as Nightmare Calibur, where the normal Calibur first appeared in the Chaos Plaza (Chaos Timeline) story wise, and this statement stating that all demons have nightmare versions of themselves, in V's Charismatic Ally story (minor note that the demons she created, all have a more powerful move set and more expansive abilities than the original)
Then getting slightly into the metaphysical aspect of Nightmares/dreams in DMC, Nightmares are transcendental beings, can exist independently from their original and retain all the memories from them too, even after the originals death, like when Nightmare Phantom (who appears at the Twilight Altar) remembered V killing the OG in the Visions of V manga and the statement that they exist in a separate realm which I got from this statement I've borrowed from Palito266's blog. Said realm which could be the one Hellfilth created as she is the source of all nightmares.
https://imgur.com/a/p0uzX5w
https://imgur.com/S8A97vN
Counter- This reasoning of mine is mainly just assumption based on her power, reach and interference with the Chaos Timeline so far in the story, PoC could easily state otherwise in future side stories.
I personally believe 1, that it's separate and Hellfilth has her own separate thing. The Chaos Timeline is separate.
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Chaos Timeline attributes
-Has a different time and space to ours.
-So far you can only get there by using the Broken Gear.
-Contains Chaos energy, said energy was able to be harvested from Demons in the Ruins of Agony area and others.
-Links to Hellfilth via Nightmares appearing within it and her just moving around it.
-Called Chaos Space-Time in the JP version
-Various Demons spawn from it, meaning it should have it's own demon world as demons originate from there, the Demon crystal's scattered around also suggest high concentrates of demonic power as crystallised demon blood is that.
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@SuperSonicTL I saw your theory about the Chaos Timeline being the DW, you mentioned no mention of DW throughout PoC, I found this if that's sufficient?
https://imgur.com/a/Mke7rX4