CLOSED.

Essentially, based on its description, I have reason to think Device IX is located in the Sea of Quanta, and its power is derived from it, too, and possibly the secret to how Polka will be able to destroy IX.

This is a rift between reality and possibilities, a dimension of imaginary theories and actual existence. —Joachim, 11-1 Manifest Corridor Mathematically speaking, the "Sea of Quanta" does not belong to the known four-dimensional space-time, but a large class of "folded planes" that exist parallel to us. [...] Unlike the "classic space-time" we live in, the "Sea of Quanta" is "fragmented" on a large scale— Basic physical laws change continuously as the coordinates shift, resulting in the worlds being unstable like soap bubbles— —However, in the gap between said fragmented worlds, there are countless "stable zones" fixated by the "Ether Anchor". Those worlds, like ours, follow a fixed set of laws. —Otto Apocalypse

Something explored in this video is the fact that the Sea of Quanta/Quantum Energy is one of the few energies in the Hoyoverse capable of countering the power of Finality, which manifests as the Coccoon of Finality in Hi3 (whose universe is limited to the Solar System), and was confirmed when the Coccon tried to "embrace" Venus (a planet that tapped into and overused the power of Quanta that destroyed its civilization) and failed to do so because of the saturation of Quantum Energy that buffered the planet against the Cocoon.

Something that is true is that the Authorities in Hi3 share parallels with HSR's Paths. So, with the Path of Erudition...

Matter Creation

World Understanding

Matter Manipulation

Regeneration/Restoration

At least, if it's like the Authority of Reason in Hi3, this could be an outline of its capabilities. The problem is, of course, that I haven't seen confirmation of this in Emanators of Erudition like Herta or Zandar/Lygus, although the nine vessels of Zandar could point to this, maybe?

Another parallel I think exists is Void/Nihility. It's Hi3 abilities are:

Matter Creation

Imaginary Renormalisation

Matter Manipulation

Imaginary Space Manipulation

Space Manipulation

Imaginary Space Travel

Bubble World Creation

Bubble World Manipulation

Black Hole Creation

World Anchor Creation

World Anchor Severing

This would seem like the sort of place the Laughter would create for THEIR own amusement, wouldn't THEY? A pocket dimension that Polka had stumbled upon that attached itself to the World End's Tavern, that den of Fools that was supposedly exclusive to those blessed by the Elation. And yet, the Lord of Silence had no trouble locating it due to a certain conundrum linked to a colleague of hers, one could say. The tinny strains of an orchestrion filtered through hallways draped in the tarp of a circus tent, garish and red, while gauzy light filtered through. A path with only one destination, but not a difficulty to ascertain.

Dragging around this false persona was the equivalent of lugging around a corpse, but 'Sophia' the Nodist would be forced to live a little longer; well into Amphoreus' genesis, too, that much was certain. And what was a year for one who was everlasting? The limits of the Everlastin Page were beginning to fray as old remnants of the previous Amphoreus responded to its inhabitants' memories, manifesting a world that was expanding beyond its established borders.

Within a pixelated Grove of Epiphany, 'Sophia' stood with a mixture of dread and awe, a rehearsed expression. Especially in the circumstance that she wasn't alone.

Across the topography of existence, causality was a domain that was hers to beckon, to command. Across the cosmos did uncountable intellectuals try to push past the limits she'd set, and Lord of Silence clashing with the Black Rose would have been inevitable. Heels clopped cavernously on tiled floors as she approached a team of scientists in a state of panic, frenzied as sensors blared and a bright portal embedded into a wall yawned wider, the seam splitting the wall as an encroaching growth began to conquer every surface.

An uncharted Memory Zone. Such places were abundant across the cosmos, and many were reflections of dead planets and places that no longer were. People milled about obliviously, unaware they were dead and gone and only the memory of their existence remained. Within the liminal space of an enormous shopping complex, Polka leaned on a glass-lined balustrade overlooking the concourse below, gaze dull with disinterest. Perhaps something might come of this place. Perhaps--

HooH THEMSELVES have been present in her doings, specifically when she killed Rubert I.

SU: Gold & Gears, Emperor Rubert II

Perhaps the most damning piece of evidence was HooH's presence during the killing of Rubert I when Polka's blade was slightly affected by the angle via HooH's interference (aid?).

She can navigate along the Chains of Karma, which in-lore, are dominantly associated with Equilibrium.

Herta, Antimonic Waltz

Equilibrium, Data Bank: Aeons

This one is a lot more self-explanatory, but I've yet to hear of any other character capable of doing this. The Chains of Karma are undeniably HooH's creation, but her being able to navigate them is extremely suspect.

Her ability to withstand/co-exist with Nihility on the path to destroy IX might be reflected in the Equilibrium.

SU: Swarm Disaster, Lepismat System: Massacre Saga VI

Acheron, Penacony 2.3 TBQ

'Sophia' glared sidelong at the muzzle of the gun that prodded her temple. To say she'd expected this was an understatement, as she'd seen it within Nous' calculations some time ago. Marauders from the Annihilation Gang sought to perform their witless acts of destruction for tribute to their indifferent Aeon, and that day, their eyes had turned in the wrong direction. Some might say it was the last mistake they'd ever make. While some pillaged the dropship they'd been traveling aboard with other civilian passengers, other bound and fettered the rest of them and the crewmen in plasma chords that hissed as it tightened around the hostages' bodies.

"Harmony, wait one moment," 'Sophia' instructed the understandably distraught cyborg, though the gunman at her flank prodded her again in annoyance.

Dark browns drifted over to one of the Annihilation Gangmen' spacecraft as if glancing at an ally to make their move, and the pull of causality responded flawlessly. A muffled, concussive boom sounded within the craft like a drum before an explosion blasted metal in an omnidirectional onslaught, shrapnel whizzing trough the air faster than bullets as several fired through the skulls of their captors, the one doing so with her crying out as he was hit and he was buffeted by the flying metal. Like bullets did the metal take out their captors effortlessly, several falling dead to the ground in unison while a harmless gust of hot wind breezed past them. 'Sophia' helped herself to Harmony's binds and cut the other woman free, a gunman's gun backfiring as the impact killed them instantly.

The chaos that unfolded was almost cartoonish, but within a minute, the marauders were dead and their fellow passengers gawked, absolutely dumbfounded.

And to think, this was barely a sliver of a fraction of her power.