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Perhaps one of the most hotly debated aspects of Polka Kakamond concerns the myriad Paths she seems to be affiliated with, let alone has encountered in some way, shape, or form in the instances she's mentioned or the lore she's shown up in. So far, two are confirmed: Erudition (as a member of the Genius Society) and Nihility (as the founder of Device IX).
But, what may come as a surprise is the fact that she seems to have ties with the Equilibrium, too.
The Chains of Karma
One of Polka's more unique skills is the ability to traverse along the Chains of Karma. The Chains of Karma, as we come to understand, are connected to the Equilibrium.
According to Equilibrium, Data Bank: Aeons, the chain(s) of karma are described as being a complicated topology, a web of logic created by HooH that allows THEM to sense aberrations within the cosmos that THEY can correct back into balance.
In Vaishnavism, "Chains of karma" symbolizes the repercussions of past actions that trap souls in the continuous cycle of birth and death. These karmic bonds hinder spiritual progress and liberation. Lord Gaura is believed to assist in breaking these chains, offering a pathway to freedom from the cycle and enabling the soul to attain higher states of existence. This concept underscores the importance of understanding and overcoming the effects of karma in spiritual practice.
This is also a prominent concept within Vaishnavism, a major branch of Hinduism. In addition, is also seems to have some aspects in common with more scientific string theory, too.
String theory is a framework that physicists use to describe how forces usually conceptualized on a gigantic level, like gravity, could affect tiny objects like electrons and protons. [...] String theory turns the page on the standard description of the universe by replacing all matter and force particles with just one element: tiny vibrating strings that twist and turn in complicated ways that, from our perspective, look like particles. A string of a particular length striking a particular note might gain the properties of a photon, another string folded and vibrating with a different frequency could play the role of a quark, and so on.
- String Theory, space.com
Within As I've Written, δ-me13.exe, Experiment Fundamentals: Containment Measures, the chains of karma being connected to string theory seems to make sense, as in these admin notes, she's said to be able to sense "ripples" across the universe. These strings or chains rippling in such a way to alert her could be a power connected to Equilibrium.
In the SU-related adventure mission, Antimonic Waltz, at the finale of the encounter with Polka, Herta makes mention of Polka's ability and how she can appear wherever mention of her name is detected, whether real or simulated, she can appear and even take "possession" of something like a data entity, like the one the SU crew recreated in the SU.
Keeping balance within the Circle of Knowledge
During Antimonic Waltz, something that Polka makes known for those involved is her modus operandi: the reason she kills geniuses like those within the Genius Society and keeps them highly regulated within the Circle of Knowledge so that the universe won't tip towards Finality.
In Recluse's Refined Timepiece, this is further elaborated upon by none other than Zandar himself. One detail I find incredibly curious is the fact that Polka seems to have been operation for some time, enough that she garnered a reputation. Furthermore, although the Genius Society is said to have been founded by Zandar with his ascension as Nous' first Emanator, he's not credited with formally establishing it the way Nyul Iman and Harald Punch were.
This much is said in Genius Society: Research Results, and I believe the deliberate founding of the Genius Society was more in part because of them, but I digress. The timeline isn't important so much as how long Polka has been active, which I believe may have been before the Genius Society was even founded.
In Back to Earth in Evernight, Night, Coming Before Dawn Breaks, Lygus tells us the intention behind the creations of Device IX, and why it was founded in the first place.
Now, what's interesting is the fact that there does seem to some confluence between Equilibrium and Nihility that may inform more of Polka's connections to Equilibrium.
In SU: Swarm Disaster, Lepismat System: Massacre Saga VI, Arbitrators of Equilibrium are demonstrated to have the ability to dispatch elements of Nihility like Shadows of Nihility. Device IX, meanwhile, is insinuated to do much of the same on a grander scale.
During the finale of the Penacony MSQs, Farewell to Penacony, Acheron believes that Device IX has the ability to somehow eradicate IX. While the means is currently unknown to us, the fact that it can is highly significant and a predicator of future plots/conflict, and may hint at Polka's connection to Equilibrium.
HooH & Polka
As a last, possible tidbit, in SU: Gold & Gears, Emperor Rubert II was HooH present when Polka made the killing blow to Rubert I, but not to prevent his death. Instead, THEY slightly righted the angle of Polka's scalpel and let her finish.
As HooH rarely, personally appears, while this simply could've been THEIR predicted involvement in Nous' third moment, it may also inform Polka's connection to Equilibrium and how THEY maybe sometimes personally appear in these drastic moments to correct great unbalance within the universe.
Whether this comes true in the future will simply remain to be seen.