The information here comes from a post made by the official account on Hoyolab on 01 November 2024.

“If the truth of the universe is cruel and stale, would you still yearn for the answer to the ultimate question?”
There were scholars who spent their entire lives searching for answers, only for a genius to transcend time and provide the solution.
For that genius — #83 Herta — being a “genius” was merely the starting point. She sought to reach higher dimensions, higher worlds, to surpass omniscience and overlook the Unknowable Domain that even Nous had never fathomed.

Should one compare one's own knowledge to a circle, the greater your knowledge, the larger your circle, and the more unknowns lay outside your circle.
Leaving the Circle of Knowledge and creating new insights from the realm of the unknown is to stride upon the Path of Erudition.^[1]

A concept proposed by a Genius Society member, describing it as a cognitive tipping point that can permanently alter the definition of knowledge.
From the initial discovery of fire, the early questionings of gravity… Each instance where a scholar has stepped beyond the boundaries of the Circle of Knowledge led to a significant impact on the world. In the world of geniuses, these impacts are exceptionally evident.

The domain of knowledge itself is a boundary set by Nous. When scholars expand their knowledge to a certain extent, approaching the edge of the known circle, they may encounter obstacles, as if an invisible hand is preventing them from stepping into the unknown, forming a continuous Unknowable Domain.

Meanwhile, the Knowable Domain is an experimental field created by #4 Polka, where probability and coincidence hold no meaning. Polka believes that chaos and the unknown will lead the universe toward Finality prematurely. To preserve the perfect future model declared by Nous using “Moments,” she relentlessly hunts down geniuses, attempting to limit the growth of universal knowledge and extinguish the possibility of chaos.

At the Futurological Congress for the division of Scepters, 95% of the computation power was monopolized by the leading schools, leaving all other scholars to scavenge the remaining scraps. Patavia, a scholar unaffiliated with any school, was allocated only one ten-thousandth of a Scepter's computational power, which she planned to use to study a strange signal that had been troubling her — a signal whose strength and frequency remained constant, regardless of time or location.

However, the Emperor's death caused all Scepters to shut down, ceasing their frightening real-time decision-making. The School of Pure Creation decided to physically link dozens of Scepters to achieve multiplicative extrapolation effects. Scholars' allocations were revoked, and their laboratories seized. No one could go against this forced migration. Patavia's years of hard work were lost, buried in the frenzy of rapidly fluctuating data.

Yet even the connections of dozens of Scepters could not awaken the inorganic intelligence created by the Emperor. The genius who had passed away mocked the incompetence of mediocrity in its silence.