Lin Yu actually had a rough idea of what that "Authority" might be.
"Drama."
Although Lin Yu couldn't guarantee that there was only one "unclaimed Authority" within this "Eternal Prison," but...
Since that fellow was a consciousness born from the "Fragment of Fate," the hints he gave could be things he had seen on his way here...
Based on Lin Yu's understanding of the Authority known as "Destiny," it might very well be an "Authority" strongly connected to himself.
In other words... the "Drama" Authority prepared for him by "Order."
However, there was no way Lin Yu could tell Cheng Shuang about these analyses.
Thus, he could only pretend he knew nothing, follow behind Cheng Shuang, and head off according to Fuzzball's guidance to search for that "Authority."
At the same time, Lin Yu fell into deep thought.
"But if it really is the 'Drama' Authority later... should I attack and seize it directly, or what?"
"Now, I'm only one victory away from completing the 'Duel' victories. Falling out with Cheng Shuang isn't impossible... After all, no matter how you put it, she's a dangerous person who caused chaos and attempted to escape the 'Eternal Prison.'"
"The deception I've used on her, and the 'false experiences' I've woven, might not be able to fool her for long. After all, I really did enter as a member of 'Order' who had come to 'undergo the Trial.' Moreover, whether it was the elf Medalo from before, or Mans and the two Guardians, Nightless Sky Yong Shang, they all know this."
"However... if I continue the deception and use 'verbal negotiation' to have Cheng Shuang take in the 'Drama' Authority and then hand it over to me for safekeeping, that might work too. After all, this woman seems highly accomplished in researching 'Authorities'...