During Faith's journey, she had accumulated a lot of power that was seemingly unexpected of an Asterio. For example, the Eternia Palm, which still has mysterious roots that cannot be traced to any single place.
Faith had abilities implanted within her body right after the fight with Cole and Sky, where Sky had broke Cole's spine and killed him in one hit. Due to previous contracts that Faith made to ensure his death, any damage Sky did to Cole would be pushed back onto her.
When Faith was struck with such a heavy amount of pain, her eyes were opened up to a wide place with millions of capabilities, she was able to locate understanding that Sky still didn't have to this day. Strands were everything.
Everything Faith had told Sky was wrong, and true development in power couldn't occur without them. Strand-Beings are able to manipulate their bodies, which is why the Eternia Palm worked. Transporting oneself to any desired location was possible, as long as the building blocks for the area already had a piece of you. As long as the Strands were yours, you could move yourself.
It started to make sense that Avie could move so fast, especially during her fight with Cole. When spreading the Strands out, she was manipulating the very building blocks of her body, even smaller and more finite than atoms themselves.
Faith realized that when Sky struck Cole with as much power as he did, he inadvertently produced so many Strands within the body of a person with another heritage: The Achamos.
When the Asterio and Achamo Strands intertwined, they produced every possible outcome in strand formation and ability usage, and implanted it into Faith's body, allowing it to multiply to near-infinite proportions.
The Eternia Palm, The Leyndell Aura, The Achamo and Asterio Strands, and the icy wrist was what she had developed for the time being, but many more abilities were sprouting within her. Perhaps her development was preconceived by Cynthia.
Faith sat on the boat, analyzing how to utilize the icy palm in her possession, and who it could've possibly belonged to. She knew that Sky possessed the ability to create ice, gathered originally from Demos, and then Belle. He had so many abilities she couldn't count and couldn't piece together.
If she asked him who it belonged to, Sky would've probably had an answer, but he saw the icy wrist before she left. Revealing it would paint the clear picture that Faith was actually there the entire time.
Not to mention, Faith had a tracker in her body placed in by Finlis Vega. His presence was more than terrifying, and knowing he didn't budge and was able to track Faith, regardless of if she had all of these abilities or was Sky Asterio's daughter, explained that he was a dangerous threat. More dangerous than Illya, and all of Quake. Perhaps, maybe even Eirikr.
Things were running rampant since Sky teleported Eirikr off to The Pinnacle, which was originally launched at him. The deflection he engaged in that launched it away would've killed a normal person; but not Sky.
It would've killed Faith. So many things Sky Asterio did could've, and would've killed Faith. She couldn't amount to him, but the abilities in her body that were still brewing under the conditions set in by her father were her only hope. There was still a chance, no matter how small, that she could defeat Finlis Vega and become more powerful than her father.
As Faith was lost in her own mind while sitting on top of the tower, she sharpened a knife by sliding Strands against her emergency dagger, peering at the mark of ice on her wrist.
Her eyes grew wide at the thought of it once more. The ice, without question, belonged to Belle Asterio, and before her, Demos. However, how could Demos be aligned with an Asterio? The answer, although she remained skeptical, was slowly inching out of its hole.
The answer to the question was that, he wasn't. Demos had no relations to an Asterio. From what Faith was able to remember about four hundred years ago, there were few people in her old group that had married.
Sky and Illya used to be married, Shike and Belle used to be married, and Carl and Red used to be married.
Belle only had the last name 'Asterio' because she married into the family with Shike... Sky's biological brother?
From what Faith previously knew, The Asterio Clan were all 'Asterios', but Sky Asterio was the Pure Asterio. He could distribute abilities, so if the ability came from Belle, Faith knew that she had to be from a different clan originally.
Faith racked her brain for the answers she was searching for.
"Asterio, Achamo, Danafall, Eternia, Leyndell, Madio, Vildian, Zerion... what others," She muttered to herself. She began to scrape out the initials into the wood analyzing them until she remembered the final two.
Silas, and Woida. One of the two most forgotten about clans from four hundred years ago prospered within Faith, leaving their mark by allowing Belle's ice to flourish underneath her skin.
It was up to Faith to figure out where Belle belonged to. Perhaps the library in Khalil's nation would hold the knowledge Faith was searching for. She couldn't find a necessary reason to stay in The Americas, but now had a reason to.
She thought about the possibility of it being Silas, having no connection to the other last names she knew, but Faith wasn't even sure about Woida. Almost nothing was known about them because they were so weak, and it's possible during a theoretical power struggle that Belle married into a stronger family. Faith was unsure if she would find Belle's name in a book at all, but it was worth the look.
The last thing Faith thought about while thinking of Belle's last name was the pattern in which things made sense. Alexia was Shike's sister, yet bestowed the powers of Sky Asterio. She wasn't sure if Alexia was around during the old times, or if Alexia was exclusively Shike's sister in The First Trial.