There were many assumptions and conjectures, but these things only made reaching the truth even more complex.
In the end, Ace decided not to invest in this issue more than he needed to because he already had all the pieces, and all that remained was to find and unlock this lock that might reveal the truth.
As for the remaining two items, the ethereal white shard was the time-space fragment, one of the two materials he needed to upgrade his thief's space. Lastly, the five-foot silver oval, which was releasing a dense life force, was a beast egg of some unknown beast; at least it looked like one.
Ace also had many to them, but they never hatched in the thief's space for some reason, nor did the system bother to entertain such a topic. The system was only interested in the egg of the Nether Paradise Bird.