Although Thor had gotten the White Porcelain Cat from Nathan, he didn't give up his position as a substitute lecturer.
That was because after Kate tested the White Porcelain Cat's effects, the abnormality surrounding it disappeared again.
Thor judged that the power capable of affecting a Tier 3 Wizard didn't reside in the cats themselves. These White Porcelain Cats, sold separately, were likely just serving as a medium.
And there was still a good chance that whatever lay at the other end of that medium was Nathan.
So Thor went back to teach during the second week.
But Nathan didn't show up that day.
He was probably busy studying the Locator modification plan Thor had given him.
Thor wasn't in a hurry. He continued with his own plan: each day, he taught them something new that was beyond the usual syllabus but inaccessible to ordinary Apprentices, startling them. Then he'd scold them until they lowered their heads and thought hard, too intimidated to disturb him, leaving him free to work on his own research.
During this time, Thor also went to White Glaze Castle to discuss with Ophelia how to establish a channel to contact the Phantom Color World.
Ophelia also asked Thor how his investigation was going. She could see where Thor was, but couldn't make out so clearly what he was actually doing.
Thor simply told her that he had a lead and was investigating it. Ophelia nodded and continued focusing all her attention on communicating with the other world.
Two weeks later, one of the Apprentices in Thor's class actually went home to prepare for advancement to Official Wizard.
The Grand Lecture Hall wouldn't reward Thor for it, but before leaving, the Apprentice said that if he successfully advanced, he would pay Thor a hefty teaching fee.