He looked toward his mother, who nodded without trying to direct him. He looked toward Okonkwo, who had stopped at the foot of the stage and was holding up his Maybe notebook like a familiar flag. Finally he looked toward the drawings on the screen, the little arrows and squares that had occupied his thoughts long before Whitfield had a place in them. "I want to finish explaining the corners," he said.
Park called a ten-minute recess. In the side room, Danielle handed him tissues and a bottle of water. Okonkwo crouched beside his chair and waited until he could breathe without shaking.
"I thought you were going to be mad because I cried," Elijah admitted. She shook her head. "I'm mad that adults put you in a position where you felt you had to be perfect to deserve respect. That's different."
Brooks joined them after asking permission. He told Elijah that the panel had genuine questions about the proof, including questions he himself had not resolved, but that the personal accusations were unnecessary. Elijah asked whether crying had ruined his chance to be taken seriously.
Brooks answered by showing him the marks on his copy of the manuscript. "These questions are still here," he said. "Your tears didn't change the equations. Neither did Dr. Whitfield's attitude."
For a moment no one spoke. Then Elijah opened Not Yet and showed Brooks a drawing from three months earlier, when he had found a seam that broke an earlier coloring rule. He explained why the example had frightened him and how the failure helped him define the admissible family more carefully. Brooks listened, asked one question, and then another, both directed at the mathematics. Soon Elijah had forgotten the wet cuffs of his blazer and was drawing arrows on the back of an old program.
When the session resumed, Park reminded the room that the purpose of the review was to evaluate a claim, not stage a contest between reputations. She gave Elijah uninterrupted time to complete his explanation. He walked back to the podium looking pale, and his eyes were still red. But he arranged the pages in order and began speaking with more care than before, because the proof was the one part of the day that still felt familiar.
He illustrated his construction with three patches. The first was easy to color and showed why ordinary examples could conceal a problem. The second failed when its boundary assignments were extended without checking whether the top and side transitions agreed. In the third, the corner compatibility rule eliminated the conflicting possibilities, allowing him to exhibit a repeated assignment with a finite certificate explaining each choice. He explained that the method reduced a potentially endless verification problem to a finite collection of allowed local states, provided the stated hypotheses held.
Ruiz asked him to distinguish the claim from a general algorithm for every planar map. He did so immediately, explaining that his method was not a replacement for the four-color theorem. Brooks asked why he had chosen the boundary-state representation rather than a more conventional combinatorial formula. "Because I got lost counting the inside colors," Elijah answered. "I could keep track of the edges. I figured if the edges were okay every time the pattern repeated, I could work backward to the inside."