He had arrived at that idea through trial, not through formal training. The explanation impressed Brooks because it was a researcher's explanation: the choice of method followed the difficulty he was trying to overcome. Elijah's notation remained unconventional, and a few steps needed rewriting, but the chain of reasoning could be tested. For the first time that morning, the judges' questions sounded like those asked of any author with a promising argument.
At the end of his prepared presentation, Elijah placed his hands on the podium and looked at the panel. "I can do an example if you want," he offered. "It might be easier to see than to hear me talk about it." Ruiz looked toward Park, who nodded. A technical demonstration would not prove the general result, but it could reveal whether Elijah understood how to carry out the construction under scrutiny.
Ruiz selected a periodic network from an older Hartwell research note, one whose repeated boundary constraints had made it a useful test for proposed methods. The diagram filled the screen with numbered regions and lines indicating which copies of the patch connected across the seams. Several reviewers had studied it before, and some had found multiple ways for careless constructions to fail. Elijah recognized the general shape but not the particular labeling Ruiz had chosen.
He asked for a moment to check the assumptions. Then he asked whether he could mark the permitted edge states first, before assigning colors. The panel agreed. Elijah drew a small transition table, crossed out a pair of incompatible states, and began building the coloring one region at a time. Blue, red, yellow, green appeared on the screen, not as guesses but as consequences he explained while he worked.
The room settled into a silence more concentrated than any Elijah had experienced. Even the reporters stopped moving their microphones. When he reached the final boundary, he returned to the beginning and checked the seam in both directions. No adjacent regions shared a color, and the displayed assignment repeated compatibly under the chosen period. Elijah set down the stylus, pushed his glasses up, and asked, "Did I miss an edge?"
Ruiz spent a full minute tracing the boundaries. Brooks checked the transition table independently. A reviewer from Berkeley identified one connection that looked suspicious until Elijah pointed out that it met another region only at a corner, which did not count as adjacency under the stated rules. Park asked whether anyone had found an error in the demonstrated example, and no one answered. It was a correct worked construction, not proof of the entire theorem, but everyone knew what it suggested.
Applause rose across the room. It became a standing ovation before Elijah could take a full breath. He looked toward his mother and saw that she was crying, too, openly now, without trying to hide it. Okonkwo stood beside her with one hand over her mouth. Elijah was not thinking about defeating Whitfield. He was thinking that he had finished his explanation, and that the people who understood it were applauding the work.