Elijah continued. He described how a state at one edge could be traced around a closed path, why certain incompatible transitions had to be excluded, and how his proposed rule avoided the corner conflicts he had discovered during months of failed attempts. He knew he had not explained every technical detail in five minutes. The judges would need his notebook and a chance to check the assumptions carefully. But he reached his conclusion without losing his voice, and for the first time all morning, he felt he had actually been heard.
When he finished, the room did not erupt immediately. The people who understood enough mathematics to recognize the stakes were quiet, already considering possible exceptions. The rest waited for a sign from the experts. Park looked toward Ruiz, who asked for the full written manuscript, including the pages of failed examples. Elijah held out his notebook with both hands as though surrendering something valuable and fragile.
"We're taking a short recess," Park announced. "The panel needs to examine this construction before offering an assessment. Elijah, please wait in the green room, and thank you for bringing your work to us." The last sentence sounded ordinary, but Elijah almost cried at hearing his name and his work treated as the same thing. He left the stage feeling both lighter and more frightened, because attention from mathematicians could now mean something beyond humiliation.
The green room contained a long table covered with bottled water and sandwiches no one had touched. Elijah sat on a vinyl chair, stared at his hands, and tried to remember the order in which the morning's disasters had happened. He had dropped his papers, been mocked, corrected a projection error, spotted a coloring mistake, and handed over his notebooks. The entire sequence felt unreal, as though he were watching a film in which a boy who looked like him had somehow become the main character.
Danielle slipped into the room after a volunteer confirmed she was his parent. Elijah stood so quickly the chair scraped backward. He walked into her arms, pressed his face against her jacket, and cried with the kind of exhaustion children cannot fully conceal even when they want to seem grown. Danielle held him without asking for an account of the presentation, because she had watched enough from the audience to know what had hurt him.
"I tried to talk," he whispered into her shoulder. "He kept making it sound like I was lying."
"I know," she said. "I saw."
"Do you think they'll send me home?"
Danielle took a breath before answering. "They can tell you your mathematics needs work. That's what judges are for. But you belonged on that stage the moment they accepted your presentation, and nothing he said can undo that." Elijah pulled away and wiped his face with the cuff of his borrowed blazer, embarrassed by the wet mark he had left on her shoulder.