"Does this mean I was wrong?" he asked Okonkwo over a video call.
"It means a careful reviewer found a gap," she answered. "Remember what we agreed before Boston? We wanted people to check your work. They have started doing exactly that." She asked him to read the specific objection aloud, then helped him translate the formal language into an ordinary coloring example. Elijah began drawing the troublesome corner and, after twenty minutes, realized why he had not seen the issue before.
He was quiet for the rest of the evening. Danielle let him put away the notebooks without trying to force a positive lesson out of his disappointment. When she checked on him before bed, he was looking at the photograph of his handshake with Whitfield. "Everybody said I solved it," he whispered. "What if I didn't?"
"Then you found something people thought was worth investigating," she said. "And you can keep investigating it. The world was in too much of a hurry to make you into a headline. You do not have to be in a hurry with the truth." She kissed his forehead and left him with the quiet comfort of a promise that did not depend on winning.
The next Saturday, Elijah brought the reviewer objection to the math center. He drew a simplified version of the case on the whiteboard and asked several children what they thought should happen if the colors lined up on one edge but not the other. The group tried rotating colors, renaming them, and expanding the repeating patch. Marcus suggested taking four copies of the patch instead of one. The idea did not immediately work, but it led Elijah to study a larger collection of boundary states than his original construction had allowed.
For the first time, a solution grew out of an afternoon when Elijah was not working alone. Okonkwo helped him state a revised compatibility condition. Brooks later showed him how to separate a lemma about allowable transitions from a stronger claim about the existence of a repeating cycle. Rachel Kim, with permission from the independent panel, suggested a computational check for small examples that might reveal hidden contradictions. None of these people wrote the proof for Elijah, but each contributed the sort of criticism that makes mathematics a shared discipline rather than a performance by isolated geniuses.
Elijah spent two weeks revising his manuscript. He added the omitted assumption explicitly and changed the title to reflect the narrower family the argument now covered. The discovery was still potentially significant because earlier researchers had not produced a comparable general constructive method for that family, but it no longer pretended to settle every formulation of Hartwell's original question. He signed the revised draft with his own name and a note acknowledging the people who had helped test his reasoning.
The next report was kinder in tone but not less demanding. Reviewers accepted the correction as addressing the identified gap and asked for a more complete explanation of how the finite boundary-state certificate could be verified independently. Kim helped set up a small program to enumerate the relevant states for test examples, while an external group checked the underlying mathematics without relying on the program. Okonkwo insisted that Elijah learn why the computer's answers agreed with his argument rather than treating a successful run as proof.