"That is a coincidence! The structures are only superficially similar—"
"It is the same generalization, Edward, with one substitution reversed and three variables renamed." Sullivan's voice was steady. "You wrote a problem on this board and told two hundred people you had been working on it privately for three years. You then asked one of your own undergraduates to solve it in front of witnesses, knowing the technique she would need was the technique she had already published." A pause. "And you sat on her thesis committee."
Walsh's face was white now, whiter than when he had seen the third substructure on the board. "This is a misreading. Anyone who actually reads the technical literature would see that my formulation is original."
"Original?"
The word came from Whitney. She had opened her eyes and turned away from the wall. She was standing at the side of the lecture hall looking at Walsh.
Walsh did not answer her. He turned to Sullivan instead. "Margaret, the terms of the demonstration still stand. She has not solved the third substructure. Let her finish. Let her prove she did not just memorize her own result."
Sullivan looked at Whitney. "Miss Tate, you do not have to continue."
Whitney walked back to the blackboard and picked up the chalk. "Dr. Sullivan, I would like to finish."
She turned to face Walsh. What did Whitney see in his face that made her decide to keep going?
Whitney turned to the third substructure. She picked up where she had left off: two lines were already on the board; she extended to a third. Her hand was steadier than it had been five minutes ago. She had Sullivan on her side now; the fraud had been named; the room understood what had happened.
But Walsh was still in the front row, watching every stroke of her chalk.
She wrote the fourth line, then the fifth, then the sixth.
On the sixth line, she made a mistake. It was a small mistake: a coefficient in the middle of a substitution—she dropped a factor of two. The kind of error a tired person makes when two hundred people are watching their hands. She didn't catch it. She wrote another line; the error propagated. She wrote one more.
Walsh stood up. "There!" He pointed at the sixth line. "There, right there! The technique fails! As I said in committee, the substitution doesn't generalize past a single parameter family!"