The light cleared, and Mark stood alone on a platform suspended in a void. Stars—or were they numbers?—swirled around him, each pulsing with Numen. Lyra was gone, and the scholar's voice echoed from nowhere: "The Trial of Duality begins. Numbers are not singular; they are pairs, opposites, balances. Prove you understand."
A matrix appeared, glowing in the air:
Solve the system:
2x + y = 5
x – y = 1
Mark's mind raced. Systems of equations were rare in Numina's teachings, but he'd seen merchants use them to balance trades. Add the equations to eliminate y: 2x + y + (x – y) = 5 + 1, so 3x = 6, x = 2. Then, from the second equation: 2 – y = 1, so y = 1.
"x = 2, y = 1," he said.
The platform shuddered, and a bridge of light extended to a new chamber. But the scholar's voice returned, colder: "One half of duality. Now, face your opposite."
Lyra appeared across the void, standing on her own platform, her Seal blazing. A new system glowed before her:
3x – 2y = 7
x + y = 6
She solved it faster than Mark expected, her voice cutting through the void: "x = 5, y = 1." The Heart pulsed, and Numen surged into her Seal, matching his.
The scholar materialized between them. "Duality is balance. One cannot exist without the other. To claim the Heart, you must unite—or destroy."
Mark's throat tightened. "Unite how?"
The Heart projected a final system, larger, its symbols twisting:
4x + 3y = 10
2x – y = 0
"Solve together," the scholar said. "Or the Tower claims you both."
Lyra's eyes met Mark's across the void. "We can do this," she said, but her voice held an edge. "Multiply the second by 3, then subtract."
Mark nodded, working it in his head: 3(2x – y) = 3(0), so 6x – 3y = 0. Subtract from the first: (4x + 3y) – (6x – 3y) = 10 – 0, so -2x = 10, x = -5. Then, from the second: 2(-5) – y = 0, so y = -10.
"x = -5, y = -10," they said in unison.
The Heart roared, and the platforms merged, bringing them face-to-face. Numen swirled, binding their Seals in a shared glow. The scholar smiled. "United, you are stronger. But the Heart allows only one."
The chamber shook, and the Heart split, revealing two cores—one gold, one shadow. "Choose," the scholar said. "Or the Tower chooses for you."
Mark looked at Lyra. Her jaw was set, but her eyes were haunted. He couldn't let her lose—not after her brother. But the Heart was his dream.