Yeah. The "proof" of theorem 2 being just a handwavy do the first proof again, but use Q_2 and normalize the result after each step to a simple fraction, which

Yeah. The "proof" of theorem 2 being just a handwavy do the first proof again, but use Q_2 and normalize the result after each step to a simple fraction, which will only increase c_1. That really sounds suspicious to me. Why not just solve this version directly with these changes. That should have been a more straightforward proof.