What are the names of the books of Usul al-Fiqh considered authoritative in the Hanafi, Maliki, Shafi'i, and Hanbali schools of thought, and is what is considered authoritative that which is earlier, or that which is more knowledgeable, or wherever benefit is found?

There are many books on the Usul al-Fiqh (principles of Islamic jurisprudence). For the Hanafi school, these include: "Usul al-Sarkhasi," "Mizan al-Usul," and "Usul al-Bazdawi." For the Maliki school: "Al-Muwafaqat fi Usul al-Shari'ah" and "Maraqi al-Su'ud." For the Shafi'i school: "Jam' al-Jawami'" and "Al-Ashbah wal-Naza'ir." For the Hanbali school: "Rawdat al-Nazir" and "Sharh al-Kawkab al-Munir." In each school, what is considered most authentic and closely related to its rules is taken into account.