Who are the Imams of Hadith criticism according to chronological order?

The critique of Hadith narrators and the verification of narrations began during the Rashidun Caliphate, as the Companions meticulously guarded against illusion and error. Abu Bakr and Umar, may Allah be pleased with them, used to verify the authenticity of reports and narrations. With the emergence of seditions and sects in the era of the Tabi'in (successors), the need to ascertain the authenticity of isnads (chains of narration) arose to preserve the noble Hadith. Efforts of great scholars like Muhammad ibn Sirin emerged, distinguishing between the Hadith of the Sunnis and that of the innovators. This effort continued by prominent imams such as Sa'id ibn al-Musayyab, al-Zuhri, Malik, Ibn al-Mubarak, then Yahya ibn Sa'id, Imam Ahmad, al-Bukhari, and Muslim, reaching al-Tirmidhi and al-Nasa'i. The science of al-Jarh wal-Ta'dil (discrediting and accrediting) expanded to critique narrators and isnads due to the increasing falsehoods and the proliferation of sects.