As for al-Baghawī’s dividing the ḥadiths of al-Maṣābīḥ into “ḥasan” and “ṣaḥīḥ,” intending by “ṣaḥīḥ” those found in the two Ṣaḥīḥs and by “ḥasan” those reported in the Sunan, this is incorrect, for the Sunan themselves contain ḥadiths that are ṣaḥīḥ, ḥasan, weak, and even munkar (rejected).
Subsidiary issues
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Al-Tirmidhī’s collection is the primary reference for identifying the ḥasan grade, and it was he who popularized the term. Manuscripts of his Jāmiʿ, however, differ in the wording he uses—ḥasan, ṣaḥīḥ, and the like—so you must carefully compare your copy with reliable exemplars and adopt the wording on which they agree. Another place to consult is the Sunan of Abū Dāwūd, for he himself said that within it he points out what is ṣaḥīḥ, what approximates it, and what is seriously weak, while whatever he leaves without comment is ṣāliḥ (acceptable). Hence, any ḥadith we find in his book left unqualified, and which no other dependable critic has explicitly authenticated or declared weak, is ḥasan in Abū Dāwūd’s view. As for the Musnad of Aḥmad ibn Ḥanbal, the Musnad of Abū Dāwūd al-Ṭayālisī, and other Musnads, they do not reach the rank of the Five Foundational Works and the like, such that one could argue from them and confidently rely on what they contain. Allah knows best.
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When a transmitter stands below the level of a meticulous ḥāfiẓ yet is widely known for truthfulness and uprightness, and his report comes to us through more than one strong chain, that report rises from the grade of ḥasan to that of ṣaḥīḥ. Allah knows best.