What is the true meaning of Al-Tirmidhi's statement: "Hasan Sahih"? And what does he mean in the hadiths where he says: "Hasan Sahih Gharib" or "Sahih Gharib" or "Hasan Gharib"?

The interpretation of Imam Al-Tirmidhi's compound terminologies for critiquing the hadiths in his Jami' is a subject of disagreement among scholars. Sheikh Al-Islam Ibn Taymiyyah strived to clarify this terminology, stating: "As for hasan (good) in Al-Tirmidhi's terminology, it refers to what has been narrated through two channels, and there is no one in its narration accused of lying, nor is it shadhdh (anomalous) contradicting authentic hadiths." He addressed the objection regarding "hasan gharib" (good and rare) by explaining that it might be gharib because it was narrated by only one Tabi'i, but it was narrated from him through two channels, thus becoming hasan due to the multiplicity of its paths from that person, while being gharib in its origin. As for Sheikh Al-Albani, he stated that Al-Tirmidhi's combination of the terms "gharib" and "hasan" means that it is hasan li-dhatihi (good in itself), unlike "hasan" alone (which means hasan li-ghayrihi - good due to external corroboration), or "gharib" alone (meaning its isnad is weak).