It is noteworthy that I'm not sure if the 5th line can be found in any other book except the one of Suyuti.The tahqiq may be found in the any of the above books (especially Siyar of Dhahabi and Bidaya of Ibn Kathir), but the problem is
(1) I don't know Arabic to understand and (also because of that)
(2) I don't know, even if it's there, whether it's the tahqiq of that particular isnad or a general tahqiq of the ahadith with the matn.
Here a short first feedback:As you mentioned the 5th line seemingly only appears in the book of as-Suyuti, and it is a matter of discussion whether this line is part of it or was added (Mualla 'Ali al-Qari mentioned a slightly different wording of this line and an additional line or verse, while az-Zurqani discussed a second version of the 8th line which he claimed is not eloquent enough).
Note: As the sources of the text are provided in the original post I didn't add a link to the sources of my translated text quotes out of these.
Basically from my superficial first go through all the provided reports are narrated on the authority of the sahabi Khoraim ibn Aws at-Taaiy خريم بن أوس الطائي who actually converted to Islam after the battle of Tabook. Al-Hakim claimed that the narrators were 'Araab (Bedouins) and they can't be liars in this regard:
In the following I'll be translating from Arabic language as these translations are of my own take them with the necessary care!
هذا حديث تفرد به رواته الأعراب عن آبائهم وأمثالهم من الرواة لا يضعون
This hadith is unique to its narrators from Arabs of the desert from their fathers, and narrators of this kind do not (tend to) fabricate (hadith).
As-Suyuti in his al-La'ali' al-Masno'ah اللآلىء المصنوعة في الأحاديث الموضوعة confirmed that the hadith claiming that this poem was attributed to Hassan ibn Thabit is a fabrication and confirmed that this poem is of al-'Abbbas, saying (See here at the bottom and at the beginning of the following page):
مَوْضُوع: وَضعه بعضُ الْقصاص وهناد لَا يوثق بِهِ وَلَعَلَّه من وضع شَيْخه أَو شيخ شَيْخه والأبيات للْعَبَّاس بِلَا خلاف
fabricated: This was fabricated by some story tellers and Hannaad is not trustworthy. Perhaps it was one of his sheikh's fabrication or the sheikh of his sheikh. And the verses are for al-Abbas without any disagreement.
It should also be noted that the length of the report has differences for example the reports of abu Nu'aym and that of al-Khateeb al-Baghdadi mention an addition which at-Tabarani and al-Bayhaqi (via al-Hakim) for example mentioned as a stand alone hadith right after this report.
Note: Evil said this could be a kind of work around to make an unknown or a person who had only reported/narrated one hadith to a person who at least reported two or three ahadith or totally the opposite. But I don't know for sure and I don't want to spread anything false or malicious.
At this point we could say that the above qualifications mean that a-Dhahabi would regard the hadith as complied by al-Hakim as da'if. While al-Hakim accepts unknown narrators as mentioned in: Is there a scale or classification for scholars and their qualification of hadith narrators?
and therefore would regard the hadith as sahih.
The same may apply to al-Haythami's qualification of the hadith from at-Tabarni's al-Kabir, however I don't know al-Haythami's position on the topic of unknown narrators and narrators who have narrated only one or two hadith.
However many scholars regard him as rather lenient for example in qualification of narrators as those of both sahih or trustworthy etc. and for the fact that he may regard a narrator who is matrook or a fabricator only da'if and for his acceptance or agreement with the qualification of ibn Hebban on a rawy ibn Hebban was not sure about, meaning an unknown (which is also mentioned in above linked post where ibn Hebban hold the same position as al-Hakim in his method of qualification).
Having that said the hadith has at least a strong tendency to be weak.The following deeper analysis will only show that many trustworthy scholars have reported the hadith from these narrators who at least would have a level of doubt.
Imam az-Zurqani in his commentary on al-Mawahib al-Laduniya شرح الزرقاني على المواهب اللدنية بالمنح المحمدية commented on the Arabic language of this poem and in cases referring to different narrations came to the conclusion that some of the lines of some versions of the verses can't be from such a fluent and eloquent speaker as al-'Abbas (See here).
The hadith has been referred to by some other scholars like ibn al-Atheer in his an-Nihaya fi gharib al-Hadith النهاية في غريب الحديث والأثر in which he explained some words quoting a verse of the poem (see here, here and here).
There also seem to be an intersection in the content and a permutation of the order between this poem and one attributed to al-'Abbas ibn Mirdas العباس بن مرداس as claimed by a-Diwan and other pages sharing Arabic poetry such as adab:
وَأَنتَ لَمّا وُلِدتَ أَشرَقَتِ ال ...-... أَرضُ وَضاءَت بِنورِكَ الأُفُقُ
مِن قَبلِها طِبتَ في الظِلالِ وَفي ...-... مُستَودَعٍ حَيثُ يُخصَفُ الوَرَقُ
All this seems to show a huge confusion about an unknown rawy (narrator). However it seems the rawy is Zahr ibn Hisn زحر بن حصن and due to ignorance some people copied the name or falsely "corrected" it while copying the book. And this Zahr ibn Hisn was the uncle of the father of his narrator Zakariya ibn Yahya زكريا بن يحيى also known as abu as-Sukayn أبو السكين as is best explained by his full name as mentioned by abu Bakr a-Shafi'i and also to some extent by al-Bukhari in his a-Tarikh al-Kabir (See #1486 here).
As for his grand father حميد بن منهب Humayd ibn Munhib ibn 'Abd al-Barr denied that he was sahabi and said he narrated from 'Ali and 'Uthman. The hadith database pretends that he also narrated from the sahabah: the mother of believers 'Aishah, Khoraim -the narrator of our hadith who is his grand father-, Mua'awiya ibn abi Sufyan and 'Urwah ibn Mudarris at-Taa'i. None of the authors of the 6 books nor imam Malik reported via him.
So basically we have discussed both narrators which create an issue here none of these both is mentioned in any of the 6-7 main sunnah references among sunni scholars nor did they report any hadith on the authorithy of the sahabi reporting the hadith wed iscuss here `horaim ibn Aws at-Taa'i خريم بن أوس.
This again shows how lenient al-Hakim was as "the origin" of the report itself can't be claimed to be as of one of both sahihs unless one regards all sahabah as trustworthy -which is the view among sunni scholars- and accepts rather unknown narrators as trustworthy even if they are not narrators from both sahihs nor do scholars know much of them except with this and some more narrations.
These are not all the paths with which this hadith was transmitted, but all of them start from one of Zakaria ibn Yahya's (abu as-Sukayn) students: Ibn 'Asakir referred to two narrator chains one of them via Abu Bakr a-Shafi'i, while the second was transmitted via the student al-Qadi abu 'Ubayd 'Ali ibn al-Hussayn ibn Harb ibn 'Isa أبو عبيد علي بن الحسين بن حرب بن عيسى and both al-Hakim and his student al-Bayhaqi reported via a fifth path via abu al-Bakhtari.
Note that some scholars among them al-Hakim and others accused ibn Qutaybah's trustworthiness as a hadith narrator and others in his 'aqidah. Imam a-Dhahabi quoted their claims in his Siyar 'Alaam an-Nubalaa', but also informed the reader that none of them came up with proof nor could any of this be concluded from his work.Further note that the person who is reporting the book is one of ibn Qutaybah's sons most likely Ahmad (he is known to have memorized all his fathers books) who died 322 a.H..
It's isnad is weak due to unknowns.Please refer to these sources check the narrator section below and this use vpn for this. having a weak narrator, hence it might be safe to say this hadith is not authentic. Allah knows best.
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