Grading: (1) With this wording, from the hadith of Sa'id bin Jumhan, this narration is weak and munkar.
Technical note / Defect ('illah): In it, Nu'aym bin Hammad is "alone" in narrating it from Ibn al-Mubarak, and Nu'aym is not strong and has munkar narrations, and this is one of his munkar narrations. Also, Yahya bin Abd al-Hamid al-Himmani narrated it from Hashraj with this same wording (as will come later), and Yahya is weak, cannot be relied upon as proof, and is accused of stealing hadith. Al-Bukhari rejected this hadith of Safinah in "al-Tarikh al-Kabir" (3/117) and "al-Tarikh al-Awsat" (2/1046), and said: "Hashraj was not corroborated in it, because Umar bin al-Khattab and Ali (may Allah be pleased with them both) said that the Prophet (peace and blessings be upon him) did not appoint a successor."

Technical note / Defect ('illah): We say: The defect in it is not "Hashraj bin Nubatah", but rather the narrators below him, because a group of trustworthy narrators narrated it from Hashraj without this wording: such as Abu Dawud al-Tayalisi in his "Musnad" (1203), Abu al-Nadr Hashim bin al-Qasim in Ahmad (36/21928), Surayj bin al-Nu'man in al-Tirmidhi (2226), Ubayd Allah bin Musa in al-Tabari's "Sarih al-Sunnah" (26) and al-Bayhaqi's "al-I'tiqad" (p. 333), and Abu Nu'aym al-Fadl bin Dukayn in al-Tabarani's "al-Kabir" (6442).
Details of the narration: All of them narrated it with the wording: "The caliphate in my Ummah will last thirty (30) years, then there will be kingship after that." None of them mentioned "the story of the stones" in it, and this is what is mahfuz (preserved).
Corroborating chains: Hashraj was corroborated on this wording (the caliphate being thirty years) by al-Awwam bin Hawshab (Abu Dawud 4647, al-Nasa'i 8099), by Hammad bin Salamah (coming later with the author at no. 4487), and by Abd al-Warith bin Sa'id (coming later at no. 4748).

Reference / Source: As for the hadith of Nu'aym bin Hammad, it is in his book "al-Fitan" (no. 258).

Reference / Source: Al-Bayhaqi narrated it in "Dala'il al-Nubuwwah" (2/553), and through his route Ibn Asakir in "Tarikh Dimashq" (42/234), from Abu Abd Allah al-Hakim, with this same chain.

Reference / Source: Al-Harith bin Abi Usamah narrated it in "al-Musnad" (Bughyat al-Bahith 593), Ibn Abi Asim in "al-Sunnah" (1157), Abu Ya'la in "al-Musnad al-Kabir" (al-Matalib al-Aliyah 3817), Ibn Hibban in "al-Majruhin" (1/277), Ibn Adi in "al-Kamil" (2/440), al-Bayhaqi in "al-Dala'il" (2/553), Ibn Asakir in "Tarikh Dimashq" (171/39 and 44/233) and Ibn al-Jawzi in "al-Ilal al-Mutanahiyah" (331), through the route of Yahya bin Abd al-Hamid al-Himmani from Hashraj bin Nubatah.

Reference / Source: Ibn Adi (7/256), and through his route Ibn Asakir (39/116), narrated something similar through the route of Yahya bin Muhammad bin Yahya (the nephew of Harmalah), from Harmalah bin Yahya, from Ibn Wahb, from Ibn Lahi'ah, from Yazid bin Abi Habib, from Sa'id bin Amr, from Safinah.
Grading: Ibn Adi said: "I have written it only from this Yahya bin Muhammad", and he declared him weak.

Technical note / Defect ('illah): We say: One sign of his weakness is that he changed the wording of the hadith and named the narrator from Safinah as "Sa'id bin Amr", whereas this narration is known only from "Sa'id bin Jumhan" from Safinah.

Details of the narration: Something like this report of Safinah is also narrated from A'ishah (may Allah be pleased with her), as will come later with the author (no. 4583), but its chain is weak.

Details of the narration: This narration is also narrated from Qutbah bin Malik in Ibn Adi's "al-Kamil" (2/441).
Technical note / Defect ('illah): In its chain is "Muhammad bin al-Fadl bin Atiyyah", and he is a "kadhdhab" (liar).