Is Hajarul Aswad from paradise?

There are Sahih (authenticated) Hadiths about Hajarul Aswad (Black Stone) which is imbedded in the left corner of Holy Kaba near its door and which is accepted as the beginning point of tawaf (where pilgrims circle Kaba for seven times), that it is a stone from Paradise.

A hadith narrated by Abdullah bin Abbas states that Prophet Muhammad (peace be upon him) said, "This Black Stone has come down from Paradise, and it was whiter than milk. But sins and mistakes of mankind turned it black." (1)

Another hadith narrated in Musnad, The Black stone is from Paradise. It used to be whiter than snow, but mistakes of polytheists turned it black. (2)

On this matter, information is given in the book of History of Kaba and Mecca,

After Hazrath Adams descent onto earth from Paradise, God sent him a Paradise Tent by angels. Hajarul Aswad was in this Tent and used to glow like a white ruby.

While Hazrath Ibrahim was building Kaba along with his son Hazrath Ismail, he requested a stone from his son as a corner stone for Kaba. Hazrath Ismail looked for one but came back empty handed. In the meantime, Angel Gabriel brought a stone to Hazrath Ibrahim. When Kaba was destroyed after the Noahs Cataclysm, God entrusted Hajarul Aswad at the top of Abu Kubays Mountain and ordered to take it out when His friend (Hazrath Ibrahim) will entrusted to build Kaba. The stone that Angel Gabriel brought was white, but as it was mentioned in the Hadiths by the touching of polytheists; and according to some narrations because of the fires, it has turned black over the years. (3)

Abdullah bin Abbas explanation is as follows, The reason why God turned Hajarul Aswad black is because of mankind not to crave for Paradise ornaments. (4)

Sources:

1. At-Tirmidhi, Hajj:49.
2. el-Fethü'r-Rabbani, 12:26.
3. Ebû'l Veled el-Ezraki. Kabe ve Mekke Tarihi, s. 36-54.
4. Tuhfetü'l-Ahvezi, 3:617.