Short answers, pulled from the story.
Babur emerged as the founder of an empire that traced its roots to Timur, a Turkic conqueror born in Kesh near Samarkand around 1336. This ruler also went by the name Timur Leng and controlled vast territories across what is now Turkistan by 1369.
Babur carried bloodlines that extended directly back to Genghis Khan through his son Chagatai Khan. Historical sources confirm that Babur was not merely a distant relative but a direct descendant of the great Mongol leader.
Timur solidified dynastic ties by taking Saray Mulk-khanum into his harem after defeating Husayn of Balkh's army in 1370. She was the daughter of Qazan, who served as the last Chaghatai Khan of Mawarannah before her marriage.
For the remainder of his life, Timur referred to himself as Temür Gurgan, meaning son-in-law of the Great Khan. This union linked him directly to the lineage of Genghis Khan through his wife's family line.
Such genealogical ties were crucial for legitimizing rule among Turco-Mongol peoples of the era. The identification of the Mughals as Mongol successors persisted even as such distinctions grew less common over time.