Is it Hu Hai or Hu who died in Qin Dynasty written on the magma?

After Qin Shihuang ascended the throne, he tried every means to pursue immortality. Lu Sheng, an alchemist, knew Qin Shihuang's psychology and told him that there was a Penglai fairy mountain on the sea, where immortals with elixir lived. So Qin Shihuang sent Lu Sheng out to sea to look for Penglai Mountain, in order to get the elixir of life. When Lu Sheng came back, he told Qin Shihuang that he couldn't find the medicine for immortality, but he got a "fairy book" with a prophecy: "Hu Ye died in Qin." When Qin Shihuang saw it, he thought that the word "Hu" in divination refers to the Xiongnu, and ordered the general Meng Tian to lead a 300,000-strong army to northern expedition the Xiongnu, so as to save Qin from extinction and build the Great Wall of Wan Li to prevent barbarians from invading south. After the death of Qin Shihuang, Li Si and others revised the testamentary edict and made Hu Hai, the youngest son of Qin Shihuang, emperor of Qin Ershi. Qin Ershi's cruelty led to the demise of the Qin Dynasty and fulfilled the prophecy of "Qin's death". But "Hu" was not originally the "Hu" clan (Xiongnu) that Qin Shihuang thought, but his son "Hu" Hai.