What is the meaning of "bih" (به - with/by him) in the Hadith: "Indeed, a man reaches one hundred virgins in a single day," and is the article in which this Hadith was mentioned authentic?

There are two narrations regarding the number of women a man will be intimate with in Paradise. One is a Hadith from Ibn Abbas, which has a weak chain of transmission. The other is a Hadith from Abu Hurairah, which some scholars have authenticated due to the apparent soundness of its chain. However, some great Imams, such as Imam al-Daraqutni, Abu Zur’ah, and Abu Hatim al-Razi, considered the chain of Abu Hurairah's Hadith to be flawed and deemed it an error. If we assume the Hadith is authentic, then "one hundred virgins" refers to demonstrating a man's capacity for intercourse, and not necessarily one hundred wives. It has been narrated that a wife returns to being a virgin after every intercourse, and that a martyr will have seventy-two wives. The strength of intercourse in Paradise varies according to the variation in deeds and the guarding of desires in this world.