Does Asim from Zirr ibn Hubaysh, or only Al-Sulami, enter into the turuq and asaneed of Al-Shatibiyyah in the riwayah of Hafs from Asim? And do Uthman, Zayd, and Ubayy enter into it, or only Ali, may Allah be pleased with them?

The difference between qira'at (readings), riwayat (transmissions), and turuq (paths) is that any disagreement attributed to one of the seven Imams and unanimously narrated from him by his transmitters is a qira'ah. What is attributed to the one who took from the Imam, even if indirectly, is a riwayah. And what is attributed to the one who took from the rawi (transmitter), even if further down the chain, is a tariq.

Thus, Hafs's riwayah from Asim, through the Tariq al-Shatibiyyah and al-Tayseer, has one tariq, which is the tariq of Ubayd ibn al-Sabbah. Its sanad (chain of narration) for Hafs's riwayah from Asim is what Al-Dani mentioned: that Hafs read to his shaykh Abu al-Hasan, who read to Al-Hashimi, who read to Al-Ushnani, from Ubayd, from Hafs, from Asim. This sanad is called the tariq al-Shatibiyyah for Hafs from Asim.

What is above Hafs from his shaykh Asim is not called a tariq; rather, it pertains to the qira'ah of the rawi from his shaykhs. Asim read from Abu Abd al-Rahman al-Sulami, who read from Ali (may Allah be pleased with him), and from Zirr ibn Hubaysh, who read from Abdullah ibn Mas'ud (may Allah be pleased with him). Asim used to teach Hafs with the qira'ah of Ali ibn Abi Talib and teach Shu'bah with the qira'ah of Ibn Mas'ud. Therefore, Hafs's riwayah is not a complete representation of Asim's qira'ah but rather a part of it, because Asim taught Shu'bah with matters that differed from what he taught Hafs.