The Kitab al-Sab'a is dated with reasonable confidence to Baghdad in the early fourth century of the Islamic calendar, the tenth century of the common era, and its content, the seven readers it names and the readings it accepts, is documented in enough later citation and commentary that the shape of Ibn Mujahid's project is not seriously in doubt. His own biographical dates are a separate matter, and this atlas does not assert birth and death years for him that no source in its catalogue actually gives.
That gap is not unusual for a figure known almost entirely through a technical scholarly work rather than through a life story anyone troubled to narrate for its own sake. What survives of Ibn Mujahid is his professional act: a Baghdadi scholar of recitation, working among the other readers and transmitters of his generation, who wrote the book that settled a contested field into seven names. The scholarship this atlas draws on, the Encyclopaedia of Islam's account of the seven readings and a modern study of Ibn Mujahid's selection, both work from that same evidentiary base, his writing and its reception, rather than from an independent biographical record of his life.
An open question is recorded here rather than a guessed answer: what were Ibn Mujahid's own birth and death years, and what source or manuscript discovery would settle them. Until that is answered, the honest description of his life is the shape of the work he left rather than a timeline the sources do not actually support.