No manuscript survives in Omar Khayyam's own hand, and the earliest surviving ruba'i attributed to him were copied down decades, in some cases well over a century, after his death (1131), at a period when it had become a literary convention to attach anonymous or unattributed quatrains to famous names. Khayyam was known in his own lifetime chiefly as a mathematician and astronomer; the poetic reputation is a later accretion whose boundaries nobody can draw with confidence from the surviving evidence alone.
What would resolve this No plausible new manuscript evidence closer to Khayyam's own lifetime is expected to surface. Scholars broadly accept a small core of quatrains as plausibly his and treat the rest of the large attributed corpus as of uncertain or mixed authorship, a permanent interpretive question about medieval attribution practice rather than a fact-finding gap a future discovery would close.
OpenPersian philology and manuscript studiesThe Princeton Encyclopedia of Poetry and Poetics