Open questions
One question, and what would settle it.
Which Indic script is the direct model for the Tibetan alphabet, and was it the work of one designer?
Why it is open. The script is plainly Brahmi-derived, but the candidates within that family are several and the letter forms have been argued both towards Gupta Brahmi transmitted through the Indian northwest and towards the scripts of Khotan and the Central Asian oasis towns. The traditional answer, a single minister trained in India, is first recorded four hundred years after the fact and cannot be tested against any imperial-period source.
What would resolve it. Dated inscriptions or manuscripts from the first century of Tibetan writing, compared letter by letter against securely dated Indic and Central Asian exemplars of the same decades. A palaeographic study of the earliest Tibetan hands against the Khotanese and northwest Indian corpora would narrow the model even if it never names a designer.
Field. Palaeography of the Brahmi-derived scripts, Old Tibetan philology, and Central Asian manuscript studies