Is there any scholarly consensus regarding which of these hypotheses is correct?
There is a gap of fifteen centuries between the demise of Indus script, and the origin of Brahmi script. More, Indus Valley script remains undeciphered despite the corpus of literature written in Brahmi script.
On the other hand, there are substantial and irreconcilable differences between Kharosthi, which was based on Aramaic, and Brahmi. The most current consensus, according to Amalia E. Gnanadesikan in his book "The Writing Revolution: Cuneiform to the Internet" is that it is a result of stimulus-diffusion; the idea of an alphasyllabary script from the middle-east by way of Iran influenced the creation of Kharosthi directly, and Brahmi indirectly, where it was created from scratch to serve as a more suitable vehicle for Prakit than any of the other contemporary writing systems. This is a common way for writing systems to come into existence, the most recent example of this in widespread use being Inuktitut.
As per my knowledge, Brahmi Script is developed from Indus valley script. The facts supporting this point are: 1. The earliest known script is found on the pottery remains of Harappa and across various parts of the world which dates around 1000 BCE to 500 BCE. and, These scripts resembles to Tamil language (Which is also a part of Indus language family) of that time. 2. Iravatham Mahadevan one of the prominent research scholar in languages has given various proof that the Brahmi language originated from Tamil. 3. Research work by Richard Salomon also states that its most likely that Brahmi originated from Tamil. 4. The archeological evidences found in Kodumanal, Chennimalai near Erode (500 BCE). Porunthal site, Palani (500 BCE). Tissamaharama, Sri Lanka (200 BCE). Tirupparankundram hill, Madurai (1 BCE). Quseir-al-Qadim, Egypt (1 BCE) suggest that the script is Tamil Brahmi script.
Based on the above facts my belief is that Brahmi is a form of Tamil which is widely in use during 500 BCE. So,this leads me to a conclusion that Brahmi is developed from Indus valley script.
Source/Further Reading 1. Corpus of Tamil-Brahmi inscriptions by Iravatham Mahadevan 2. Akam and Puram : ‘Address’ Signs of the Indus Script by Iravatham Mahadevan 3. http://www.hindu.com/2007/11/21/stories/2007112158412400.htm 4. Indian Epigraphy: A Guide to the Study of Inscriptions in Sanskrit, Prakrit, and the other Indo-Aryan Languages by Richard Salomon 5.Tamil litrature by Kamil Zvelebil