I would endure it for myriad lifetimes
As your companion in practice"
--- Gandavyuha Sutra
The dates are obviously ideal or generalised and assume the late dating of the Buddha's parinirvāṇa.
As far as I know, all the schools which descend from the Mahāsāṃghika do have followers which 'did' follow the Bodhisattva path 'eventually.' All of the Mahāsāṃghika sects accepted to multiple degrees the doctrines of the Bodhisattvayāna, if not, eventually, the texts. I am completely ignorant as to whether Sautrāntikas or Mahāvaibhāṣikas had any Bodhisattvayana practitioners, but the other three Sarvāstivāda offshoots certainly do to my knowledge.
As for a full and specifically Mahāyāna tradition, if you go by Ch'an orthodoxy and take Bodhidharma to have founded Ch'an in c. 475, then that would be the first. None of the others prior are founded, to my knowledge, with specific intention of making an exclusive Mahāyāna school. Is not the general opinion on them that there would have been practitioners with many inclinations in each monastery within India? No clue.
But if you take the position that Ch'an is a later development, then T'an-luan's Pureland, Ching-t'u, tradition is certainly a specifically Mahāyāna school - where Pureland is for the attainment of Buddhahood specifically.
I'm probably mistaken in a number of places there, but I hope some of it moves the discussion forward. As for the issue of Bhiksunis and the Vinaya, I am ignorant.
Are there Vinayas which have any specific Mahāyāna content? Wouldn't that be what the answer to the question boils down to? Does an ordination using just a sutra count as an ordination in the regular sense? These seem to be very complex issues.
Edit: The file I uploaded before was over 3 pages and hard to read, I just attached one onto one page.
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The dates are, of course, all ideal and just works with the assumption that what information we do have about the schools from primary resources is correct - which we should not do if they are not corroborated, which most are not. The dates given are usually nice and round, which makes them more or less unlikely and conventional.
Date of the Buddha
Heinz Bechert's argument for the later date of the Buddha is more convincing to me. I.e. 85-105 (traditionally 100) years before Aśoka's coronation and 30-50 years before Alexander's arrival. Not only does the Ceylonese chronology claim to be incomplete itself, but it looks very unlikely that there would be more than 100 years of stasis in the Sangha. The patriarchs of other traditions, likewise, fit the late date easier if we assume they were not all living as long as biblical patriarchs (yet also assuming they are historical).
The Second and Third Council
Similarly, tradition holds that the second council occurred 100 years after Parinirvana, at the time of Aśoka's coronation. This makes sense, approximately, since the second council would have to occur prior to the third which is held to have occured 17 years into Aśoka's reign, i.e. 251 BCE. Aśoka apparently sent out the missions at this time, giving travel time, I took 250 as a likely date for the founding of the Tamraparnia, i.e. Ceylonese Vibhajyavada. Once again, taking tradition hook, line, and sinker. The Pudgalavada apparently break away around the same time as the Second council, but giving time for consolidation of the Sthaviravada, I set their date as slightly after, as for all of the Pudgalavada schools, I have no clue, Priestly doesn't even give dates for them, so I just ignored them.
The date for the Kasyapiyas is just taken from Warder's "Indian Buddhism." I don't know where he gets the estimate for the turn of the 2nd Century BCE, but assuming he is right, and I don't know of any reasons why he wouldn't, 200 BCE is what I chose to go with. Of course, there is dispute over whether the Kasyapiyas descend from Sarvastivada or Vibhajyavada. Just going with the Mahasangika perspective, which I trust over the Ceylonese due to vicinity, I went with Vibhajyavada - but I also linked it with light arrows to both Sarvastivada and Mahasangika because they apparently held doctrines which were familiar to those schools at the time as well - which may be the source of the mix up in the first place.
The information on these is very clear in the Sariputrapariprccha and Paramartha also provides some estimates. Taking these on face value, the organisation here is quite simple. The Lokottaravada, Ekavyaharikas and Gokulikas, according to Paramatha, all split away 200 years after the Buddha's Parinirvana, i.e. 168 BCE. They did this according to the degree to which they accepted new doctrines - though they all accepted the transcendental character of the Buddha.
Apparently the Bahusrutiya split away from the Gokulikas, according to the Dipavamsa, who initially rejected new doctrines, after having listened i.e. "srutiya" a lot "bahu" to one of the Buddha's arhats who had meditated for 200 years, awoke and told them that the new doctrines are different levels of revelation - obviously this is likely a later interpolation, but it's nice so I assumed it is also around the time of 168 BCE, but decided to not provide a date just to be safe. The Bahusrutiyas did develop an extensive Mahayana corpus, according to Paramartha and Vasumitra. The Prajnaptivada have doctrines very similar to the Bahusrutiyas, but I have no estimate for their date.
The Caitikas were formed 300 years after the Buddha's Parinirvana according to the Sariputrapariprccha, and it has four break aways, two early on, two later on. The Aparasailika and Uttarasailika both emphasised the transcendece of the Buddha, i.e. "beyond stone." The Rajagirikas and Siddharthikas' dates are both from Warder again. Apparently they were certainly 'transcendental' in tendency and considering when they developed, perhaps may have had something to do with particular tendencies in Mahayana at the time. They also "are said to have held that principles are not classified under other principles, nor conjoined with other principles, and that 'mental principles' ( caitasikas, i.e. the 'forces') do not exist." (313)
The Mahisasika and Dharmaguptika lineage is attested in all sources: Dipavamsa, Samayabhedo Paracana Cakra, Vinitadeva, Sariputrapariprccha and Chinese sources. The date of the Mahisasika is entirely my own estimate, but is based upon the fact that, according to Warder, the Dharmaguptikas flourished in Gandhara and Gujarat-Sindh in the 1st Century, and must have thus been developed, at the latest at the turn of the Millennium. Apparently the Mahisasikas may go back to the 2nd council, but I am not convinced, I think it is best to assume that they started to develop at the latest in the 1st Century BCE but then again, I am not sure to what degree the Dharmaguptikas are said to have developed out of them. If they developed as a full break away, an earlier date for the Mahisasikas is more likely, if they developed as the Mahisasikas were developing, then later.
As for the other Sarvastivada lineages, what I provided is pretty shaky. But going with the Macmillan Encyclopedia of Buddhism, the middle of the 2nd Century for the Sautrantikas and Vaibhasikas, and the beginning of the 3rd for the Mulasarvastivadins is what I found relatively satisfying for the sake of the diagram. I am aware that these three schools are the subjects of issues which are not completely clear as of yet, but it does agree with most primary sources on the question.
So there you have it. In order to get anything scientifically accurate this is the kind of thing which is worth a few years intense study. But for ease of thinking about what is likely to have occurred, I have found this layout more useful than no layout. Just like speech or the notion of "I," it may not exist in the real world, but exists to aid communication and make thinking about these issues generally an easier process.
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