Caodemarte wrote:Theravada histories and claims are that it derived from a sect that broke away from a sect that broke away from this faction (or "dissolved into" rather than "break away")
Why do you think so?
‘Some sub-divisions of Sthavira school which adopted this approach were regrouped and termed as the followers of Vibhajjavāda. Those not included in the Vibhajjavāda group were the Mahāsāṃghikas, Sarvāstivāda and Sammitīya, who were regarded as having the ‘wrong view’ by the Vibhajjavādins, according to the Theravadin Kathavatthu, a work ascribed to Moggaliputta Tissa.
The Theravada tradition holds that after the Third Council, the Vibhajjavādins evolved into four groups: the Mahīśāsaka, Kāśyapīya, Dharmaguptaka, and the Tāmraparnīya. Theravada is descended from the Tāmraparnīya, which means 'the Sri Lankan lineage'. On the other hand, some sources suggest that Mahīśāsaka, Kāśyapīya and Dharmaguptaka did not evolve directly from the Vibhajjavādins, although an original connection between these groups is posited due to the similarities of their respective Vinayas.
The Vibhajjavadins are claimed to have seen themselves as orthodox Sthaviras.
According to Sinhalese tradition, Buddhism under the name of Vibhajjavāda was brought to Sri Lanka by Mahinda, who is believed to be the son of Emperor Asoka, an event dated by modern scholars to 246 BCE.’
'Here the fundamental issue was the conception of time, the special Sarvastivadin doctrine being
that all dhammas past, present, and future, exist. The Sarvastivada schism produced, as well as
the Sarvastivada, another school sometimes called the Vibhajjavada, the 'Analytical School'. This
label is used widely and inconsistently, but it is convenient to use it here as a term for the school
ancestral to the Theravada and the Dharmaguptaka.'
A HISTORY OF MINDFULNESS
How Insight Worsted Tranquillity in the Satipatthana Sutta
It is important to remember that these were not necessarily hard and fast divisions, but rather often what appear to be, at least at first, groupings of rather vague tendencies. What did cause sharper divisions were, in my humble opinion, not ideas, but more likely lineage differences or over vinaya. Hence I like Skilton's ( and others') usage of Sthavira community or Sthavira rather than Sthaviravada which may be a back formation by Warder as pointed out in the H-Buddhism links.