Sometimes, language presents evidence so clearly, you are kind of surprised that it works.
While working out the Aujila phonology, I ran into severe problems with Paradisi's transcription, which is incredibly precise on a phonetic level, but for phonological analysis is mostly a lot of unecessary clutter.
One of the sequences I had trouble dealing with was what Paradisi transcribes as <ōū> (which in the Italian tradition is used for a short diphthong, while <ōu> is used for a long diphthong, I swear I'm not making this up.), to make my system 'work'I needed it to be read as /əw/, while this is of course possible, but you have to bridge a gap from phonetics to phonology to actuall show it.
The proof I found presents itself in the verbal conjugation of Aujila. Aujila shares a tense with Siwa Berber which Lameen Souag calls 'relevance', I prefer to call it 'resultative', it is a derivation of the perfect, which expresses an action finished in the past, of which the result is evident or relevant in the present. To me the function seems to be almost identical to the Greek Perfect.
Despite Aujila and Siwa being quite different phonetically, somehow one of the two languages succesfully transfered this innovative tense to the other language. Citing from Lameen Souag's PhD thesis (pg. 389): "A feature of the system [...] is the marker -a; this is places at the end of the verbal word, following any subject or indirect object agreement markers or direct object pronominal suffixes. If the form to which it was suffixed would otherwise have ended in əC, the ə changes into i" (emphasis is my own)
The crazy thing is, the above description is just as valid for Siwa as it is for Aujila, including the i-insertion.
Because of this, the <ōū> = /əw/ correspondence can now be established clearly.
perfect. 3sg.m. yeddér /yəddə́r/'he lived'
resultative 3sg.m. yeddîra /yeddír-a/ 'he's lived (and the result of this is obvious/this is relevant to the present)'
perfect 3sg.f. terṓū /tərə́w/ 'she gave birth'
resultative 3sg.f. tirîwa /təríw-a/ 'she's given birth (and the result of this is obvious/this is relevant to the present)'
And there we have it <ōū> = /əw/.