Not sure whether A.R stands for Antiquarian Remains or Archaeological Records, but The mentioned A.R sources/quotations  are directly taken from Archaeological Records of Archaeological Survey of India, 
(http://www.whatisindia.com/inscriptions/south_indian_inscriptions/volume_9/eastern_chalukyas.html)
Mainly from Eastern Chalukyas period and Kakatiya period inscriptions. These are not speculative but inscriped records.