Using sources I then had I identified this as the remains of a temple for Zeus Karios. However, I since found several references to it being something else. An article in a Brill publication (https://brill.com/view/book/9789004461277/BP000013.xml?language=en) confirms this: "The extent of construction activity in the town itself from this early period is largely obscured by the modern infrastructure. A glimpse came to light, however, in 2010: the monumental platform on Hisarbaşı hill, long considered the stylobate of the temple of Zeus Karios, was postulated by Frank Rumscheid as a proto-Maussolleion, based on similarity of architectural details with the Maussolleion in Halikarnassos. Clandestine excavations confirmed this, revealing spectacular subterranean chambers with some of the earliest vault architecture, painted walls, and a sculpted sarcophagus from the fourth century that surely belonged to one of the rulers. Like the Maussolleion in Halikarnassos, this major funerary monument was located at the heart of the new urban center." Indeed the whole is now presented as a mausoleum. About the column "The Menandros Honor Column is a Corinthian column erected in the 1st century BC in the middle of the eastern edge of the podium. It is an independent structure from the tomb. It was built by Menandros, the grandson of Euthydemos, the famous speaker and people's leader of the city of Mylasa." A good article is at https://www.hurriyetdailynews.com/kings-tomb-becoming-center-of-attraction-in-western-turkey-59653 As I mainly show the column (and the platform, but before the new finds) I use the local name, for "High nest", referring to the stork's nest on top.
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