Did the Byzantine/Roman civilization end when the ottomans took over? Social organization changed, but not wholesale. social organization in which populations, Economic and political activity continued, concentrated in cities. Greek remained a major language, as did many Greek laws.

Incidentally, why was Rome/Byzantine civilization Greek speaking in anatolia? Because it had been Hellenised long before Rome conquered it. ..and language isn't everything. Before the Greeks were others, notably the hittites, a great civilization.

What I mean by arbitrary is that whether your chart shows continuity of a civilisation or not depends on how you define the term. One chart will show continuity from the bronze age to the present (or maybe until 1908). You could make that case. The cities mostly remaining occupied and the political organization probably had a lot of continuity. Another chart (like this one) will have Hittite, Hellenic, greco-roman, Byzantine, ottoman, etc. Civilisations lined up one after the other