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The challenge: provide a reasonable time-line that arrives at this geopolitical outcome c. 1900.
Clarifications:
1. Ignore the "new" continent in the Pacific. It doesn't exist, for the purposes of this timeline.
2. The burgundy polity in Anatolia, Thrace, and Egypt is the Byzantine Empire. The various small polities in the Levant are the Crusader States.
3. France must emerge as the leading world power, followed by Russian, then the British, although the latter would retain the world's largest navy.
4. The territory outlined in red is the Holy Roman Empire.