Urban Hermit@leon @ewen H. Beam Piper, 1950s and 60s SciFi author, wrote 1 book and a series of short stories in his "Paratime" series all with this exact plot. The first civilization to discover alternate probability time travel monopolizes the technology and colonizes all the time lines where humans never developed or went extinct, and manipulate more primitive cultures to exploit specific resources. Endless worlds sliced finely like pages in a book, with similar groupings around major global events.
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