No, I wouldn't say that GR stems directly from Mach's philosphy, although of course, Einstein was greatly influenced by his thinking. Relativity theory is very much about clocks and meter sticks and could have been arrived at without knowing about Mach's philosophy.
I am thinking of the application of philosphy leading directly to the setup of a specific experiment resulting in a single experimental result conforming to the philosphical idea. Very specific.
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Non sunt multiplicanda entia praeter necessitatem.
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