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Math sick or not, that detector (be it a ccd as you requested, or sagnac's photographic plates) is sitting on the turntable and is in the frame.
That the whole frame turns, and a non null result is recorded, indicates a universal frame.
obs1: emitter (in rotation with all mirrors)
obs2: result (photographic plate in rotation with all mirrors)
obs3: observer (not in frame)<-- introduced in your explanation. Not in experiment!
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