Physical measurements cannot definitively distinguish between geometries at human scales; curvature effects require astronomical or quantum observations with inherent measurement uncertainty.
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Physical measurements(as what abstract axioms are linked to)
Concrete data you collect by actually observing or testing something in the real world—like measuring distance with a ruler or timing something with a clock.
Quantum observations(as used in philosophy of science and physics)
Measurements of extremely tiny things like atoms and subatomic particles, which behave differently from everyday objects and are affected by the act of measuring them.