= Solution
The <cosmological principle> assumes statistical <spatial homogeneity> and <cosmological isotropy> on sufficiently large scales. <Spatial homogeneity> means that coarse-grained statistical properties do not depend on location; <cosmological isotropy> means that they do not depend on direction. The claim concerns a large-scale description, allowing individual <galaxies>, clusters and voids. It motivates the <FRW metric> and makes <cosmic expansion> describable by a single <scale factor> and a small number of matter variables.
Its adoption combines empirical large-scale regularity with the <Copernican principle>, the assumption that our location is typical. The resulting models provide a coherent account of <cosmic expansion>, the <cosmic microwave background> and primordial abundances. Neither the <Einstein field equations> alone nor <cosmological isotropy> around just one observer proves global <spatial homogeneity>: a <spherically symmetric> universe specially centred on that observer would also look isotropic. Observations of a finite <past light cone> support the principle over sampled scales without establishing it beyond the observed region.
Three supporting observations probe complementary aspects. First, after the observer-motion dipole and local foregrounds are removed, the <cosmic microwave background> is extremely isotropic, with intrinsic <temperature> fluctuations of order $10^{-5}$ and a nearly identical thermal spectrum across the sky. Second, suitably corrected all-sky counts of distant radio sources and extragalactic background intensities show no large preferred direction; Galactic obscuration and survey selection must be accounted for. Third, three-dimensional <galaxy> <redshift> surveys show that clustering and voids average toward statistically similar distributions in sufficiently large regions: large-volume number counts approach volume scaling and correlations weaken on large separation scales. The first two primarily test <cosmological isotropy>, while the third adds evidence for large-scale <spatial homogeneity>. \b[The principle is a well-supported large-scale working hypothesis whose observational and typicality assumptions remain explicit.]
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