= Solution
The <cosmological principle> asserts that, after averaging over sufficiently large scales, the universe is spatially homogeneous and isotropic on constant-<cosmic time> slices. Homogeneity means no distinguished location; isotropy means no distinguished spatial direction. These are statistical large-scale statements, not assertions that individual galaxies, clusters or the <cosmic web> are uniform, and they do not require the universe to be unchanging in time.
The nearly isotropic <cosmic microwave background> is strong evidence for large-scale isotropy about us. Its dominant dipole is explained by our <peculiar velocity>; the much smaller residual fluctuations provide the seeds and record of <structure formation>, rather than invalidating the principle. Large-area galaxy and radio-source distributions and deep galaxy surveys support <statistical isotropy> and a tendency towards <statistical homogeneity> after smoothing beyond the strongly clustered scales. An approximately isotropic <Hubble flow> and broadly uniform background radiation supply complementary checks.
There is an important logical distinction: isotropy seen by one observer alone does not prove homogeneity. A spherically symmetric inhomogeneous universe centered on that observer could look isotropic. Combining the observations with the assumption that our location is not privileged, so comparable observers would see comparable large-scale isotropy, motivates the homogeneous <FLRW metric>. Selection effects, foregrounds, finite survey volumes and the fact that observations lie on our past light cone must be accounted for. \b[The evidence supports a large-scale statistical principle, not exact uniformity on every scale.]
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