Epistemological Weakness of CMB and Cosmological Redshift

The cosmic microwave background (CMB) at 2.7 K (peak 1.06 mm) is interpreted as radiation emitted at 3000 K (peak 966 nm) and stretched by the expansion of space over 13.8 Gyr. The standard derivation preserves blackbody shape via the FLRW scale factor a(t), but assumes empty space can act as a thermodynamic cooler and source of cosmological redshift. No laboratory experiment demonstrates this mechanism. Gravitational redshift is verified to 1% in the Pound-Rebka experiment with defined potential and energy exchange in time-invariant space; cosmological redshift has no equivalent potential and implies energy loss by a factor of 1100 without work, in tension with the first law. COBE, WMAP, and Planck confirm the final temperature and shape, not the cooling mechanism. Spatial flatness is compatible with time-invariant Euclidean space. Bijective analysis indicates that time as a fourth dimension lacks experimental support. Until direct experimental proof exists, CMB cooling and cosmological redshift remain mathematical invariances without a demonstrated physical mechanism.