Cosmology has a formal microscope for broken symmetry, and it keeps finding smudges. The bipolar spherical harmonic (BipoSH) formalism generalizes the power spectrum: where the standard C_ell coefficients assume statistical isotropy and would miss its violation entirely, the BipoSH expansion measures correlations between different multipoles, the off-diagonal structure that any direction-dependent physics necessarily produces. A statistically isotropic sky yields zero in every BipoSH coefficient beyond the standard spectrum; the measured sky does not comply. The dipolar (L=1) BipoSH sector captures the hemispherical power modulation at its 2-to-3 sigma persistence; WMAP's quadrupolar (L=2) BipoSH detection famously dissolved into the satellite's non-circular beams, a cautionary instrument success; and Planck's residual BipoSH structure beyond the known systematics remains the formal statement that the sky's symmetry tests do not close cleanly.
The formalism matters because it removes the a-posteriori escape: where individual anomalies (a cold spot here, an alignment there) can each be accused of being noticed after the fact, BipoSH is the systematic, blind, complete decomposition of every way isotropy can fail, with the look-elsewhere accounting built in. ΛCDM's prediction in this language is unambiguous, every coefficient zero, so each persistent nonzero entry is a direct verdict rather than a curiosity, and the model's remaining defenses reduce to unmodeled systematics or the same chance that must also cover the anomaly family the coefficients formalize.
The standing is methodological maturity awaiting better data: the temperature BipoSH sector is measured to its cosmic-variance floor, the dipolar modulation persists in it, and polarization BipoSH from LiteBIRD-class missions is the designed instrument for deciding whether the symmetry violations are real physics with a preferred frame.