The BipoSH formalism is the complete, blind decomposition of every way statistical isotropy can fail: ΛCDM predicts zero in every coefficient beyond the standard spectrum. The measured sky declines: the dipolar sector carries the hemispherical modulation at its stubborn 2-to-3σ, and residual structure persists beyond the systematics that famously explained WMAP's beam-induced quadrupolar detection. In the one language with look-elsewhere built in, the symmetry tests do not close.
Isotropy enters the model as an axiom of the generating mechanism, so the entire BipoSH sector is forced to zero with no parameter to adjust. Any persistent coefficient is therefore a verdict the model can only appeal on grounds of systematics or chance, and the formalism exists precisely to make those appeals expensive.
SCT does not negotiate with the formalism; it predicts work for it. A patch deposited by an oriented collision has a physical preferred frame, the collision axis and its inherited J (P48, P31), and direction-dependent deposition necessarily populates the off-diagonal correlations BipoSH measures: the dipolar sector carries the deposition gradient (the hemispherical modulation, derived at the observed 7 percent), the alignment family appears as the corresponding low-L structure, and the formal completeness of the decomposition becomes an asset, since one oriented event makes correlated predictions across coefficients rather than scattered curiosities. Where ΛCDM requires every entry zero, SCT requires the specific pattern of one axis read through the BipoSH lens, with everything sub-horizon staying clean (P29, P30).
The framework inherits the formalism's discipline willingly: correlated coefficients, a common axis recoverable from the L=1 and L=2 sectors jointly, and recurrence in polarization, the signature chance cannot produce twice. The imprint structure is developed in Paper 8, From Chaos To Constructive Relativity, with the unified large-angle amplitudes in Paper 11, From Chaos to Covariant Completeness.
Two premises hand the microscope its subject: a deposition with a direction, and the inheritance that preserves it. The smudges are fingerprints.
The formal kill: polarization BipoSH from LiteBIRD or CMB-S4 measuring the full sector consistent with zero, no recurrence of the dipolar modulation, no common axis across coefficients, would falsify the preferred-frame deposition and certify the temperature-era structure as systematics plus chance. Conversely, coefficients recurring in polarization with mutually inconsistent axes would break the one-event reading while keeping isotropy violated, the worst world for both frameworks.