Single-field inflation's consistency relation forbids long-wavelength curvature modes from observably modulating small-scale power, and the sky keeps hinting at exactly that: the hemispherical modulation is formally a long-short coupling, the BipoSH off-diagonals and clustering-fossil searches return persistent 2-to-3σ structure, and the model must hold the fluctuation defense across the whole correlated family. The flagship mechanism forbids what the flagship dataset suggests.
The squeezed-limit theorem is the price of the model's simplicity: one field generating all perturbations decouples scales by construction. Any genuine coupling requires the model to abandon either single-field inflation or the observation, and the framework offers no native mechanism by which scales could legitimately know about each other.
SCT generates perturbations through a cascade whose stages are causally nested: each collision stage deposits power at its characteristic scale and sets the environment, density, geometry, deposition gradient, in which the next stage's smaller-scale structure forms (P36, P37). Long-short mode coupling is therefore not forbidden but mandatory: the largest deposit scales modulate the statistics of the smaller ones as a matter of construction, with the hemispheric gradient (P44) as the leading instance and the BipoSH structure as its formal expression. The consistency relation never held in this framework because the generating process was never a single field stretching independent modes; it was a hierarchy of events, each conditioning its descendants.
The coupling comes with discipline rather than freedom: its amplitude is tied to the same finite stage count that sets the spectral tilt (n_s = 1 - 1/L) and the non-Gaussianity floor (1/√N_coll), so SCT predicts weak, correlated, axis-aligned coupling at precisely the few-sigma persistence observed, not the large violations multi-field freedom permits. The cascade statistics are developed in Paper 3, From Chaos To Concordance Spectra, and Paper 4, From Chaos To Collisothermal Cosmogenesis (the stage-structure derivations), with the imprint geometry in Paper 8.
Two cascade premises convert a forbidden signature into a fingerprint with a budget: the coupling the theorem fears is the deposition history showing through.
Both directions cut: polarization-era squeezed-sector measurements (LiteBIRD, CMB-S4) finding all coupling statistics consistent with zero would erase the cascade's conditioning signature along with the anomaly family it explains, while a confirmed coupling far above the cascade budget, large, scale-free, or axis-free, would exceed what nested stages can produce and favor multi-field freedom instead. SCT requires the middle: weak, axis-aligned, family-correlated coupling that recurs in polarization.