Local small-scale power varies with large-scale environment, direction, and location more strongly than the Gaussian separate-universe response predicts (Chiang 2014; Barreira 2019). The standard response function is not adjustable, so a genuine excess means extra primordial couplings or growth that differs from place to place, and the model permits neither.
The model computes one response: a long-wavelength overdensity modifies local growth exactly as a slightly curved homogeneous background would, identically everywhere, with Gaussian initial conditions contributing no further coupling. Growth is the same physics in every environment by construction, so position dependence beyond the calculated response has no home.
SCT breaks the assumption directly: growth is not the same physics in every environment. The keystone is the expansion side: Λ_eff(x,t) varies with environment at the canonical one-percent level on 100 to 300 Mpc scales (P17, P19), so the effective background each sub-volume's structure grows against genuinely differs, adding environmental response beyond the separate-universe calculation. That alone is the anomaly: an environment-dependent effective background breaks the separate-universe response by construction, and position-dependent power is the statistic a dynamical Λ_eff was built to light up.
Two labeled secondary modulations ride on top: the coherent superposition mesh (P50, P52) amplifies growth where comoving coherence is high, coupling local power to the large-scale velocity environment in a way no linear bias absorbs, and the cascade origin leaves a small primordial coupling at the registered f_NL of order 10⁻² from N_coll ≈ 10⁴ independent collision events (P36, P37), far below the environmental terms but with a definite squeezed-limit signature. The growth-side structure is laid out in Paper 14, From Chaos To Cosmic Expansion, and the superposition formalism in Paper 11, From Chaos to Cosmic Collisions. The same keystone carries the S₈ sector and the ISW landscape (recid 67); this statistic simply reads it at sub-volume resolution.
DESI, Euclid, and SPHEREx sub-volume response measurements carry the kill: if the position-dependent power response matches the Gaussian separate-universe prediction at the percent level in every environment and direction, with no correlation between response excess and sightline density structure, the environment-dependent growth of M5 and the coherent-mesh amplification of M6 are both refuted in this sector. SCT requires the response to carry the Λ_eff geography; a universal response function ends that reading.