Standard ΛCDM with single-field inflation predicts local-type primordial non-Gaussianity should be nearly scale-independent. CMB and LSS studies have weakly preferred scale-dependent or running f_NL to explain features such as suppressed small-scale power or environment-dependent clustering (LoVerde 2008; Becker 2012). The signal is hard to reconcile with strictly constant f_NL.
The standard model assumes inflation produces scale-invariant non-Gaussianity. A running f_NL(k) demands evolution in the underlying generation mechanism (multi-field inflation, time-dependent inflaton-potential features, etc.), none of which is parsimonious.
SCT replaces the hot-dense-center with a superluminal collision and the thermalized debris field. From this single change, f_NL is intrinsically scale-dependent because the cascade has a hierarchy of characteristic length scales, one per cascade generation. Different angular scales integrate over different numbers of cascade-stage events: largest scales (k < 0.01 Mpc⁻¹) sample only the few first-stage cascade events at Λ_max ≈ 5 Gpc (P22, P36, P55), while smallest scales (k > 1 Mpc⁻¹) sample many more daughter-stage events (P37).
The Central Limit Theorem applied stage-by-stage gives f_NL(k) on the order of 10⁻¹·⁵ at the largest scales, decreasing to roughly 10⁻³ at the smallest scales. The predicted running coefficient α_running ≈ +0.5 to 1.0 dex per decade in k captures the cascade-stage transition. Cascade termination (P38, P40) sets the lower-bound transition scale where the f_NL running flattens to a noise-like floor below the present-day quantum-scale cutoff.
The same M2 framework that produces the local f_NL signal (recid 78), the CMB bispectrum scale-dependence (recid 27), and LSS non-Gaussianity (recid 70) produces the f_NL running. Each is a different observational projection of the same finite-cascade origin. There is no need to invoke multi-field inflation or time-dependent inflaton features.
If precision Euclid + SPHEREx + LSST multi-tracer bispectrum analysis finds f_NL(k) is scale-invariant at the α_running = 0 level (no cascade-stage transition signature in the running), the M2 finite-cascade prediction is refuted. Equivalently, if the running is detected with the wrong sign (negative rather than positive, with smaller-scale f_NL exceeding larger-scale), the cascade-stage hierarchy interpretation fails.