The higher non-Gaussian moments are unconstrained territory: Planck gives g_NL = (-5.8 +/- 6.5) x 10⁴, tau_NL below 2800, and essentially no constraint on the running of f_NL. Single-field inflation predicts undetectably small values, multi-field models populate the entire accessible plane, and no standard-model variant commits to what the cumulant hierarchy must be. The sector that could discriminate mechanisms has no ΛCDM entry to test.
The model delegates the entire higher-point sector to an unspecified inflaton landscape, so g_NL, tau_NL, and n_fNL are free functions rather than predictions. A framework with adjustable potentials can match any measured hierarchy after the fact, which means it risks nothing in advance.
SCT replaces the hot-dense-center with a cascade of order 10⁴ collision events (P36, P37, P38), and the full statistical hierarchy follows from one counting rule: each higher connected cumulant of a sum of N independent deposits is suppressed by a further power of 1/√N. The bispectrum residual gives |f_NL| of about 10⁻²; the trispectrum sits one rung down, with g_NL-type amplitudes of order 1/N_coll, about 10⁻⁴ in the same normalization, and tau_NL pinned near its Suyama-Yamaguchi floor of (6 f_NL/5)² because the cascade adds no multi-source coupling beyond the shared event count. The hierarchy is rigid: no member can be large while another is small.
The running is equally fixed: each cascade stage deposits at its own scale with its own event count, and the largest scales were built by the fewest events, so every cumulant drifts gently upward toward small wavenumbers with a running set by the stage spectrum, the same 1/L structure that tilts the power spectrum. One mechanism therefore commits, in advance, to the amplitudes, the hierarchy, the inequality saturation, and the sign of the running, a full multi-observable target where ΛCDM offers a landscape.
This is the same counted cascade that fixes n_s, f_NL, the isocurvature suppression, and r below 10⁻⁵: six locked predictions from one event count, none adjustable.
Multiple registered kills. A detected tau_NL significantly exceeding its (6 f_NL/5)² floor implies multi-field-style couplings the cascade lacks. A measured |g_NL| above the 1/N_coll scaling, or any cumulant detection requiring N_coll below a few hundred, contradicts the event count the spectral tilt demands. And a confirmed running of f_NL with the wrong sign, decreasing toward large scales, inverts the stage-count structure and falsifies the cascade statistics outright. CMB-S4 and SPHEREx test all three.