Joint tSZ-kSZ power spectra show statistical tensions: kSZ power lower than expected given tSZ + cluster abundances; tSZ-kSZ correlation shows unexpected directional dependence; implied peculiar velocities from kSZ are systematically higher than ΛCDM structure-formation predictions (Hand 2012; Schaan 2016). The same density field + gravitational potential should produce consistent tSZ + kSZ signatures, yet observations suggest hotter, faster-moving, or differently distributed gas.
The standard model expects tSZ + kSZ joint statistics tracking standard CDM-halo + structure-growth predictions. Recovering observed deviations demands fine-tuned cluster gas physics + modified peculiar-velocity field, neither of which is parsimonious within minimal ΛCDM.
SCT replaces the hot-dense-center with a superluminal collision and the thermalized debris field. From this single change, tSZ + kSZ joint statistics come from cascade-thermalized + gravitational-superposition + frame-velocity signatures. The cascade collision energy regime (P22, P23) deposits cluster-progenitor matter with born-hot thermodynamics that supplies the cascade-thermalized initial pressure profile (recid 217 SZ power excess: cascade-deposited E_therm/E_vir ≈ 4.5).
The Plasma Equivalence Theorem (P29, P30) preserves the cascade-deposited thermodynamic + relativistic-plasma populations through cluster assembly. Gravitational superposition (P50, P51, P52) gives cluster-scale A ≈ 1.10 to 1.20 amplification (Paper 6 A6) that modifies the tSZ + kSZ scaling relations. Per recid 216: C_l^tSZ(SCT) = A^(-7/3) C_l^tSZ(ΛCDM) for tSZ amplitude; per recid 167 + recid 31: kSZ dipole has two-axis structure (kinematic + cascade-J component) that modifies expected kSZ statistics.
P57 large-scale-structure alignment (cascade-stream J coherence) gives the directional dependence in tSZ-kSZ correlations that ΛCDM cannot accommodate. Pre-existing matter (P25) provides cluster baryon heterogeneity. Cluster peculiar-velocity systematics include cascade-residual frame velocity contributions (P63, P64) on top of standard gravitational infall, naturally producing the observed higher implied velocities. The same M2 framework that resolves the y-distortion deficit (recid 26), the polarization-bump anomaly (recid 39), the ICM entropy floor (recid 126), the kSZ null hint (recid 166), the kSZ dipoles (recid 167), the tSZ power spectrum modifications (recid 216), the SZ power excess (recid 217), the tSZ scaling deviations (recid 219), and the broader cascade-thermodynamic cluster signatures accounts for tSZ + kSZ joint statistics.
If precision Simons Observatory + CMB-S4 + Athena tSZ + kSZ joint surveys find statistics fully consistent with ΛCDM CDM-halo + standard-structure-growth predictions at the 5% level (no cascade-thermalized + mesh + frame-velocity signatures), the M2 explanation is refuted. The signature SCT prediction is the joint tSZ + kSZ statistics matching cascade-deposited thermodynamic state + A factor + frame-velocity components.