Breaking the Optical Depth Gravity Degeneracy: Scale-Dependent kSZ Velocity Profiles and Growth Friction in the \delta I Substrate

Abstract

Recent ACT DR6 measurements of the kinematic Sunyaev–Zeldovich (kSZ) effect provide a high‑precision test of gravity at 30–230 Mpc, confirming strict inverse‑square behavior (F ∝ r⁻²). We show that this force law emerges naturally as the sparse‑regime limit of the emergent correlation metric tensor gμν(x) = ∂μ∂ν[−ln(I/I₀)]|x'→x in the pre‑geometric SI‑substrate. We demonstrate that global substrate closure imposes strict, non‑divergent gradient bounds |∇I| ≤ Gmax, enforcing a physical peculiar‑velocity ceiling |v| ≤ 2500 km/s. Furthermore, the temporal drift of the correlation‑scale field ξ(t) generates a scale‑dependent cosmic growth friction term γξ = ξ̇/ξ that naturally suppresses large‑scale structure growth, resolving the S₈ tension without free parameters. By analytically fixing the peculiar velocity field V₁₂(r) from first principles, we break the fundamental optical‑depth/velocity degeneracy pₖSZ ∝ τV₁₂. This enables the first absolute, un‑degenerated reconstruction of cluster thermodynamic gas profiles. The observed kSZ momentum profiles are shown to be direct, non‑local signatures of the underlying correlation substrate.