The Partition of Cosmological Tensions: Frame Artifacts, Local Structure, and Physical Residuals

We apply ξ-normalized coordinates (ξ ≡ dc / dH, where dH = c/H₀) to partition ten cosmological tensions into three distinct classes: (1) coordinate-frame artifacts arising from H₀-dependent measurement comparisons, (2) local-structure effects including the KBC void and bulk flows, and (3) genuine physical residuals requiring new cosmological physics. Across the full tension landscape — Hubble constant, matter clustering (S₈), baryon acoustic oscillations, lensing amplitude (AL), age, and Lyman-α forest — we find that ~93% of the H₀ tension is a frame artifact, 64% of the local-expansion anomaly is explained by the KBC void and bulk flow, and the strong-lensing H0LiCOW tension is fully accounted for by the mass-sheet degeneracy. The physical residuals converge on two signals: a matter density deficit (Ωₘ ≈ 0. 295, confirmed by DESI DR1) and an evolving dark energy equation of state (w₀ = -0. 634, wₐ = -1. 388, Δχ² = 4. 74). A multi-probe convergence test demonstrates that the DESI low-z BAO w₀ wₐ fit extrapolates to the Ly-α BAO at z=2. 33 within 0. 94σ, suggesting a coherent dark energy evolution signal across z = 0. 3–2. 3. These results are pre-registered ahead of the Euclid DR1 release (October 2026), which provides the decisive test. Manuscript: MN-26-0967-P (MNRAS, in press).