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

We apply ξ-normalized coordinates (ξ ≡ d_c / d_H, where d_H = c/H_0) to partition ten cosmological tensions into three distinct classes: (1) coordinate-frame artifacts arising from H_0-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 (S_8), baryon acoustic oscillations, lensing amplitude (A_L), age, and Lyman-α forest — we find that ~93% of the H_0 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 (Ω_m ≈ 0.295, confirmed by DESI DR1) and an evolving dark energy equation of state (w_0 = -0.634, w_a = -1.388, Δχ² = 4.74). A multi-probe convergence test demonstrates that the DESI low-z BAO w_0 w_a 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).