Late-time distance consistency and model-independent curvature inference with strong lensing, quasars, and galaxy clusters

Abstract: We revisit a late-time, model-independent distance-consistency framework that combines strong gravitational lensing systems (SGLS), ultraviolet/X-ray quasars (QSOs), and 38 Sunyaev--Zel'dovich/X-ray galaxy-cluster angular-diameter distances. The analysis focuses on systematics rather than on presenting a competitive curvature measurement. Starting from the 158-system SGLS catalog, we exclude 30 systems that violate the lensing-geometric requirement $D_{A,ls}/D_{A,s}&lt;1$ in the isothermal reference case $γ<em>{\rm lens}=2$, leaving a fixed 128-system SGLS parent sample for cross-matching with 1598 QSOs. A deterministic maximum-cardinality, minimum-mismatch one-to-one assignment yields 100 SGLS--QSO pairs at the nominal $Δd/d=5\%$ threshold. We propagate the measured X-ray flux uncertainties and the intrinsic QSO scatter, and, crucially, we include the full $38\times38$ covariance induced by using the same QSO distances in the kernel-smoothed cluster predictions. With $Ω_K\sim\mathcal{U}[-10,10]$, the joint posterior is $Ω_K=2.085^{+1.634}</em>{-1.103}$ (68\%; central 95\% interval $[0.269,6.028]$). We do not interpret the positive shift as evidence for an open Universe. \added{This positive posterior offset is driven by cross-probe calibration tensions, sample-assignment effects, and the cluster anchor; it cannot be attributed to the intrinsic spatial geometry of the Universe.} The SGLS+QSO data alone leave curvature essentially prior dominated, $Ω<em>K=0.70^{+6.33}</em>{-7.12}$, whereas removing only the off-diagonal cluster covariance moves the posterior to $Ω<em>K=5.21^{+2.46}</em>{-2.07}$. Thus the cluster anchor supplies most of the curvature constraining power and its covariance materially changes the posterior location.