Model-independent late-universe measurements of $H_0$ and ${\mathrm{\Omega }}_{\mathrm{K}}$ with the PAge-improved inverse distance ladder

The standard $\mathrm{\Lambda }\mathrm{C}\mathrm{D}\mathrm{M}$ model has encountered serious challenges and the $H_0$ tension has become more significant with increasingly precise cosmological observation. Meanwhile, inconsistencies in measurements of the curvature parameter ${\mathrm{\Omega }}_{\mathrm{K}}$ between different datasets also have emerged. In this work, we employ two global and cosmic age-based parameterizations, PAge and MAPAge, to perform model-independent measurements of the Hubble constant $H_0$ and ${\mathrm{\Omega }}_{\mathrm{K}}$ by utilizing the inverse distance ladder (IDL). To construct the PAge-improved IDL, we utilize the strong gravitational lensing (SGL), cosmic chronometers (CC), and gamma ray bursts (GRB) data to calibrate the latest DESI DR2 baryon acoustic oscillation data and DESY5 type Ia supernova data. Our analysis indicate that DESI+DESY5+SGL+CC+GRB gives $H_0=71.59\pm 0.94\mathrm{k}\mathrm{m}{\mathrm{s}}^{-1}{\mathrm{M}\mathrm{p}\mathrm{c}}^{-1}$ in the MAPAge model, reducing the $H_0$ tension to the $1.0\sigma$ level. Extending to MAPAge$+{\mathrm{\Omega }}_{\mathrm{K}}$ model, we obtain ${\mathrm{\Omega }}_{\mathrm{K}}=0.001\pm 0.038$, which suggests that current late-time data are consistent with a flat universe. Finally, the Bayesian analysis indicates that the present late-universe data provide weak to moderate evidence in favor of PAge and MAPAge relative to $\mathrm{\Lambda }\mathrm{C}\mathrm{D}\mathrm{M}$.