Using GPR-reconstructed angular diameter distances from DESI DR2 BAO and H0LiCOW time-delay lenses, the paper measures γ_PPN = 0.93^{+0.16}_{-0.17} and r_d = 136.36^{+5.14}_{-3.20} Mpc simultaneously without cosmological or gravity assumptions, consistent with GR within 1σ.
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Dynamical dark energy with perturbations reverses the alleviation of neutrino mass tension seen in smooth models, preferring smaller masses due to degeneracies in growth data from CMB, BAO, RSD, and supernovae.
No CMB-consistent CPL dark energy model can simultaneously fit both the BAOtr and DESI datasets; the 3.7-sigma disagreement at z=0.51 sets an irreducible floor.
ACT DR6 CMB lensing map gives σ8 = 0.819 ± 0.015 and H0 = 68.3 ± 1.1 km/s/Mpc, consistent with Planck ΛCDM but 1.7-2.1σ higher in S8 than KiDS, DES, and HSC galaxy surveys.
Pantheon+ delivers tighter SN Ia constraints on Ω_M, w0, wa, and H0 from 1550 events, consistent with a cosmological constant, with SN systematics contributing less than one third to H0 uncertainty.
KiDS-Legacy cosmic shear plus external probes yields S8 = 0.816 ± 0.006 in Lambda-CDM and consistent bounds on w0, wa, sum m_nu and Omega_K with no strong preference for extensions.
Union3 compilation of 2087 SNe Ia with UNITY1.5 framework shows 1.7-2.6 sigma tension with LambdaCDM and possible thawing dark energy.
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KiDS-Legacy: Constraining dark energy, neutrino mass, and curvature
KiDS-Legacy cosmic shear plus external probes yields S8 = 0.816 ± 0.006 in Lambda-CDM and consistent bounds on w0, wa, sum m_nu and Omega_K with no strong preference for extensions.