We suggest a crucial direct-observational test for measuring distinction between the standard ΛCDM model and recently proposed phantom dark energy positive curvature cosmological model. The test is based on the fundamental distance–flux–redshift relation for general Friedmann models. It does not depend on the CMBR data, on the large-scale structure growth models, and also on the value of the Hubble constant H0. Our crucial test can be performed by future gamma-ray burst observations with THESEUS space mission and by using gravitational-wave standard siren observations with modern advanced LIGO–Virgo and also forthcoming LISA detectors.