A crucial test of the phantom closed cosmological model
  We suggest a crucial direct-observational test for measuring distinction
between the standard $\Lambda$CDM 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 $H_0$. 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.
