Topological characterization of [0,∞)^* in some model

Determine whether there exists a model of ZFC in which the Cech–Stone remainder [0,∞)^* admits a Parovičenko-style topological characterization, i.e., an intrinsic topological description that uniquely identifies [0,∞)^* up to homeomorphism.

Background

Under CH, ω* has a Parovičenko-style characterization and serves as a universal compact zero-dimensional F-space of weight 𝔠 in the sense of continuous surjections. Dow and Hart showed that [0,∞)^* is universal among continua of weight 𝔠 (mapping onto) under CH, but no analogous topological characterization is known.

The authors explicitly highlight the uncertainty about whether such a characterization might hold in some (possibly different) model of set theory.