  In this work, we show that the same theoretical tools that successfully
explain other hydrides systems under pressure seem to be at odds with the
recently claimed conventional room temperature superconductivity of the
carbonaceous sulfur hydride. We support our conclusions with I) the absence of
a dominant low-enthalpy stoichiometry and crystal structure in the ternary
phase diagram. II) Only the thermodynamics of C-doping phases appears to be
marginally competing in enthalpy against H$_3$S. III) Accurate results of the
transition temperature given by ab initio Migdal-Eliashberg calculations differ
by more than 110 K to recently theoretical claims explaining the
high-temperature superconductivity in carbonaceous-hydrogen sulfide. A novel
mechanism of superconductivity or a breakdown of current theories in this
system is possibly behind the disagreement.

Superconductivity;Materials Science