Planet X revamped after the discovery of the Sedna-like object 2012 VP$_{113}$?

Abstract: The recent discovery of the Sedna-like dwarf planet 2012 VP${\rm 113}$ by Trujillo and Sheppard has revamped the old-fashioned hypothesis that a still unseen trans-Plutonian object of planetary size, variously dubbed over the years as Planet X, Tyche, Thelisto, may lurk in the distant peripheries of the Solar System. This time, the presence of a super-Earth with mass $m{\rm X} = 2-15m_{\oplus}$ at a distance $d_{\rm X}\approx 200-300$ astronomical units (AU) was proposed to explain the observed clustering of the arguments of perihelion $\omega$ near $\omega \approx 0^{\circ}$ but not $\omega\approx 180^{\circ}$ for Sedna, 2012 VP${\rm 113}$ and other minor bodies of the Solar System with perihelion distances $q>30$ AU and semimajor axes $a>150$ AU. Actually, such a scenario is strongly disfavored by the latest constraints $\Delta\dot\varpi$ on the anomalous perihelion precessions of some Solar System's planets obtained with the INPOP and EPM ephemerides. Indeed, they yield $d{\rm X}\gtrsim 496-570$ AU ($m_{\rm X}=2m_{\oplus}$), and $d_{\rm X}\gtrsim 970-1111$ AU ($m_{\rm X} = 15 m_{\oplus}$). Much tighter constraints could be obtained in the near future from the New Horizons mission to Pluto.