Does sulfoxide H₂SO exist? The question Does H2SO or H2CO have a higher dipole moment? left me wondering whether $\ce{H2SO}$ has already been synthesized.

There are experimental evidences that both hydrogen thioperoxide $\ce{HSOH}$ (1) and  thiooxonium ylide $\ce{H2OS}$ (3) exist, whereas sulfoxide $\ce{H2SO}$, despite possessing global energy level lower than (3), is not [1]:


  The global minimum corresponds to hydrogen thioperoxide $\ce{HSOH}$ (1). The sulfoxide $\ce{H2SO}$ (2) is predicted to be $&gt; \pu{25 kcal/mol}$ higher in energy (relative to 1) and the thiooxonium ylide 3 is the least stable
  isomer $(&gt; \pu{34 kcal/mol}$ relative to 1). 




There were numerous theoretical investigations (ab initio) suggesting that (2) is possible, but one of the most recent ones I found [2] still claims there is no experimental evidences to support its existence.
One of the problems with its structure the paper [2] refers to is that predicted $\ce{S-O}$ bond is abnormally short (1.4749 Å) and the valence state of sulfur is too high.

It would be nice if someone could point me towards a reputable source proofing/refuting existence of (2).
Additionally, what would be the complete preferred name of $\ce{H2SO}$?
MarvinSketch generates quite an amusing one: oxidanethione.

References


Iraqi, M.; Schwarz, H. Experimental Evidence for the Gas Phase Existence of $\ce{HSOH}$ (Hydrogen Thioperoxide) and $\ce{SOH2}$ (Thiooxonium Ylide). Chemical Physics Letters 1994, 221 (5), 359–362. https://doi.org/10/ct4m2m.   
Denis, P. Theoretical Characterization of the $\ce{HSOH},$ $\ce{H2SO}$ and $\ce{H2OS}$ Isomers. Mol. Phys. 2008, 106 (21), 2557–2567. https://doi.org/10/dnrk2v.
This is not an answer to the question "can the sulfoxide be synthesized in significant yield" (and under which conditions). Instead, this is a "naive" prediction based on the data you provide and two assumptions: 


The predicted thermodynamic values in the articles you cite are accurate at $\pu{298 K}.$
The heat and entropy of formation of (2) and (3) from (1) are constant over $T.$  


From the references we can build a data table of energies and entropies relative to "the ground state" $\ce{HSOH}$ assuming the $\Delta G^\circ$ values correspond to $T = \pu{298 K}:$

$$\begin{array}{lccc}
\hline
\text{Compound} &amp; \Delta G/\pu{kcal mol-1} &amp; \Delta H/\pu{kcal mol-1}^* &amp; \Delta S/\pu{cal mol-1 K-1} &amp; K_\mathrm{eq}\\
\hline
\ce{H2SO} &amp; 25 &amp; 15.8 &amp; -31 &amp; 10^{-19} \\
\ce{H2OS} &amp; 34 &amp; 38.2 &amp; 14 &amp; 10^{-25} \\
\hline
\end{array}$$

I include the order of magnitude of the equilibrium constants $K_\mathrm{eq}$ only to illustrate their ludicrously small values (and these are upper estimates!).

Could you find a temperature that would make $\Delta G^\circ&lt;0$ for the reaction to $\ce{H2SO}$? The answer is no.  To see why we turn to the enthalpies. Since the reaction is endothermic you might hope that an increase in $T$ would help, but the accompanying entropy change is negative, so there is no way you can sufficiently increase the temperature to drive the reaction forward. The highest equilibrium constant you could hope for is $K_\mathrm{eq} = \pu{1.7E-7}$. 

Things are not so bleak for $\ce{H2OS}$: the reaction is also endothermic but the entropy change is positive. At about $\pu{2800 K}$ $K_\mathrm{eq} = 1,$ and if we increase $T$ sufficiently, we can crank up $K_\mathrm{eq}$ to any arbitrarily large value. 

This is of course not remotely exhaustive (therefore "naive") but hopefully a start to answering your question. 



* Quoting your second reference: 


  At the CCSD(T)/CBS limit and including corrections for scalar relativistic, spin orbit and core-valence correlation effects, the estimated enthalpies of formation are $\pu{−28.1 ± 1},$ $\pu{−12.3 ± 1},$ and $\pu{10.1 ± 1 kcal/mol}$ for $\ce{HSOH},$ $\ce{H2SO}$ and $\ce{H2OS},$ respectively.