The compact radio source Sagittarius~A$^*$ (Sgr~A$^*$)in the Galactic Center is the primary supermassive black hole candidate. General relativistic magnetohydrodynamical (GRMHD) simulations of the accretion flow around Sgr,A$^*$ predict the presence of sub-structure at observing wavelengths of $sim 3$,mm and below (frequencies of 86,GHz and above). For very long baseline interferometry (VLBI) observations of Sgr,A$^*$ at this frequency the blurring effect of interstellar scattering becomes subdominant, and arrays such as the High Sensitivity Array (HSA) and the global mm-VLBI Array (GMVA) are now capable of resolving potential sub-structure in the source. Such investigations improve our understanding of the emission geometry of the mm-wave emission of Sgr,A$^*$, which is crucial for constraining theoretical models and for providing a background to interpret 1,mm VLBI data from the Event Horizon Telescope (EHT). We performed high-sensitivity very long baseline interferometry (VLBI) observations of Sgr,A$^*$ at 3,mm using the Very Long Baseline Array (VLBA) and the Large Millimeter Telescope (LMT) in Mexico on two consecutive days in May 2015, with the second epoch including the Green Bank Telescope (GBT). We find an overall source geometry that matches previous findings very closely, showing a deviation in fitted model parameters less than 3% over a time scale of weeks and suggesting a highly stable global source geometry over time. The reported sub-structure in the 3,mm emission of Sgr,A$^*$ is consistent with theoretical expectations of refractive noise on long baselines. However, comparing our findings with recent results from 1,mm and 7,mm VLBI observations, which also show evidence for east-west asymmetry, an intrinsic origin cannot be excluded. Confirmation of persistent intrinsic substructure will require further VLBI observations spread out over multiple epochs.
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