We present the first results from the Fundamental Reference AGN Monitoring Experiment (FRAMEx), an observational campaign dedicated to understanding the physical processes that affect the apparent positions and morphologies of AGNs. In this work, we obtained simultaneous Swift X-ray Telescope (XRT) and Very Long Baseline Array (VLBA) radio observations for a snapshot campaign of 25 local AGNs that form a volume-complete sample with hard X-ray (14-195 keV) luminosities above $10^{42}$erg s$^{-1}$, out to a distance of 40 Mpc. Despite achieving an observation depth of $sim20$ $mu$Jy, we find that 16 of 25 AGNs in our sample are not detected with the VLBA on milli-arcsecond (sub-parsec) scales, and the corresponding core radio luminosity upper limits are systematically below predictions from the Fundamental Plane of black hole activity. Using archival Jansky Very Large Array (VLA) radio measurements, our sample jumps back onto the Fundamental Plane, suggesting that extended radio emission is responsible for the apparent correlation between radio emission, X-ray emission, and black hole mass. We suggest that this discrepancy is likely due to extra-nuclear radio emission produced via interactions between the AGN and host environment. We compare VLBA observations of AGNs to VLA observations of nearby Galactic black holes (GBHs) and we find a mass-independent correlation between radio and X-ray luminosities of black holes of $L_mathrm{6cm}$/$L_mathrm{2-10 keV}$ $sim$ 10$^{-6}$, in line with predictions for coronal emission, but allowing for the possibility of truly radio silent AGNs.
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