  The origin of a compact millimeter (mm, 100-250 GHz) emission in radio-quiet
active galactic nuclei (RQ AGN) remains debated. Recent studies propose a
connection with self-absorbed synchrotron emission from the accretion disk
X-ray corona. We present the first joint ALMA ($\sim$100 GHz) and X-ray
(NICER/XMM-Newton/Swift; 2-10 keV) observations of the unobscured RQ AGN, IC
4329A ($z = 0.016$). The time-averaged mm-to-X-ray flux ratio aligns with
recently established trends for larger samples (Kawamuro et al. 2022, Ricci et
al. 2023), but with a tighter scatter ($\sim$0.1 dex) compared to previous
studies. However, there is no significant correlation on timescales of less
than 20 days. The compact mm emission exhibits a spectral index of $-0.23 \pm
0.18$, remains unresolved with a 13 pc upper limit, and shows no jet
signatures. Notably, the mm flux density varies significantly (factor of 3)
within 4 days, exceeding the contemporaneous X-ray variability (37% vs. 18%)
and showing the largest mm variations ever detected in RQ AGN over daily
timescales. The high amplitude variability rules out scenarios of heated dust
and thermal free-free emission, pointing toward a synchrotron origin for the mm
radiation in a source of $\sim$1 light day size. While the exact source is not
yet certain, an X-ray corona scenario emerges as the most plausible compared to
a scaled-down jet or outflow-driven shocks.}
