  We present long baseline Atacama Large Millimeter/submillimeter Array (ALMA)
observations of the 870$\,\mu$m dust continuum emission and CO (3-2) from the
protoplanetary disk around the Herbig Ae/Be star HD 100546, which is one of the
few systems claimed to have two young embedded planets. These observations
achieve a resolution of 4 au (3.8 mas), an rms noise of 66$\mu$Jy/beam, and
reveal an asymmetric ring between $\sim$20-40 au with largely optically thin
dust continuum emission. This ring is well fit by two concentric and
overlapping Gaussian rings of different widths and a Vortex. In addition, an
unresolved component is detected at a position consistent with the central
star, which may trace the central inner disk ($<$2au in radius). We report a
lack of compact continuum emission at the positions of both claimed
protoplanets. We use this result to constrain the circumplanetary disk (CPD)
mass and size of 1.44M$_{\rm Earth}$ and 0.44au in the optically thin and thick
regime, respectively, for the case of the previously directly imaged
protoplanet candidate at $\sim$55 au (HD100546 b). We compare these empirical
CPD constraints to previous numerical simulations. This suggests that HD100546
b is inconsistent with several planet accretion models, while gas-starved
models are also still compatible. We estimate the planetary mass as 1.65 M$_J$
by using the relation between planet, circumstellar, and circumplanetary masses
derived from numerical simulations. Finally, the CO integrated intensity map
shows a possible spiral arm feature that would match the spiral features
identified in Near-Infrared scattered light polarized emission, which suggests
a real spiral feature in the disk surface that needs to be confirmed with
further observations.
