  Aims. To comprehend the efficiency of dust evolution within protoplanetary
disks, it is crucial to conduct studies of these disks using high-resolution
observations at multiple wavelengths with the Atacama Large
Millimeter/submillimeter Array (ALMA). Methods. In this work, we present
high-frequency ALMA observations of the HL Tau disk using its Band 9 centered
at a wavelength of 0.45 mm. These observations achieve the highest angular
resolution in a protoplanetary disk to date, 12 milliarcseconds (mas), allowing
the study of the dust emission at scales of 2 au. We use these data to extend
the previously published multi-wavelength analysis of the HL Tau disk. Results.
Our new 0.45 mm data traces mainly optically thick emission, providing a tight
constraint to the dust temperature profile. We derive maximum particle sizes of
$\sim$1 cm from the inner disk to $\sim$60 au. Beyond this radius, we find
particles between 300 $\mu$m and 1 mm. Moreover, an intriguing asymmetry is
observed at 32 au in the northeast inner part of the HL Tau disk at 0.45 mm. We
propose that this asymmetry is the outcome of a combination of factors
including the optically thick nature of the emission, the orientation of the
disk, and a relatively large dust scale height of the grains. To validate this,
we conducted a series of radiative transfer models using the RADMC-3D software.
If this scenario is correct, our measured dust mass within 32 au would suggest
a dust scale height H/R> 0.08 for the inner disk. Finally, the unprecedented
resolution allowed us to probe for the first time the dust emission down to a
few au scales. We observed an increase in brightness temperature inside the
estimated water snowline and speculate whether it could indicate the presence
of a traffic jam effect in the inner disk. Abridge
