The fragmentation of high-mass gas clumps and the formation of the accompanying accretion disks lie at the heart of high-mass star formation research. We resolve the small-scale structure around the high-mass hot core G351.77-0.54 to investigate its disk and fragmentation properties. Using the Atacama Large Millimeter Array at 690GHz with baselines exceeding 1.5km, we study the dense gas, dust, and outflow emission at an unprecedented spatial resolution of 0.06" (130AU at 2.2kpc). Within the inner few 1000AU, G351.77 is fragmenting into at least four cores (brightness temperatures between 58 and 201K). The central structure around the main submm source #1 with a diameter of ~0.5" does not show additional fragmentation. While the CO(6-5) line wing emission shows an outflow lobe in the northwestern direction emanating from source #1, the dense gas tracer CH_3_CN shows a velocity gradient perpendicular to the outflow that is indicative of rotational motions. Absorption profile measurements against the submm source #2 indicate infall rates on the order of 10^-4^ to 10^-3^M_{sun}_/yr, which can be considered as an upper limit of the mean accretion rates. The position-velocity diagrams are consistent with a central rotating disk-like structure embedded in an infalling envelope, but they may also be influenced by the outflow. Using the CH_3_CN(37k-36k) k-ladder with excitation temperatures up to 1300K, we derive a gas temperature map for source #1 exhibiting temperatures often in excess of 1000K. Brightness temperatures of the submm continuum barely exceed 200K. This discrepancy between gas temperatures and submm dust brightness temperatures (in the optically thick limit) indicates that the dust may trace the disk mid-plane, whereas the gas could trace a hotter gaseous disk surface layer. We conduct a pixel-by-pixel Toomre gravitational stability analysis of the central rotating structure. The derived high Q values throughout the structure confirm that this central region appears stable against gravitational instability. Resolving for the first time a high-mass hot core at 0.06 resolution at submm wavelengths in the dense gas and dust emission allowed us to trace the fragmenting core and the gravitationally stable inner rotating disk-like structure. A temperature analysis reveals hot gas and comparably colder dust that may be attributed to different disk locations traced by dust emission and gas lines. The kinematics of the central structure #1 reveal contributions from a rotating disk, an infalling envelope, and potentially an outflow as well, whereas the spectral profile toward source #2 can be attributed to infall.