Assemblies are provided for rotational equipment. One of these assemblies includes a bladed rotor assembly, a stator vane assembly, a fixed stator structure and a seal assembly. The bladed rotor assembly includes a rotor disk structure. The stator vane assembly is disposed adjacent the bladed rotor assembly. The fixed stator structure is connected to and radially within the stator vane assembly. The seal assembly is configured for sealing a gap between the stator structure and the rotor disk structure, wherein the seal assembly includes a non-contact seal.