An assembly is provided for rotational equipment such as a gas turbine engine for an aircraft propulsion system. This assembly includes a stator, a rotor and a seal assembly. The rotor extends axially along a centerline. The rotor includes a linkage, a first rotor disk, and a second rotor disk. The linkage extends axially from the first rotor disk to the second rotor disk. The linkage is removably attached to the second rotor disk. The seal assembly is configured for sealing a gap radially between the stator and the linkage. The seal assembly includes a hydrostatic non-contact seal.