  Superperiodic conductance oscillations were recently observed in the
quasiparticle interferometer, where an edge channel of the 1/3 fractional
quantum Hall fluid encircles an island of the 2/5 fluid. We present a
microscopic model of the origin of the 5h/e flux superperiod based on the
Haldane-Halperin fractional-statistics hierarchical construction of the 2/5
condensate. Since variation of the applied magnetic field does not affect the
charge state of the island, the fundamental period comprises the minimal 2/5
island neutral reconstruction. The period consists of incrementing by one the
state number of the e/3 Laughlin quasielectron circling the island and the
concurrent excitation of ten e/5 quasiparticles out of the island 2/5
condensate. The Berry phase quantization condition yields anyonic quasiparticle
braiding statistics consistent with the hierarchical construction. We further
discuss a composite fermion representation of quasiparticles consistent with
the superperiods. It is shown to be in one-to-one correspondence with the
Haldane-Halperin theory, provided a literal interpretation of the 2/5
condensate as comprised of an integer multiple of two-composite fermion,
one-vortex blocks is postulated.
