  A formalism is developed for the rigorous study of solvable fractional
quantum Hall parent Hamiltonians with Landau level mixing. The idea of
organization through "generalized Pauli principles" is expanded to allow for
root level entanglement, giving rise to "entangled Pauli principles". Through
the latter, aspects of the effective field theory description become ingrained
in exact microscopic solutions for a great wealth of phases for which no
similar single Landau level description is known. We discuss in detail braiding
statistic, edge theory, and rigorous zero mode counting for the Jain-221 state
as derived from a microscopic Hamiltonian. The relevant root-level entanglement
is found to feature an AKLT-type MPS structure associated with an emergent
SU(2) symmetry.
