  We present microscopic, multiple Landau level, (frustration-free and positive
semi-definite) parent Hamiltonians whose ground states, realizing different
quantum Hall fluids, are parton-like and whose excitations display either
Abelian or non-Abelian braiding statistics. We prove ground state energy
monotonicity theorems for systems with different particle numbers in multiple
Landau levels, demonstrate S-duality in the case of toroidal geometry, and
establish complete sets of zero modes of special Hamiltonians stabilizing
parton-like states. The emergent Entangled Pauli Principle (EPP), introduced in
Phys. Rev. B 98, 161118(R) (2018) and which defines the ``DNA'' of the quantum
Hall fluid, is behind the exact determination of the topological
characteristics of the fluid, including charge and braiding statistics of
excitations, and effective edge theory descriptions. When the closed-shell
condition is satisfied, the densest (i.e., the highest density and lowest total
angular momentum) zero-energy mode is a unique parton state. We conjecture that
parton-like states generally span the subspace of many-body wave functions with
the two-body $M$-clustering property within any given number of Landau levels.
General arguments are supplemented by rigorous considerations for the $M=3$
case of fermions in four Landau levels. For this case, we establish that the
zero mode counting can be done by enumerating certain patterns consistent with
an underlying EPP. We apply the coherent state approach to show that the
elementary (localized) bulk excitations are Fibonacci anyons. This demonstrates
that the DNA associated with fractional quantum Hall states encodes all
universal properties. Specifically, for parton-like states, we establish a link
with tensor network structures of finite bond dimension that emerge via root
level entanglement.
