A major challenge in the study of strongly correlated electron systems is to establish a firm link between microscopic models and effective field theory. Quite often, this step involves a leap of faith, and/or extensive numerical studies. For fractional quantum Hall model wave functions, there exists — in some cases — a scheme to infer the long distance physics of a state that is both compelling and simple, and leaves very little room for ambiguity. This scheme involves a local parent Hamiltonian for the state, which unambiguously defines a ``zero mode space’’ of elementary excitations,  and what’s known as a ``generalized Pauli principle’’. The latter efficiently organizes the zero mode space through one-dimensional patterns satisfying local rules.
Where this works, universal properties of the state unambiguously emerge from counting exercises in terms of these patterns, which efficiently encode degeneracies, quasi-particle types and charges, and which completely determine an edge conformal field theory. There is even a natural scheme to infer braiding statistics directly, for both Abelian and non-Abelian states. 

While for many interesting but mostly exotic fractional quantum Hall states a parent Hamiltonian description as advertised above exists, such Hamiltonian descriptions are sparse within the most important class of fractional quantum Hall states: Jain composite fermion states. This talk will provide the underlying reasons for this and present a formalism for composite fermions in Fock space that can be used to construct local, two-body parent Hamiltonians with proper zero mode counting for every (unprojected) Jain composite fermion state. Time permitting, applications to the non-Abelian Jain 221-state will also be developed under the general umbrella of ``entangled Pauli Principles’’.