Abstract: One of the enduring questions in the study of strongly correlated electrons is how to read the universal, long-distance physics directly from a microscopic Hamiltonian. In fractional quantum Hall systems, certain solvable models achieve this through generalized Pauli principles—local rules that organize their zero-energy excitations and encode the essential topological information of the phase, much like a strand of DNA encodes the blueprint of an organism.

I will discuss how this organizing principle can be extended beyond the familiar holomorphic setting to more complex composite-fermion and parton states, where entangled Pauli principles emerge. These developments point toward a broader and more constructive framework for understanding and building solvable models of topological matter.