We show that model states of fractional quantum Hall fluids at all experimentally detected plateaus can be uniquely determined by imposing translational invariance with a particular scheme of Hilbert space truncation. The truncation is based on classical local exclusion conditions, motivated by constraints on physical measurements. The scheme allows us to identify filling factors, topological shifts and clustering of topological quantum fluids universally without resorting to microscopic Hamiltonians. This prompts us to propose the notion of emergent commensurability as a fundamental property for many known FQH states, which allows us to predict families of new FQH state that can be realised in principle. We also discuss the implications of certain missing states proposed from other phenomenological approaches, and suggest that the physics of FQH effect could fundamentally arise from the algebraic structure of the Hilbert space in a single Landau level.A large number of fractional quantum Hall (FQH) states with distinct topological orders have been observed experimentally and proposed theoretically, ever since the surprising discovery of the quantised Hall conductivity at 1/3 filling factor [1, 2]. The physics of the FQH effect is mainly derived from the formation of an incompressible quantum fluid with a charge excitation gap, which could be realised at specific rational filling factors when a two-dimensional electron gas system is subject to a perpendicular magnetic field. We now understand that both Abelian and non-Abelian FQH states are likely observed in the experiments [1, 3]. In addition to the single component FQH states (e.g. the Read-Rezayi series [4,5]), there can also be multi-component or hierarchical states from the coexistence of more than one type of quantum fluids in a strongly correlated manner [6,7].There has been much development in the microscopic theories of the FQH effect since the first proposition of the Laughlin wavefunctions[2] and later on, the model Hamiltonians [8]. One major approach is the phenomenological formation of "composite fermions" (CF) with flux attachment [7], and the parton construction inspired from it [9,10]. It leads to the systematic construction of microscopic wavefunctions for almost all observed and proposed FQH states [11]. Another major approach is to exploit the rich algebraic structures of many-body wavefunctions in a single Landau level (LL) on genus 0 geometries (e.g. sphere or disk), leading to very efficient constructions of microscopic model wavefunctions with the Jack polynomial formalism [1,12,14,15]. The method is particularly useful for the Read-Rezayi (RR) series including the coveted non-Abelian states, revealing the particle clustering properties in an intuitive manner. The Jack polynomial formalism and the related techniques are also closely linked to the wavefunction constructions from parafermion correlators in conformal field theory (CFT) [4,5], and in contrast to the CF approach, in many cases model projection Hamiltonians can be found [16], o...