  We show that model states of fractional quantum Hall fluids at all
experimentally detected plateau can be uniquely determined by imposing
translational invariance with a particular scheme of Hilbert space truncation
motivated from physical local measurements. The scheme allows us to identify
filling factors, topological shifts and pairing/clustering of topological
quantum fluids unambiguously in a universal way without resorting to
microscopic Hamiltonians. This prompts us to propose the notion of emergent
commensurability as a fundamental property for at least most of the known FQH
states, which allows us to predict if a particular FQH state conforming to a
set of paradigms can be realised \emph{in principle}. We also discuss the
implications of certain missing states proposed from other phenomenological
approaches, and suggest that the physics of fractional quantum Hall physics
could fundamentally arise from the algebra of the Hilbert space in a single
Landau level.
