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The quantum oscillation data from a whole variety of underdoped HTSC systemsand physical measurements has almost universally been presented in veryclassical terms following the Lifshitz-Kosevich formulation for Fermi-Landauquasiparticles, quantized into vortices and Landau levels under the highapplied magnetic fields. The Fermi surface always emerges as a very smallfraction of the large parent Fermi surface detected at higher doping. This thencalls for some Fermi surface reconstruction to have occurred, as from a chargeddensity wave, etc.. The paper refutes this reciprocal space approach, and showsthat many of the more recent detailed works taking this line are not consistentwith the data. The present author developed an alternative real-spaceinterpretation of these matters a couple of years ago. This was in terms ofinteraction of the vortex array with the stripe array, using a 2D modelling forthe latter. This approach has here been revised slightly and copes well withaddressing the wide variety of new data. The paper pursues and justifies theBEC/BCS, negative-U based, two-subsystem modelling advocated earlier, alongwith the strength and geometry of the striping acquired in a strong magneticfield. A wide variety of recent experiments are expounded to produce an overallappreciation of a situation far from being appropriately treated within aFermi-Landau quasiparticle framework. Indeed it is demonstrated that theuniversality of the 'QO' observations ensues from the fractional quantum Halleffect. The data all point to FQHE state with filling factor nu = 2/5. Thisstate in its genesis and expression finds a much greater alignment with theBEC/BCS crossover condition and the proximity of the HTSC materials toMott-Anderson localization than does any model for this highly correlatedmaterial appealing to well-metallized Fermi-Landau quasiparticle physics.

Underdoped cuprates, manifestations of boson-fermion crossover, `quantum oscillations' and the robust fractional quantum Hall state nu = 2/5