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How paired electrons form an insulator, and what sets its conduction, is open.","posed_since":"","precise":"In amorphous InOx, TiN and nanopatterned Bi films on the insulating side of the field-tuned transition, $\\rho \\sim \\exp(T_{0}/T)$ with $T_{0}$ peaking at a field $B_{\\mathrm{peak}}$, the magnetoresistance peak spans several orders of magnitude, and patterned films show $h/2e$ periodic magnetoresistance (Stewart et al. 2007). Explain the pair-localization mechanism and $T_{0}(B)$, and determine whether abrupt current jumps in the $I-V$ curves reflect electron overheating (Altshuler, Kravtsov, Lerner and Aleiner 2009) or a distinct phase (proposed superinsulator).","problem_ref":"387c78650fe6ba2d48d45d84bf572342120c702dbd87fb90db1537ccf4db9a11","references":"","settled_by":"Electron-temperature measurement during nonlinear transport plus local probes of pair density in the insulator, compared with a theory of localized preformed pairs.","status_note":"","title":"Nature of the Cooper-pair insulator beyond the 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