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Description: Critical taper theory permits the modelling of an orogenic wedge as a single mechanical entity. However, although shallow-crustal orogens dominated by brittle failure have been successfully modelled using critical taper, this remains controversial for major, ductile-failure-dominated orogens. In critical taper models, the steepness of the basal and upper orogenic surfaces defines the critical taper angle, dictates whether the orogen is supercritical, subcritical, or critical, and governs failure location during shortening. Here, we exploit a key prediction of critical taper: internally-shortening (subcritical) wedges must build topography. This promotes migration of the primary orogenic drainage divide toward the pro-foreland, shutting off sediment supply from the high-metamorphic grade orogenic core. We utilise the apatite and rutile U-Pb thermochronometers (temperature sensitivities of ca. 375-550 and 490-640 °C, respectively) to track Oligo-Miocene sediment supply to the pro-foreland of the central and western Alps. We show that the drainage connection to the high metamorphic-grade internal Alps was interrupted from ca. 26-25 Ma to ca. 19-16 Ma, which we link to divide migration caused by the out-of-sequence rise of the External Alpine crystalline massifs. This record of divide migration indicates subcritical wedge behaviour, and demonstrates that critical taper models are applicable to major, ductile-failure-dominated orogens such as the central and western Alps.