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Abstract Capillary breakup of cores is an exclusive approach to fabricating fiber-integrated optoelectronics and photonics. A physical understanding of this fluid-dynamic process is necessary for yielding the desired solid-state fiber-embedded multimaterial architectures by design rather than by exploratory search. We discover that the nonlinearly complex and, at times, even chaotic capillary breakup of multimaterial fiber cores becomes predictable when the fiber is exposed to the spatiotemporal temperature profile, imposing a viscosity modulation comparable to the breakup wavelength. The profile acts as a notch filter, allowing only a single wavelength out of the continuous spectrum to develop predictably, following Euler-Lagrange dynamics. We argue that this understanding not only enables designing the outcomes of the breakup necessary for turning it into a technology for materializing fiber-embedded functional systems but also positions a multimaterial fiber as a universal physical simulator of capillary instability in viscous threads.