An intergalactic magnetic field stronger than 3×10^-13 G would explain the lack of a bright, extended degree-scale, GeV-energy inverse Compton component in the gamma-ray spectra of TeV-blazars. A robustly predicted consequence of the presence of such a field is the existence of degree-scale GeV-energy gamma-ray halos -- gamma-ray bow ties -- about TeV-bright active galactic nuclei, corresponding to more than half of all radio galaxies. However, the emitting regions of these halos are confined

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... and aligned with the direction of the relativistic jets associated with gamma-ray sources. Based on the orientation of radio jets, we align and stack corresponding degree-scale gamma-ray images of isolated Fanaroff-Riley class I and II objects and exclude the existence of these halos at overwhelming confidence, limiting the intergalactic field strength to <10^-15 G for large-scale fields and progressively larger in the diffusive regime when the correlation length of the field becomes small in comparison to 1 Mpc. When combined with prior limits on the strength of the intergalactic magnetic field, this excludes a purely magnetic explanation for the absence of halos. Thus, it requires the existence of novel physical processes that preempt the creation of halos, e.g., the presence of beam-plasma instabilities in the intergalactic medium or a drastic cutoff of the very high energy spectrum of these sources.