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The outer atmosphere of the Sun is composed of plasma heated to temperatures well in excess of the visible surface. We investigate short cool and warm (<1 MK) loops seen in the core of an active region to address the role of field-line braiding in energising these structures. We report observations from the High-resolution Coronal imager (Hi-C) that have been acquired in a coordinated campaign with the Interface Region Imaging Spectrograph (IRIS). In the core of the active region, the 172 A band of Hi-C and the 1400 A channel of IRIS show plasma loops at different temperatures that run in parallel. There is a small but detectable spatial offset of less than 1 arcsec between the loops seen in the two bands. Most importantly, we do not see observational signatures that these loops might be twisted around each other. Considering the scenario of magnetic braiding, our observations of parallel loops imply that the stresses put into the magnetic field have to relax while the braiding is applied: the magnetic field never reaches a highly braided state on these length-scales comparable to the separation of the loops. This supports recent numerical 3D models of loop braiding in which the effective dissipation is sufficiently large that it keeps the magnetic field from getting highly twisted within a loop.