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Open Access article, published by EDP Sciences, under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. ; We directly measured twenty overhanging cliffs on the surface of comet 67P/Churyumov-Gerasimenko extracted from the latest shape model and estimated the minimum tensile strengths needed to support them against collapse under the comet's gravity. We find extremely low strengths of around 1 Pa or less (1 to 5 Pa, when scaled to a metre length). The presence of eroded material at the base of most overhangs, as well as the observed collapse of two features and the implied previous collapse of another, suggests that they are prone to failure and that the true material strengths are close to these lower limits (although we only consider static stresses and not dynamic stress from, for example, cometary activity). Thus, a tensile strength of a few pascals is a good approximation for the tensile strength of the 67P nucleus material, which is in agreement with previous work. We find no particular trends in overhang properties either with size over the ~10-100 m range studied here or location on the nucleus. There are no obvious differences, in terms of strength, height or evidence of collapse, between the populations of overhangs on the two cometary lobes, suggesting that 67P is relatively homogenous in terms of tensile strength. Low material strengths are supportive of cometary formation as a primordial rubble pile or by collisional fragmentation of a small body (tens of km). ; his project has received funding from the European Union's Horizon 2020 research and innovation programme under grant agreement no. 686709. This work was supported by the Swiss State Secretariat for Education, Research and Innovation (SERI) under contract number 16.0008-2. The opinions expressed and arguments employed herein do not necessarily reflect the official view of the Swiss Government. OSIRIS was built by a consortium of the Max-Planck-Institut fur Sonnensystemforschung, Gottingen, Germany; the CISAS University of Padova, Italy; the Laboratoire d'Astrophysique de Marseille, France; the Instituto de Astrofisica de Andalucia, CSIC, Granada, the Universidad Politechnica de Madrid, Spain; the Department of Physics and Astronomy of Uppsala University, Sweden; and the Institut fur Datentechnik und Kommunikationsnetze der Technischen Universitat Braunschweig, Germany. The support of the national funding agencies of Germany (DLR), France (CNES), Italy (ASI), Spain (MEC), Sweden (SNSB), and the ESA Technical Directorate is gratefully acknowledged. We thank the Rosetta Science Operations Centre and the Rosetta Mission Operations Centre for the successful rendezvous with comet 67P/Churyumov-Gerasimenko.