We report the first weak-lensing detection of a large-scale filament funneling matter onto the core of the massive galaxy cluster MACSJ0717.5+3745. Our analysis is based on a mosaic of 18 multi-passband images obtained with ACS aboard the HST, covering an area of sim 10x20 arcmin^2. We use a weak-lensing pipeline developed for the COSMOS survey, modified for the analysis of galaxy clusters, to produce a weak-lensing catalogue. A mass map is then computed by applying a weak-gravitational-lensing multi-scale reconstruction technique designed to describe irregular mass distributions such as the one investigated here. We test the resulting mass map by comparing the mass distribution inferred for the cluster core with the one derived from strong-lensing constraints and find excellent agreement. The filament is detected within the 3 sigma detection contour of the lensing mass reconstruction, and underlines the importance of filaments for theoretical and numerical models of the mass distribution in the Cosmic Web. We measure the filaments projected length as sim 4.5 h_{74}^{-1} Mpc, and its mean density as (2.92 pm 0.66)10^8 h_{74} M_{odot} kpc^{-2}. Combined with the redshift distribution of galaxies obtained after an extensive spectroscopic follow-up in the area, we can rule out any projection effect resulting from the chance alignment on the sky of unrelated galaxy group-scale structures. Assuming plausible constraints concerning the structures geometry based on its galaxy velocity field, we construct a 3D model of the large-scale filament. Within this framework, we derive the three-dimensional length of the filament to be 18 h_{74}^{-1} Mpc, and a deprojected density in terms of the critical density of the Universe of (206 pm 46) rho_{crit}, a value that lies at the very high end of the range predicted by numerical simulations.
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