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In this paper we give an alternative proof of our recent result that totally unrectifiable 1-sets which satisfy a measure-theoretic flatness condition at almost every point and sufficiently small scales, satisfy Besicovitch's 1 2 -Conjecture which states that the lower spherical density for totally unrectifiable 1-sets should be bounded above by 1 2 at almost every point. This is in contrast to rectifiable 1-sets which actually possess a density equal to unity at almost every point. Our presentdoi:10.4171/rmi/310 fatcat:khj247yftvfc3p435ypqxru374