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Even a power-law improvement over straight-line growth is unproven.","posed_since":"","precise":"Self-avoiding walk on $Z^3$ with $n$ steps, uniform measure. Prove $\\langle \\mid w(n)\\mid^2\\rangle^{1/2} = n^{\\nu+o(1)}$ with $\\nu\\ \\text{approximately}\\ 0.5876$, or at least $\\langle \\mid w(n)\\mid^2\\rangle^{1/2} \\le n^{1-\\delta}$ for some $\\delta > 0$. Answer: a proof.","problem_ref":null,"references":"","settled_by":"A polynomial sub-ballistic bound, then existence of $\\nu$.","status_note":"Sub-ballistic behavior $o(n)$ is proven (Duminil-Copin and Hammond, 2013); in $d = 4$ weakly self-avoiding walk has proven logarithmic corrections (Bauerschmidt, Brydges and Slade).","title":"Endpoint-distance exponent of the 3D self-avoiding 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