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Predicted repulsion across empty space, using magnetic, chiral or topological materials, has never been seen.","posed_since":"1974","precise":"Repulsive Casimir-Lifshitz force between two solid bodies across vacuum. Mirror-symmetric arrangements of identical bodies always attract (Kenneth-Klich theorem, 2006); repulsion is predicted for dielectric-magnetic pairs (Boyer, 1974), topological insulators with axion electrodynamics, and chiral metamaterials, but material dispersion usually restores attraction. An answer is a measured repulsive force with sign and magnitude matching Lifshitz theory for the measured permittivities and permeabilities, or a theorem that excludes repulsion for all passive materials at accessible gaps.","problem_ref":null,"references":"","settled_by":"A sphere-plate or plate-plate force measurement across vacuum showing a repulsive force at a given gap, reproduced by Lifshitz theory with independently measured material response.","status_note":"Repulsion has been measured only across fluids (Munday, Capasso and Parsegian, Nature 2009).","title":"Casimir repulsion between solid bodies separated by 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