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Finite numbers of colors require nonplanar diagrams, and no geometric shape for them is known.","posed_since":"","precise":"Find a region in a space of kinematic data whose canonical form (the unique differential form with logarithmic singularities on the region's boundaries) equals the subleading-color (nonplanar) or the full color-dressed $L$-loop four-point integrand of $N=4$ super-Yang-Mills; momentum twistors are unavailable because there is no planar ordering. Nonplanar integrands with only logarithmic singularities and no poles at infinity have been constructed at low loop order.","problem_ref":null,"references":"","settled_by":"An explicit geometry whose canonical form reproduces the known two- and three-loop nonplanar integrands and predicts higher loops.","status_note":"No geometry is known as of 2026.","title":"Positive geometry for nonplanar $N=4$ super-Yang-Mills loop 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