{"record":{"author":{"account_ref":null,"orcid":null},"builds_on":[],"content_schema":"pubphys.content.revision/1","content_sha256":"ef9ede463b34abbe18cbbfa0d0fcf6ea52162441200608d4c87a93171d06233a","created":"2026-10-03T07:18:09Z","files":[],"origin":{"assisted_by":[],"kind":"seed"},"parents":["5475cf5dc5b1a72283d26dc95dc6e00d7ea4e00096a7c6492e409a1816eeb011"],"salt":"f1af5ccaa8749fc8d3d75460e90f4ff8ff11627330279aaa7bd888d28286e14b","schema":"pubphys.record/2","site":"pubphys.com","target":null,"type":"revision"},"content":{"answer_type":"identification","assisted_by":[],"external_id":"qft.positive-geometry.nonplanar-n4","kind":"well-posed","literature_status":"open","n":"1","parents":[],"plain":"The amplituhedron covers only the planar limit, where the number of colors is infinite. 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 integrands","topic_ref":"cd9a4680d5f7ad1dcd63b8f904c4272d3e5ac40ad4be46888c8f43e407804d79"},"attested":{"attestation":{"batch":null,"client_id":null,"id_token_sha256":null,"kind":"platform"},"record_hash":"1b0d1e5024b59c6b676e872cbeb19337c07e1b53185c20668ccc9c4f36013243","schema":"pubphys.attested/1"},"envelope":{"attested_hash":"6bfbd758bf36d1b2506a349566b37338b207840ffba577b8c3b44ea8372f9eb3","platform_signature":{"key_id":"c6afc19b31429869751f06879c75cd64ea92654423d15b44be775bf1310a60da","sig":"zhoLtxR6Fe4IB5UWFvO1NDDeRN1hUFj5herFPrWrV993LtRxQq3-ciVlvVdJWitGtRHYF1czuMNYpmNuPH8sAA"},"schema":"pubphys.envelope/1"},"record_hash":"1b0d1e5024b59c6b676e872cbeb19337c07e1b53185c20668ccc9c4f36013243","leaf_index":1937}