{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:NZ7HVI4IOEPJAPAP7BNIZESFSM","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"be2c2ce4e0d7de73eac2a990802ee8a5e1f685077abe0494079785babc47e145","cross_cats_sorted":["math.AG","math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2012-12-21T21:00:02Z","title_canon_sha256":"28ea7667df0053de12ff5f702e0ded1e8b87cf3c43018fcdaff63c8c58bcad38"},"schema_version":"1.0","source":{"id":"1212.5605","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1212.5605","created_at":"2026-05-18T02:56:12Z"},{"alias_kind":"arxiv_version","alias_value":"1212.5605v2","created_at":"2026-05-18T02:56:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1212.5605","created_at":"2026-05-18T02:56:12Z"},{"alias_kind":"pith_short_12","alias_value":"NZ7HVI4IOEPJ","created_at":"2026-05-18T12:27:16Z"},{"alias_kind":"pith_short_16","alias_value":"NZ7HVI4IOEPJAPAP","created_at":"2026-05-18T12:27:16Z"},{"alias_kind":"pith_short_8","alias_value":"NZ7HVI4I","created_at":"2026-05-18T12:27:16Z"}],"graph_snapshots":[{"event_id":"sha256:f3f186ffb514be11878ba03ad73b01d54dcd7ccd348a29d0113b4ee7d0d82440","target":"graph","created_at":"2026-05-18T02:56:12Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"We establish a direct connection between scattering amplitudes in planar four-dimensional theories and a remarkable mathematical structure known as the positive Grassmannian. The central physical idea is to focus on on-shell diagrams as objects of fundamental importance to scattering amplitudes. We show that the all-loop integrand in N=4 SYM is naturally represented in this way. On-shell diagrams in this theory are intimately tied to a variety of mathematical objects, ranging from a new graphical representation of permutations to a beautiful stratification of the Grassmannian G(k,n) which gene","authors_text":"Alexander B. Goncharov, Alexander Postnikov, Freddy Cachazo, Jacob L. Bourjaily, Jaroslav Trnka, Nima Arkani-Hamed","cross_cats":["math.AG","math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2012-12-21T21:00:02Z","title":"Scattering Amplitudes and the Positive Grassmannian"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.5605","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:5404ff6a55bf6a3805080bb9827780e85d6ae878919ed44cc22a4842f800bde0","target":"record","created_at":"2026-05-18T02:56:12Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"be2c2ce4e0d7de73eac2a990802ee8a5e1f685077abe0494079785babc47e145","cross_cats_sorted":["math.AG","math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2012-12-21T21:00:02Z","title_canon_sha256":"28ea7667df0053de12ff5f702e0ded1e8b87cf3c43018fcdaff63c8c58bcad38"},"schema_version":"1.0","source":{"id":"1212.5605","kind":"arxiv","version":2}},"canonical_sha256":"6e7e7aa388711e903c0ff85a8c9245930073382a4a8e76acc085c975e193c5be","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6e7e7aa388711e903c0ff85a8c9245930073382a4a8e76acc085c975e193c5be","first_computed_at":"2026-05-18T02:56:12.795032Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:56:12.795032Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Vow7ybBLfNDnP5DIuK80IixvhMM/gscuJqX7dONqmMyflB9yiXeq1A4DCHy6bj4KNccV9QpIHoLITiSLsrI4Cw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:56:12.795427Z","signed_message":"canonical_sha256_bytes"},"source_id":"1212.5605","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5404ff6a55bf6a3805080bb9827780e85d6ae878919ed44cc22a4842f800bde0","sha256:f3f186ffb514be11878ba03ad73b01d54dcd7ccd348a29d0113b4ee7d0d82440"],"state_sha256":"f496f9edaef365a8654f5b43b548178e6abbc3863eb60cb7f5c8ccc1c45bafe2"}