{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:MO2UFOTM7YHTY36LIRBLWKJK3I","short_pith_number":"pith:MO2UFOTM","canonical_record":{"source":{"id":"1012.6030","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2010-12-29T20:44:42Z","cross_cats_sorted":[],"title_canon_sha256":"6fc4cf7215afdc7bd7e9974c11d30ef2e8cf083d58f98527f81f6c60f0f99941","abstract_canon_sha256":"3e18770c82dfc26fb795f945fe31c873c4f059cdefe577a4ba0f70a09f9300ae"},"schema_version":"1.0"},"canonical_sha256":"63b542ba6cfe0f3c6fcb4442bb292ada2a56e05999382803a8fbec837397252e","source":{"kind":"arxiv","id":"1012.6030","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1012.6030","created_at":"2026-05-18T02:04:16Z"},{"alias_kind":"arxiv_version","alias_value":"1012.6030v1","created_at":"2026-05-18T02:04:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1012.6030","created_at":"2026-05-18T02:04:16Z"},{"alias_kind":"pith_short_12","alias_value":"MO2UFOTM7YHT","created_at":"2026-05-18T12:26:10Z"},{"alias_kind":"pith_short_16","alias_value":"MO2UFOTM7YHTY36L","created_at":"2026-05-18T12:26:10Z"},{"alias_kind":"pith_short_8","alias_value":"MO2UFOTM","created_at":"2026-05-18T12:26:10Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:MO2UFOTM7YHTY36LIRBLWKJK3I","target":"record","payload":{"canonical_record":{"source":{"id":"1012.6030","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2010-12-29T20:44:42Z","cross_cats_sorted":[],"title_canon_sha256":"6fc4cf7215afdc7bd7e9974c11d30ef2e8cf083d58f98527f81f6c60f0f99941","abstract_canon_sha256":"3e18770c82dfc26fb795f945fe31c873c4f059cdefe577a4ba0f70a09f9300ae"},"schema_version":"1.0"},"canonical_sha256":"63b542ba6cfe0f3c6fcb4442bb292ada2a56e05999382803a8fbec837397252e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:04:16.672078Z","signature_b64":"C9ZJx5RsDjM+1TGVJ4uUQECs81giuGZDbH21FyUSpkBX2h5NXWTyGsa6qKCIbUDcAZ3VgFd5coqv/n96QC3qDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"63b542ba6cfe0f3c6fcb4442bb292ada2a56e05999382803a8fbec837397252e","last_reissued_at":"2026-05-18T02:04:16.671423Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:04:16.671423Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1012.6030","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:04:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ksEUMHE8Djyp0FGx4ponPM63LxkEkzzWpVhm5idu077JDZEkXBcvCTXJ56dA2dK9ZA82Y4jMp+rvxbZYTQNGDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T04:02:03.440219Z"},"content_sha256":"cde9b398c19936a0b1179a95e21f6953d972fff138b9cc97f180a2ba3b8e8bdc","schema_version":"1.0","event_id":"sha256:cde9b398c19936a0b1179a95e21f6953d972fff138b9cc97f180a2ba3b8e8bdc"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:MO2UFOTM7YHTY36LIRBLWKJK3I","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A Note on Polytopes for Scattering Amplitudes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"hep-th","authors_text":"Andrew Hodges, Freddy Cachazo, Jacob L. Bourjaily, Jaroslav Trnka, Nima Arkani-Hamed","submitted_at":"2010-12-29T20:44:42Z","abstract_excerpt":"In this note we continue the exploration of the polytope picture for scattering amplitudes, where amplitudes are associated with the volumes of polytopes in generalized momentum-twistor spaces. After a quick warm-up example illustrating the essential ideas with the elementary geometry of polygons in CP^2, we interpret the 1-loop MHV integrand as the volume of a polytope in CP^3x CP^3, which can be thought of as the space obtained by taking the geometric dual of the Wilson loop in each CP^3 of the product. We then review the polytope picture for the NMHV tree amplitude and give it a more direct"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1012.6030","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:04:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"28g8k98yZjGf7Wphm2avyf+JAtEtKOlfQUswSWwwSdUg6MRwsjnRDyDuk9X7PJUQMc6QUXs+Q93i6235hiQrAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T04:02:03.440951Z"},"content_sha256":"5e3d5e601441348c4b443a46beee7998f9b9909b07fd33659d1af6b944f0047e","schema_version":"1.0","event_id":"sha256:5e3d5e601441348c4b443a46beee7998f9b9909b07fd33659d1af6b944f0047e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/MO2UFOTM7YHTY36LIRBLWKJK3I/bundle.json","state_url":"https://pith.science/pith/MO2UFOTM7YHTY36LIRBLWKJK3I/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/MO2UFOTM7YHTY36LIRBLWKJK3I/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-05-25T04:02:03Z","links":{"resolver":"https://pith.science/pith/MO2UFOTM7YHTY36LIRBLWKJK3I","bundle":"https://pith.science/pith/MO2UFOTM7YHTY36LIRBLWKJK3I/bundle.json","state":"https://pith.science/pith/MO2UFOTM7YHTY36LIRBLWKJK3I/state.json","well_known_bundle":"https://pith.science/.well-known/pith/MO2UFOTM7YHTY36LIRBLWKJK3I/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:MO2UFOTM7YHTY36LIRBLWKJK3I","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":"3e18770c82dfc26fb795f945fe31c873c4f059cdefe577a4ba0f70a09f9300ae","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2010-12-29T20:44:42Z","title_canon_sha256":"6fc4cf7215afdc7bd7e9974c11d30ef2e8cf083d58f98527f81f6c60f0f99941"},"schema_version":"1.0","source":{"id":"1012.6030","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1012.6030","created_at":"2026-05-18T02:04:16Z"},{"alias_kind":"arxiv_version","alias_value":"1012.6030v1","created_at":"2026-05-18T02:04:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1012.6030","created_at":"2026-05-18T02:04:16Z"},{"alias_kind":"pith_short_12","alias_value":"MO2UFOTM7YHT","created_at":"2026-05-18T12:26:10Z"},{"alias_kind":"pith_short_16","alias_value":"MO2UFOTM7YHTY36L","created_at":"2026-05-18T12:26:10Z"},{"alias_kind":"pith_short_8","alias_value":"MO2UFOTM","created_at":"2026-05-18T12:26:10Z"}],"graph_snapshots":[{"event_id":"sha256:5e3d5e601441348c4b443a46beee7998f9b9909b07fd33659d1af6b944f0047e","target":"graph","created_at":"2026-05-18T02:04:16Z","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":"In this note we continue the exploration of the polytope picture for scattering amplitudes, where amplitudes are associated with the volumes of polytopes in generalized momentum-twistor spaces. After a quick warm-up example illustrating the essential ideas with the elementary geometry of polygons in CP^2, we interpret the 1-loop MHV integrand as the volume of a polytope in CP^3x CP^3, which can be thought of as the space obtained by taking the geometric dual of the Wilson loop in each CP^3 of the product. We then review the polytope picture for the NMHV tree amplitude and give it a more direct","authors_text":"Andrew Hodges, Freddy Cachazo, Jacob L. Bourjaily, Jaroslav Trnka, Nima Arkani-Hamed","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2010-12-29T20:44:42Z","title":"A Note on Polytopes for Scattering Amplitudes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1012.6030","kind":"arxiv","version":1},"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:cde9b398c19936a0b1179a95e21f6953d972fff138b9cc97f180a2ba3b8e8bdc","target":"record","created_at":"2026-05-18T02:04:16Z","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":"3e18770c82dfc26fb795f945fe31c873c4f059cdefe577a4ba0f70a09f9300ae","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2010-12-29T20:44:42Z","title_canon_sha256":"6fc4cf7215afdc7bd7e9974c11d30ef2e8cf083d58f98527f81f6c60f0f99941"},"schema_version":"1.0","source":{"id":"1012.6030","kind":"arxiv","version":1}},"canonical_sha256":"63b542ba6cfe0f3c6fcb4442bb292ada2a56e05999382803a8fbec837397252e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"63b542ba6cfe0f3c6fcb4442bb292ada2a56e05999382803a8fbec837397252e","first_computed_at":"2026-05-18T02:04:16.671423Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:04:16.671423Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"C9ZJx5RsDjM+1TGVJ4uUQECs81giuGZDbH21FyUSpkBX2h5NXWTyGsa6qKCIbUDcAZ3VgFd5coqv/n96QC3qDw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:04:16.672078Z","signed_message":"canonical_sha256_bytes"},"source_id":"1012.6030","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cde9b398c19936a0b1179a95e21f6953d972fff138b9cc97f180a2ba3b8e8bdc","sha256:5e3d5e601441348c4b443a46beee7998f9b9909b07fd33659d1af6b944f0047e"],"state_sha256":"50a1256cc6203e159ed31dc1e11632810f1a13b8b88e8be71d88e29b034c94da"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Ni0OeUiMZvX1Gr6JTD0Ufbec3hG3lA7rdLaQvS/AFOKw9JMO2S8XityO8y/a73KufVgrtjVZcr4jfAlfU1GVAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-25T04:02:03.444711Z","bundle_sha256":"72b8d081c915d172d5de5b1c898f108a7e5f46aad6c568f62f3feb0a9c8aa938"}}