{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:JKBJSRGRWIO23PV5PPQIBGJ5LJ","short_pith_number":"pith:JKBJSRGR","canonical_record":{"source":{"id":"1909.01358","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2019-09-03T18:00:02Z","cross_cats_sorted":["gr-qc","hep-ph"],"title_canon_sha256":"83149f2ce152d9f594c601bdd0910aa5f6a758cdde36ea196d1fd662adbb246c","abstract_canon_sha256":"01fc2b5170096ced20a285d434de0f572451fe1ad1bfa45fbfda231563f5b460"},"schema_version":"1.0"},"canonical_sha256":"4a829944d1b21dadbebd7be080993d5a5a68b1c3788d15e79dea241a5ea97862","source":{"kind":"arxiv","id":"1909.01358","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1909.01358","created_at":"2026-07-05T00:02:15Z"},{"alias_kind":"arxiv_version","alias_value":"1909.01358v1","created_at":"2026-07-05T00:02:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1909.01358","created_at":"2026-07-05T00:02:15Z"},{"alias_kind":"pith_short_12","alias_value":"JKBJSRGRWIO2","created_at":"2026-07-05T00:02:15Z"},{"alias_kind":"pith_short_16","alias_value":"JKBJSRGRWIO23PV5","created_at":"2026-07-05T00:02:15Z"},{"alias_kind":"pith_short_8","alias_value":"JKBJSRGR","created_at":"2026-07-05T00:02:15Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:JKBJSRGRWIO23PV5PPQIBGJ5LJ","target":"record","payload":{"canonical_record":{"source":{"id":"1909.01358","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2019-09-03T18:00:02Z","cross_cats_sorted":["gr-qc","hep-ph"],"title_canon_sha256":"83149f2ce152d9f594c601bdd0910aa5f6a758cdde36ea196d1fd662adbb246c","abstract_canon_sha256":"01fc2b5170096ced20a285d434de0f572451fe1ad1bfa45fbfda231563f5b460"},"schema_version":"1.0"},"canonical_sha256":"4a829944d1b21dadbebd7be080993d5a5a68b1c3788d15e79dea241a5ea97862","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T00:02:15.528536Z","signature_b64":"1+S6/691IbIJtwhcnQW0kgrqDcRLEu2c1xgbpP0tMjAPzo0lZaNvrG/ywec+RgemlTmUVOMYAkKZ/vMK8NStCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4a829944d1b21dadbebd7be080993d5a5a68b1c3788d15e79dea241a5ea97862","last_reissued_at":"2026-07-05T00:02:15.528125Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T00:02:15.528125Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1909.01358","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":"2026-07-05T00:02:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"W2z32CPHdU6vsBVNIYBNivfJaIy4nm4aMd8rKr8lfv9wlrTVPAm43H1XXJ7CfTY/+eSB2BMz2kZlS9Unlf0KCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-05T02:17:21.955683Z"},"content_sha256":"a12b187e80a471fd78e4bd4db13bbd3fdf7189b816458dd37dc60a667c1524aa","schema_version":"1.0","event_id":"sha256:a12b187e80a471fd78e4bd4db13bbd3fdf7189b816458dd37dc60a667c1524aa"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:JKBJSRGRWIO23PV5PPQIBGJ5LJ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The Duality Between Color and Kinematics and its Applications","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["gr-qc","hep-ph"],"primary_cat":"hep-th","authors_text":"Henrik Johansson, John Joseph Carrasco, Marco Chiodaroli, Radu Roiban, Zvi Bern","submitted_at":"2019-09-03T18:00:02Z","abstract_excerpt":"This review describes the duality between color and kinematics and its applications, with the aim of gaining a deeper understanding of the perturbative structure of gauge and gravity theories. We emphasize, in particular, applications to loop-level calculations, the broad web of theories linked by the duality and the associated double-copy structure, and the issue of extending the duality and double copy beyond scattering amplitudes. The review is aimed at doctoral students and junior researchers both inside and outside the field of amplitudes and is accompanied by various exercises."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1909.01358","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1909.01358/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T00:02:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7QvPq8B6cY80sCekA8Dm12gejv53g6c8t1+T9bKrT9hVU++H8gTnBFqAEOAwiMPDOytrV2KfSsrnEC67UePPAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-05T02:17:21.956270Z"},"content_sha256":"0f07f04fd2c941d3eead4e49130e7ae7512877bcf6753eb344bd2d49371df304","schema_version":"1.0","event_id":"sha256:0f07f04fd2c941d3eead4e49130e7ae7512877bcf6753eb344bd2d49371df304"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/JKBJSRGRWIO23PV5PPQIBGJ5LJ/bundle.json","state_url":"https://pith.science/pith/JKBJSRGRWIO23PV5PPQIBGJ5LJ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/JKBJSRGRWIO23PV5PPQIBGJ5LJ/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":"2026-08-05T02:17:21Z","links":{"resolver":"https://pith.science/pith/JKBJSRGRWIO23PV5PPQIBGJ5LJ","bundle":"https://pith.science/pith/JKBJSRGRWIO23PV5PPQIBGJ5LJ/bundle.json","state":"https://pith.science/pith/JKBJSRGRWIO23PV5PPQIBGJ5LJ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/JKBJSRGRWIO23PV5PPQIBGJ5LJ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:JKBJSRGRWIO23PV5PPQIBGJ5LJ","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":"01fc2b5170096ced20a285d434de0f572451fe1ad1bfa45fbfda231563f5b460","cross_cats_sorted":["gr-qc","hep-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2019-09-03T18:00:02Z","title_canon_sha256":"83149f2ce152d9f594c601bdd0910aa5f6a758cdde36ea196d1fd662adbb246c"},"schema_version":"1.0","source":{"id":"1909.01358","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1909.01358","created_at":"2026-07-05T00:02:15Z"},{"alias_kind":"arxiv_version","alias_value":"1909.01358v1","created_at":"2026-07-05T00:02:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1909.01358","created_at":"2026-07-05T00:02:15Z"},{"alias_kind":"pith_short_12","alias_value":"JKBJSRGRWIO2","created_at":"2026-07-05T00:02:15Z"},{"alias_kind":"pith_short_16","alias_value":"JKBJSRGRWIO23PV5","created_at":"2026-07-05T00:02:15Z"},{"alias_kind":"pith_short_8","alias_value":"JKBJSRGR","created_at":"2026-07-05T00:02:15Z"}],"graph_snapshots":[{"event_id":"sha256:0f07f04fd2c941d3eead4e49130e7ae7512877bcf6753eb344bd2d49371df304","target":"graph","created_at":"2026-07-05T00:02:15Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/1909.01358/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"This review describes the duality between color and kinematics and its applications, with the aim of gaining a deeper understanding of the perturbative structure of gauge and gravity theories. We emphasize, in particular, applications to loop-level calculations, the broad web of theories linked by the duality and the associated double-copy structure, and the issue of extending the duality and double copy beyond scattering amplitudes. The review is aimed at doctoral students and junior researchers both inside and outside the field of amplitudes and is accompanied by various exercises.","authors_text":"Henrik Johansson, John Joseph Carrasco, Marco Chiodaroli, Radu Roiban, Zvi Bern","cross_cats":["gr-qc","hep-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2019-09-03T18:00:02Z","title":"The Duality Between Color and Kinematics and its Applications"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1909.01358","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:a12b187e80a471fd78e4bd4db13bbd3fdf7189b816458dd37dc60a667c1524aa","target":"record","created_at":"2026-07-05T00:02:15Z","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":"01fc2b5170096ced20a285d434de0f572451fe1ad1bfa45fbfda231563f5b460","cross_cats_sorted":["gr-qc","hep-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2019-09-03T18:00:02Z","title_canon_sha256":"83149f2ce152d9f594c601bdd0910aa5f6a758cdde36ea196d1fd662adbb246c"},"schema_version":"1.0","source":{"id":"1909.01358","kind":"arxiv","version":1}},"canonical_sha256":"4a829944d1b21dadbebd7be080993d5a5a68b1c3788d15e79dea241a5ea97862","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4a829944d1b21dadbebd7be080993d5a5a68b1c3788d15e79dea241a5ea97862","first_computed_at":"2026-07-05T00:02:15.528125Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T00:02:15.528125Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"1+S6/691IbIJtwhcnQW0kgrqDcRLEu2c1xgbpP0tMjAPzo0lZaNvrG/ywec+RgemlTmUVOMYAkKZ/vMK8NStCg==","signature_status":"signed_v1","signed_at":"2026-07-05T00:02:15.528536Z","signed_message":"canonical_sha256_bytes"},"source_id":"1909.01358","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a12b187e80a471fd78e4bd4db13bbd3fdf7189b816458dd37dc60a667c1524aa","sha256:0f07f04fd2c941d3eead4e49130e7ae7512877bcf6753eb344bd2d49371df304"],"state_sha256":"135c5cb573b81c7e54932c48586b3729dabeea5d5e3a443caef36c44010bb58a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HB+tYqCsypkMYrm0K+igpCO29ov+jNrrNjUmKUl8BsKsgWxqTjTCecDTOUGrKFgX3kktI4wKVrX+AlI3ucDXDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-05T02:17:21.960301Z","bundle_sha256":"2dccb763bbd7e1962d732a8368db19c4915c088bca832a9a340e1b1bf852c4f9"}}