{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:LIBLG6MOGMMAF7Z25WE2EADQVF","short_pith_number":"pith:LIBLG6MO","canonical_record":{"source":{"id":"1111.3821","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2011-11-16T14:38:24Z","cross_cats_sorted":["hep-ph"],"title_canon_sha256":"d8de5a90db4fa64de706b9fb7de2b064ab0f408aec47ca786f776ba79eccc018","abstract_canon_sha256":"5bd204a44a3cf0a80469445975fa8e57b4fd66d5527ba3e970427dbaa2b08d5c"},"schema_version":"1.0"},"canonical_sha256":"5a02b3798e331802ff3aed89a20070a9534d3fac5a641bacb8447053ac96b9b7","source":{"kind":"arxiv","id":"1111.3821","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1111.3821","created_at":"2026-05-18T01:59:32Z"},{"alias_kind":"arxiv_version","alias_value":"1111.3821v2","created_at":"2026-05-18T01:59:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1111.3821","created_at":"2026-05-18T01:59:32Z"},{"alias_kind":"pith_short_12","alias_value":"LIBLG6MOGMMA","created_at":"2026-05-18T12:26:34Z"},{"alias_kind":"pith_short_16","alias_value":"LIBLG6MOGMMAF7Z2","created_at":"2026-05-18T12:26:34Z"},{"alias_kind":"pith_short_8","alias_value":"LIBLG6MO","created_at":"2026-05-18T12:26:34Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:LIBLG6MOGMMAF7Z25WE2EADQVF","target":"record","payload":{"canonical_record":{"source":{"id":"1111.3821","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2011-11-16T14:38:24Z","cross_cats_sorted":["hep-ph"],"title_canon_sha256":"d8de5a90db4fa64de706b9fb7de2b064ab0f408aec47ca786f776ba79eccc018","abstract_canon_sha256":"5bd204a44a3cf0a80469445975fa8e57b4fd66d5527ba3e970427dbaa2b08d5c"},"schema_version":"1.0"},"canonical_sha256":"5a02b3798e331802ff3aed89a20070a9534d3fac5a641bacb8447053ac96b9b7","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:59:32.317069Z","signature_b64":"z4OMvUDLQXRDOJYtZ/+JIdjNmUpOjl1T4ha0refI7rswy9b0F/d4MVSQE18+jcFodb0Vwe8nHWyap3TYWrHSAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5a02b3798e331802ff3aed89a20070a9534d3fac5a641bacb8447053ac96b9b7","last_reissued_at":"2026-05-18T01:59:32.316497Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:59:32.316497Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1111.3821","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:59:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Yz/zhfxucr3POeTVrzhlJO5zTeqVIP2E4TAt7vVh1fTQyP04Y7+4al6rvba1hLbSsgFHVav+Aygvd7xZFfPdDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T23:13:38.719584Z"},"content_sha256":"0bb364596bab2cc106759ae6df3cd56c63aa828729b0cd1467843f811737a927","schema_version":"1.0","event_id":"sha256:0bb364596bab2cc106759ae6df3cd56c63aa828729b0cd1467843f811737a927"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:LIBLG6MOGMMAF7Z25WE2EADQVF","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"SU(N) group-theory constraints on color-ordered five-point amplitudes at all loop orders","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-ph"],"primary_cat":"hep-th","authors_text":"Alexander C. Edison, Stephen G. Naculich","submitted_at":"2011-11-16T14:38:24Z","abstract_excerpt":"Color-ordered amplitudes for the scattering of n particles in the adjoint representation of SU(N) gauge theory satisfy constraints arising solely from group theory. We derive these constraints for n=5 at all loop orders using an iterative approach. These constraints generalize well-known tree-level and one-loop group theory relations."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1111.3821","kind":"arxiv","version":2},"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":"2026-05-18T01:59:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YthnIzTJOthZcdakqYEUQlEj83kl6eN9OTMTJ5fc959wLMuaptQISeC3hbjTQ3/I0Th6QYO6EQ2zV2zEbvhpCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T23:13:38.720227Z"},"content_sha256":"e938fd3b527da68bae363caa6906e40856f89956f3bed6570b7421838eb6434e","schema_version":"1.0","event_id":"sha256:e938fd3b527da68bae363caa6906e40856f89956f3bed6570b7421838eb6434e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/LIBLG6MOGMMAF7Z25WE2EADQVF/bundle.json","state_url":"https://pith.science/pith/LIBLG6MOGMMAF7Z25WE2EADQVF/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/LIBLG6MOGMMAF7Z25WE2EADQVF/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":"2026-05-28T23:13:38Z","links":{"resolver":"https://pith.science/pith/LIBLG6MOGMMAF7Z25WE2EADQVF","bundle":"https://pith.science/pith/LIBLG6MOGMMAF7Z25WE2EADQVF/bundle.json","state":"https://pith.science/pith/LIBLG6MOGMMAF7Z25WE2EADQVF/state.json","well_known_bundle":"https://pith.science/.well-known/pith/LIBLG6MOGMMAF7Z25WE2EADQVF/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:LIBLG6MOGMMAF7Z25WE2EADQVF","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":"5bd204a44a3cf0a80469445975fa8e57b4fd66d5527ba3e970427dbaa2b08d5c","cross_cats_sorted":["hep-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2011-11-16T14:38:24Z","title_canon_sha256":"d8de5a90db4fa64de706b9fb7de2b064ab0f408aec47ca786f776ba79eccc018"},"schema_version":"1.0","source":{"id":"1111.3821","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1111.3821","created_at":"2026-05-18T01:59:32Z"},{"alias_kind":"arxiv_version","alias_value":"1111.3821v2","created_at":"2026-05-18T01:59:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1111.3821","created_at":"2026-05-18T01:59:32Z"},{"alias_kind":"pith_short_12","alias_value":"LIBLG6MOGMMA","created_at":"2026-05-18T12:26:34Z"},{"alias_kind":"pith_short_16","alias_value":"LIBLG6MOGMMAF7Z2","created_at":"2026-05-18T12:26:34Z"},{"alias_kind":"pith_short_8","alias_value":"LIBLG6MO","created_at":"2026-05-18T12:26:34Z"}],"graph_snapshots":[{"event_id":"sha256:e938fd3b527da68bae363caa6906e40856f89956f3bed6570b7421838eb6434e","target":"graph","created_at":"2026-05-18T01:59:32Z","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":"Color-ordered amplitudes for the scattering of n particles in the adjoint representation of SU(N) gauge theory satisfy constraints arising solely from group theory. We derive these constraints for n=5 at all loop orders using an iterative approach. These constraints generalize well-known tree-level and one-loop group theory relations.","authors_text":"Alexander C. Edison, Stephen G. Naculich","cross_cats":["hep-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2011-11-16T14:38:24Z","title":"SU(N) group-theory constraints on color-ordered five-point amplitudes at all loop orders"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1111.3821","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":"sha256:0bb364596bab2cc106759ae6df3cd56c63aa828729b0cd1467843f811737a927","target":"record","created_at":"2026-05-18T01:59:32Z","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":"5bd204a44a3cf0a80469445975fa8e57b4fd66d5527ba3e970427dbaa2b08d5c","cross_cats_sorted":["hep-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2011-11-16T14:38:24Z","title_canon_sha256":"d8de5a90db4fa64de706b9fb7de2b064ab0f408aec47ca786f776ba79eccc018"},"schema_version":"1.0","source":{"id":"1111.3821","kind":"arxiv","version":2}},"canonical_sha256":"5a02b3798e331802ff3aed89a20070a9534d3fac5a641bacb8447053ac96b9b7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5a02b3798e331802ff3aed89a20070a9534d3fac5a641bacb8447053ac96b9b7","first_computed_at":"2026-05-18T01:59:32.316497Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:59:32.316497Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"z4OMvUDLQXRDOJYtZ/+JIdjNmUpOjl1T4ha0refI7rswy9b0F/d4MVSQE18+jcFodb0Vwe8nHWyap3TYWrHSAg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:59:32.317069Z","signed_message":"canonical_sha256_bytes"},"source_id":"1111.3821","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0bb364596bab2cc106759ae6df3cd56c63aa828729b0cd1467843f811737a927","sha256:e938fd3b527da68bae363caa6906e40856f89956f3bed6570b7421838eb6434e"],"state_sha256":"034e0a2ce3163a3d8bf27e33c133f4baf0580e9daeba7f0ccbd33f4c17efc253"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fWU9itnEV75nsb0mrzF/5iBD88QdBPqfvyS724f7AxSRPwbn276u2rizGM1WdhF4mm2k2FbdvXL2M2m9TU2TBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T23:13:38.723635Z","bundle_sha256":"a09187a36b4c5db1762fbe5d1e1d1c15dc5d063e81139adb8f19c0745495f298"}}