{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:LG6YANQGRGXPR6VXVA7PQZLXZV","short_pith_number":"pith:LG6YANQG","canonical_record":{"source":{"id":"1110.1859","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2011-10-09T17:10:10Z","cross_cats_sorted":["hep-ph"],"title_canon_sha256":"4eb82d19d2fc3b5836824d3076e4305812bed8b8b60a28827ae81c6da2018d0d","abstract_canon_sha256":"64bc79e843d8610d489bc9fccebe314493fedb684d7ed5b552c78599cc6186e6"},"schema_version":"1.0"},"canonical_sha256":"59bd80360689aef8fab7a83ef86577cd78422569c32d9f4ba0c8e4ef0c8fe914","source":{"kind":"arxiv","id":"1110.1859","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1110.1859","created_at":"2026-05-18T02:00:15Z"},{"alias_kind":"arxiv_version","alias_value":"1110.1859v3","created_at":"2026-05-18T02:00:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1110.1859","created_at":"2026-05-18T02:00:15Z"},{"alias_kind":"pith_short_12","alias_value":"LG6YANQGRGXP","created_at":"2026-05-18T12:26:34Z"},{"alias_kind":"pith_short_16","alias_value":"LG6YANQGRGXPR6VX","created_at":"2026-05-18T12:26:34Z"},{"alias_kind":"pith_short_8","alias_value":"LG6YANQG","created_at":"2026-05-18T12:26:34Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:LG6YANQGRGXPR6VXVA7PQZLXZV","target":"record","payload":{"canonical_record":{"source":{"id":"1110.1859","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2011-10-09T17:10:10Z","cross_cats_sorted":["hep-ph"],"title_canon_sha256":"4eb82d19d2fc3b5836824d3076e4305812bed8b8b60a28827ae81c6da2018d0d","abstract_canon_sha256":"64bc79e843d8610d489bc9fccebe314493fedb684d7ed5b552c78599cc6186e6"},"schema_version":"1.0"},"canonical_sha256":"59bd80360689aef8fab7a83ef86577cd78422569c32d9f4ba0c8e4ef0c8fe914","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:00:15.935096Z","signature_b64":"/zwfva3RkvHJKNLTTiEm5nlmcgSRMy/FFKgUWAiVElW4zTsqF0E2RECYwkyMu9h3kEx0hRbiYeUvTwOYHGaZDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"59bd80360689aef8fab7a83ef86577cd78422569c32d9f4ba0c8e4ef0c8fe914","last_reissued_at":"2026-05-18T02:00:15.934502Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:00:15.934502Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1110.1859","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:00:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IhBA/FRidYhAcTAe7vVX233ulOXRMGNFnuG8ZxE48qNUhy1prV4dI5C1NvyPm81/QG1yV1byB2TJ675P5YnEDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T13:00:27.303055Z"},"content_sha256":"ca76bc99dbf3b94d743c1ed81c74ebcbffd35000a53db68c7bccc734a57cdb05","schema_version":"1.0","event_id":"sha256:ca76bc99dbf3b94d743c1ed81c74ebcbffd35000a53db68c7bccc734a57cdb05"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:LG6YANQGRGXPR6VXVA7PQZLXZV","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"All-loop group-theory constraints for color-ordered SU(N) gauge-theory amplitudes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-ph"],"primary_cat":"hep-th","authors_text":"Stephen G. Naculich","submitted_at":"2011-10-09T17:10:10Z","abstract_excerpt":"We derive constraints on the color-ordered amplitudes of the L-loop four-point function in SU(N) gauge theories that arise solely from the structure of the gauge group. These constraints generalize well-known group theory relations, such as U(1) decoupling identities, to all loop orders."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.1859","kind":"arxiv","version":3},"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":"2026-05-18T02:00:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"e48oXaMj/x41FJx3gQ2Ii/1gRMFuzOLrjtPjIb3VffQz2cBiE5KQWRIWyw3h4tLBgA/gnHquNYndVxcLw4fZCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T13:00:27.303751Z"},"content_sha256":"caa5d4110393c4a8444057499c55ec374749dcd9516117bfd8493ae683dc53db","schema_version":"1.0","event_id":"sha256:caa5d4110393c4a8444057499c55ec374749dcd9516117bfd8493ae683dc53db"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/LG6YANQGRGXPR6VXVA7PQZLXZV/bundle.json","state_url":"https://pith.science/pith/LG6YANQGRGXPR6VXVA7PQZLXZV/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/LG6YANQGRGXPR6VXVA7PQZLXZV/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":"2026-05-28T13:00:27Z","links":{"resolver":"https://pith.science/pith/LG6YANQGRGXPR6VXVA7PQZLXZV","bundle":"https://pith.science/pith/LG6YANQGRGXPR6VXVA7PQZLXZV/bundle.json","state":"https://pith.science/pith/LG6YANQGRGXPR6VXVA7PQZLXZV/state.json","well_known_bundle":"https://pith.science/.well-known/pith/LG6YANQGRGXPR6VXVA7PQZLXZV/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:LG6YANQGRGXPR6VXVA7PQZLXZV","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":"64bc79e843d8610d489bc9fccebe314493fedb684d7ed5b552c78599cc6186e6","cross_cats_sorted":["hep-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2011-10-09T17:10:10Z","title_canon_sha256":"4eb82d19d2fc3b5836824d3076e4305812bed8b8b60a28827ae81c6da2018d0d"},"schema_version":"1.0","source":{"id":"1110.1859","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1110.1859","created_at":"2026-05-18T02:00:15Z"},{"alias_kind":"arxiv_version","alias_value":"1110.1859v3","created_at":"2026-05-18T02:00:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1110.1859","created_at":"2026-05-18T02:00:15Z"},{"alias_kind":"pith_short_12","alias_value":"LG6YANQGRGXP","created_at":"2026-05-18T12:26:34Z"},{"alias_kind":"pith_short_16","alias_value":"LG6YANQGRGXPR6VX","created_at":"2026-05-18T12:26:34Z"},{"alias_kind":"pith_short_8","alias_value":"LG6YANQG","created_at":"2026-05-18T12:26:34Z"}],"graph_snapshots":[{"event_id":"sha256:caa5d4110393c4a8444057499c55ec374749dcd9516117bfd8493ae683dc53db","target":"graph","created_at":"2026-05-18T02:00:15Z","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"},"paper":{"abstract_excerpt":"We derive constraints on the color-ordered amplitudes of the L-loop four-point function in SU(N) gauge theories that arise solely from the structure of the gauge group. These constraints generalize well-known group theory relations, such as U(1) decoupling identities, to all loop orders.","authors_text":"Stephen G. Naculich","cross_cats":["hep-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2011-10-09T17:10:10Z","title":"All-loop group-theory constraints for color-ordered SU(N) gauge-theory amplitudes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.1859","kind":"arxiv","version":3},"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:ca76bc99dbf3b94d743c1ed81c74ebcbffd35000a53db68c7bccc734a57cdb05","target":"record","created_at":"2026-05-18T02:00:15Z","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":"64bc79e843d8610d489bc9fccebe314493fedb684d7ed5b552c78599cc6186e6","cross_cats_sorted":["hep-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2011-10-09T17:10:10Z","title_canon_sha256":"4eb82d19d2fc3b5836824d3076e4305812bed8b8b60a28827ae81c6da2018d0d"},"schema_version":"1.0","source":{"id":"1110.1859","kind":"arxiv","version":3}},"canonical_sha256":"59bd80360689aef8fab7a83ef86577cd78422569c32d9f4ba0c8e4ef0c8fe914","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"59bd80360689aef8fab7a83ef86577cd78422569c32d9f4ba0c8e4ef0c8fe914","first_computed_at":"2026-05-18T02:00:15.934502Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:00:15.934502Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"/zwfva3RkvHJKNLTTiEm5nlmcgSRMy/FFKgUWAiVElW4zTsqF0E2RECYwkyMu9h3kEx0hRbiYeUvTwOYHGaZDg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:00:15.935096Z","signed_message":"canonical_sha256_bytes"},"source_id":"1110.1859","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ca76bc99dbf3b94d743c1ed81c74ebcbffd35000a53db68c7bccc734a57cdb05","sha256:caa5d4110393c4a8444057499c55ec374749dcd9516117bfd8493ae683dc53db"],"state_sha256":"52f063a670a33c657e163fb6668e88c77943ed676a4edbe4cc8639b801b919c4"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"B2kEWd3yF3N/emzSPkwZ/GBNb68yxms5TgTPaMciTN+irA30d7NxNcnI5S8//h+WlYsTCvJVkDIIYzgEZNaTBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T13:00:27.307034Z","bundle_sha256":"879a6ec0db10eb486a1a04853ba8bbdf9578dc96cf8fcc9cce7b6717989b2c5a"}}