{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:KCUJCEPSFCZSSOB6QT7FQHN3AC","short_pith_number":"pith:KCUJCEPS","canonical_record":{"source":{"id":"2412.20950","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"hep-th","submitted_at":"2024-12-30T13:46:26Z","cross_cats_sorted":[],"title_canon_sha256":"601524c5bb97acbd0acd35a3db09e8598a40eab9b3b92f1461728342852bb368","abstract_canon_sha256":"3b790444e80119111f75614c85b35d50bfae4b9c08a2b4274bf2b0d65a9ef037"},"schema_version":"1.0"},"canonical_sha256":"50a89111f228b329383e84fe581dbb00bc61df43b5055b4c4fa8f5203c853adb","source":{"kind":"arxiv","id":"2412.20950","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2412.20950","created_at":"2026-07-05T10:26:12Z"},{"alias_kind":"arxiv_version","alias_value":"2412.20950v2","created_at":"2026-07-05T10:26:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2412.20950","created_at":"2026-07-05T10:26:12Z"},{"alias_kind":"pith_short_12","alias_value":"KCUJCEPSFCZS","created_at":"2026-07-05T10:26:12Z"},{"alias_kind":"pith_short_16","alias_value":"KCUJCEPSFCZSSOB6","created_at":"2026-07-05T10:26:12Z"},{"alias_kind":"pith_short_8","alias_value":"KCUJCEPS","created_at":"2026-07-05T10:26:12Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:KCUJCEPSFCZSSOB6QT7FQHN3AC","target":"record","payload":{"canonical_record":{"source":{"id":"2412.20950","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"hep-th","submitted_at":"2024-12-30T13:46:26Z","cross_cats_sorted":[],"title_canon_sha256":"601524c5bb97acbd0acd35a3db09e8598a40eab9b3b92f1461728342852bb368","abstract_canon_sha256":"3b790444e80119111f75614c85b35d50bfae4b9c08a2b4274bf2b0d65a9ef037"},"schema_version":"1.0"},"canonical_sha256":"50a89111f228b329383e84fe581dbb00bc61df43b5055b4c4fa8f5203c853adb","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:26:12.234932Z","signature_b64":"ihbkhBtbIzAiApziAfP0ro9zzz0nE98K/SdySWeU+ljJ47wDokRPB8wkApvcFp8Z/KPhVHKSbsCaFrKtyFHxBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"50a89111f228b329383e84fe581dbb00bc61df43b5055b4c4fa8f5203c853adb","last_reissued_at":"2026-07-05T10:26:12.234502Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:26:12.234502Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2412.20950","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":"2026-07-05T10:26:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Q0J7NrKu0+vfRpuDPV3JV2vd3qYBwq9FS2JcHddS7o/lTEhNK3IJ/eN0EBBVHNrF/ShFb5cDMqtUpzKqwUC6BQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-11T16:48:29.564262Z"},"content_sha256":"62c37a76a2a8d6a6db10c080d1df6f8b386a1d34b93676996640e87deb2c2cc0","schema_version":"1.0","event_id":"sha256:62c37a76a2a8d6a6db10c080d1df6f8b386a1d34b93676996640e87deb2c2cc0"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:KCUJCEPSFCZSSOB6QT7FQHN3AC","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Four loop renormalization of QCD in the Curci-Ferrari gauge","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"hep-th","authors_text":"J.A. Gracey","submitted_at":"2024-12-30T13:46:26Z","abstract_excerpt":"We renormalize Quantum Chromodynamics (QCD) when gauge fixed in the nonlinear Curci-Ferrari gauge to four loops in the modified minimal subtraction (MSbar) scheme. We reproduce the four loop QCD MSbar beta-function from the Slavnov-Taylor identity for this gauge which relates the coupling constant renormalization to the gluon, Faddeev-Popov ghost and gauge parameter anomalous dimensions. This is carried out for a nonzero gauge parameter, without having to evaluate a vertex function. The anomalous dimension of the BRST invariant dimension two gluon and ghost mass term is deduced from a similar "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2412.20950","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2412.20950/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":"2026-07-05T10:26:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7VBNquHcNMVllaXIuUIe/MzE/YSRMEcOdyeF8BH/Yq27Ac5aTug6I7698HdZ93zxS+6QTnyOnvCGUj3cxBKfAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-11T16:48:29.564763Z"},"content_sha256":"e1cd6436b3887e4d23bfcc660c2678b0c0d09ea70b29e7cb11e2c2425c3a0e9f","schema_version":"1.0","event_id":"sha256:e1cd6436b3887e4d23bfcc660c2678b0c0d09ea70b29e7cb11e2c2425c3a0e9f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/KCUJCEPSFCZSSOB6QT7FQHN3AC/bundle.json","state_url":"https://pith.science/pith/KCUJCEPSFCZSSOB6QT7FQHN3AC/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/KCUJCEPSFCZSSOB6QT7FQHN3AC/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":"2026-08-11T16:48:29Z","links":{"resolver":"https://pith.science/pith/KCUJCEPSFCZSSOB6QT7FQHN3AC","bundle":"https://pith.science/pith/KCUJCEPSFCZSSOB6QT7FQHN3AC/bundle.json","state":"https://pith.science/pith/KCUJCEPSFCZSSOB6QT7FQHN3AC/state.json","well_known_bundle":"https://pith.science/.well-known/pith/KCUJCEPSFCZSSOB6QT7FQHN3AC/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:KCUJCEPSFCZSSOB6QT7FQHN3AC","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":"3b790444e80119111f75614c85b35d50bfae4b9c08a2b4274bf2b0d65a9ef037","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"hep-th","submitted_at":"2024-12-30T13:46:26Z","title_canon_sha256":"601524c5bb97acbd0acd35a3db09e8598a40eab9b3b92f1461728342852bb368"},"schema_version":"1.0","source":{"id":"2412.20950","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2412.20950","created_at":"2026-07-05T10:26:12Z"},{"alias_kind":"arxiv_version","alias_value":"2412.20950v2","created_at":"2026-07-05T10:26:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2412.20950","created_at":"2026-07-05T10:26:12Z"},{"alias_kind":"pith_short_12","alias_value":"KCUJCEPSFCZS","created_at":"2026-07-05T10:26:12Z"},{"alias_kind":"pith_short_16","alias_value":"KCUJCEPSFCZSSOB6","created_at":"2026-07-05T10:26:12Z"},{"alias_kind":"pith_short_8","alias_value":"KCUJCEPS","created_at":"2026-07-05T10:26:12Z"}],"graph_snapshots":[{"event_id":"sha256:e1cd6436b3887e4d23bfcc660c2678b0c0d09ea70b29e7cb11e2c2425c3a0e9f","target":"graph","created_at":"2026-07-05T10:26:12Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2412.20950/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We renormalize Quantum Chromodynamics (QCD) when gauge fixed in the nonlinear Curci-Ferrari gauge to four loops in the modified minimal subtraction (MSbar) scheme. We reproduce the four loop QCD MSbar beta-function from the Slavnov-Taylor identity for this gauge which relates the coupling constant renormalization to the gluon, Faddeev-Popov ghost and gauge parameter anomalous dimensions. This is carried out for a nonzero gauge parameter, without having to evaluate a vertex function. The anomalous dimension of the BRST invariant dimension two gluon and ghost mass term is deduced from a similar ","authors_text":"J.A. Gracey","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"hep-th","submitted_at":"2024-12-30T13:46:26Z","title":"Four loop renormalization of QCD in the Curci-Ferrari gauge"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2412.20950","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":"sha256:62c37a76a2a8d6a6db10c080d1df6f8b386a1d34b93676996640e87deb2c2cc0","target":"record","created_at":"2026-07-05T10:26:12Z","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":"3b790444e80119111f75614c85b35d50bfae4b9c08a2b4274bf2b0d65a9ef037","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"hep-th","submitted_at":"2024-12-30T13:46:26Z","title_canon_sha256":"601524c5bb97acbd0acd35a3db09e8598a40eab9b3b92f1461728342852bb368"},"schema_version":"1.0","source":{"id":"2412.20950","kind":"arxiv","version":2}},"canonical_sha256":"50a89111f228b329383e84fe581dbb00bc61df43b5055b4c4fa8f5203c853adb","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"50a89111f228b329383e84fe581dbb00bc61df43b5055b4c4fa8f5203c853adb","first_computed_at":"2026-07-05T10:26:12.234502Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T10:26:12.234502Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ihbkhBtbIzAiApziAfP0ro9zzz0nE98K/SdySWeU+ljJ47wDokRPB8wkApvcFp8Z/KPhVHKSbsCaFrKtyFHxBw==","signature_status":"signed_v1","signed_at":"2026-07-05T10:26:12.234932Z","signed_message":"canonical_sha256_bytes"},"source_id":"2412.20950","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:62c37a76a2a8d6a6db10c080d1df6f8b386a1d34b93676996640e87deb2c2cc0","sha256:e1cd6436b3887e4d23bfcc660c2678b0c0d09ea70b29e7cb11e2c2425c3a0e9f"],"state_sha256":"66e5a0ecb9371a93e4e93f39de04067d5c13da6ba30ab145cb7586e6018e03b4"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ub0k3XYtNvLuqng0nv7Nn6xS5a5Zkn8Ymj6kRm8tOCfkdhCQRik16+0Iq1Np7LyQ8jjIENuL0LNOc2GKJ1gADQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-11T16:48:29.569422Z","bundle_sha256":"48ad9d3eff5dba502a7d08f6b837c54f31a2877fd1226ad1c4e17886ca9b7fba"}}