{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:1996:DUZNOQ27V42RIXYNWJMJ2C5OJ7","short_pith_number":"pith:DUZNOQ27","schema_version":"1.0","canonical_sha256":"1d32d7435faf35145f0db2589d0bae4fe8c6bc600e1a593b81266d82fbc60190","source":{"kind":"arxiv","id":"hep-ph/9602214","version":1},"attestation_state":"computed","paper":{"title":"The QCD beta-function at O(1/N_f)","license":"","headline":"","cross_cats":[],"primary_cat":"hep-ph","authors_text":"J.A. Gracey","submitted_at":"1996-02-02T10:14:11Z","abstract_excerpt":"The leading order coefficients of the beta-function of QCD are computed in a large N_f expansion. They are in agreement with the three loop MSbar calculation. The method involves computing the anomalous dimension of the operator (G^2_{mu nu})^2 at the d-dimensional fixed point in the non-abelian Thirring model to which QCD is equaivalent in this limit. The effect the O(1/N_f) corrections have on the location of the infrared stable fixed point for a range of N_f is also examined."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"hep-ph/9602214","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"hep-ph","submitted_at":"1996-02-02T10:14:11Z","cross_cats_sorted":[],"title_canon_sha256":"603aba8b54cdc472602133a5601cc0a3c445f532d2e003a3ebf2587d341770cf","abstract_canon_sha256":"a891fcb485f0c90cbb2fb924cecd601f2d7596d41d36524797f878a8401aeafd"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T16:01:28.500367Z","signature_b64":"3tiBt99LDpLQulhTJ4smzIupbS2CKRitTkYNvy444s1ytfIFfpumy8D22I0w0nRygbjEVoZkWc2C5Z/91bneBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1d32d7435faf35145f0db2589d0bae4fe8c6bc600e1a593b81266d82fbc60190","last_reissued_at":"2026-07-04T16:01:28.500012Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T16:01:28.500012Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The QCD beta-function at O(1/N_f)","license":"","headline":"","cross_cats":[],"primary_cat":"hep-ph","authors_text":"J.A. Gracey","submitted_at":"1996-02-02T10:14:11Z","abstract_excerpt":"The leading order coefficients of the beta-function of QCD are computed in a large N_f expansion. They are in agreement with the three loop MSbar calculation. The method involves computing the anomalous dimension of the operator (G^2_{mu nu})^2 at the d-dimensional fixed point in the non-abelian Thirring model to which QCD is equaivalent in this limit. The effect the O(1/N_f) corrections have on the location of the infrared stable fixed point for a range of N_f is also examined."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"hep-ph/9602214","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/hep-ph/9602214/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"},"aliases":[{"alias_kind":"arxiv","alias_value":"hep-ph/9602214","created_at":"2026-07-04T16:01:28.500071+00:00"},{"alias_kind":"arxiv_version","alias_value":"hep-ph/9602214v1","created_at":"2026-07-04T16:01:28.500071+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.hep-ph/9602214","created_at":"2026-07-04T16:01:28.500071+00:00"},{"alias_kind":"pith_short_12","alias_value":"DUZNOQ27V42R","created_at":"2026-07-04T16:01:28.500071+00:00"},{"alias_kind":"pith_short_16","alias_value":"DUZNOQ27V42RIXYN","created_at":"2026-07-04T16:01:28.500071+00:00"},{"alias_kind":"pith_short_8","alias_value":"DUZNOQ27","created_at":"2026-07-04T16:01:28.500071+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":2,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2601.07596","citing_title":"Asymptotic Pad\\'e Predictions up to Six Loops in QCD and Eight Loops in $\\lambda\\phi^4$","ref_index":39,"is_internal_anchor":true},{"citing_arxiv_id":"2605.05349","citing_title":"All-loop four-quark Bethe-Salpeter kernel","ref_index":72,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/DUZNOQ27V42RIXYNWJMJ2C5OJ7","json":"https://pith.science/pith/DUZNOQ27V42RIXYNWJMJ2C5OJ7.json","graph_json":"https://pith.science/api/pith-number/DUZNOQ27V42RIXYNWJMJ2C5OJ7/graph.json","events_json":"https://pith.science/api/pith-number/DUZNOQ27V42RIXYNWJMJ2C5OJ7/events.json","paper":"https://pith.science/paper/DUZNOQ27"},"agent_actions":{"view_html":"https://pith.science/pith/DUZNOQ27V42RIXYNWJMJ2C5OJ7","download_json":"https://pith.science/pith/DUZNOQ27V42RIXYNWJMJ2C5OJ7.json","view_paper":"https://pith.science/paper/DUZNOQ27","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=hep-ph/9602214&json=true","fetch_graph":"https://pith.science/api/pith-number/DUZNOQ27V42RIXYNWJMJ2C5OJ7/graph.json","fetch_events":"https://pith.science/api/pith-number/DUZNOQ27V42RIXYNWJMJ2C5OJ7/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/DUZNOQ27V42RIXYNWJMJ2C5OJ7/action/timestamp_anchor","attest_storage":"https://pith.science/pith/DUZNOQ27V42RIXYNWJMJ2C5OJ7/action/storage_attestation","attest_author":"https://pith.science/pith/DUZNOQ27V42RIXYNWJMJ2C5OJ7/action/author_attestation","sign_citation":"https://pith.science/pith/DUZNOQ27V42RIXYNWJMJ2C5OJ7/action/citation_signature","submit_replication":"https://pith.science/pith/DUZNOQ27V42RIXYNWJMJ2C5OJ7/action/replication_record"}},"created_at":"2026-07-04T16:01:28.500071+00:00","updated_at":"2026-07-04T16:01:28.500071+00:00"}