{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:MAI6DFNTD3XAF4VKSS4Z3VALQ2","short_pith_number":"pith:MAI6DFNT","schema_version":"1.0","canonical_sha256":"6011e195b31eee02f2aa94b99dd40b86a3aa334ae798ef0103fe34fb5d9be6da","source":{"kind":"arxiv","id":"1302.5434","version":1},"attestation_state":"computed","paper":{"title":"Higher-Loop Calculations of the Ultraviolet to Infrared Evolution of a Vectorial Gauge Theory in the Limit $N_c \\to \\infty$, $N_f \\to \\infty$ with $N_f/N_c$ Fixed","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"hep-th","authors_text":"Robert Shrock","submitted_at":"2013-02-21T21:07:24Z","abstract_excerpt":"We consider an asymptotically free vectorial SU($N_c$) gauge theory with $N_f$ fermions in the fundamental representation and analyze higher-loop contributions to the evolution of the theory from the ultraviolet to the infrared in the limit where $N_c \\to \\infty$ and $N_f \\to \\infty$ with $r=N_f/N_c$ a fixed, finite constant. We focus on the case where the $n$-loop beta function has an infrared zero, at $\\xi=\\xi_{IR,n\\ell}$, where $\\xi=\\alpha N_c$. We give results on $\\xi_{IR,n\\ell}$, the anomalous dimension of the fermion bilinear evaluated at $\\xi_{IR,n\\ell}$, denoted $\\gamma_{IR,n\\ell}$, an"},"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":"1302.5434","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2013-02-21T21:07:24Z","cross_cats_sorted":[],"title_canon_sha256":"d2f6dc2cac29c70015a92a3676e5893cb3882fcd2a52059ee2ad8daa4060bacb","abstract_canon_sha256":"6ed1ba78dc296327c4ddb3105a4da62108ecc8701ff2bc11bdc6814b71257ae5"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:19:59.034419Z","signature_b64":"8Y8awYIILTXMrqv5VS08hfAacraH/E8hQOWwwPDWKOatUy+nZIC0OFY1IVv4cJAd59d+SAATsUPennQlgrVxBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6011e195b31eee02f2aa94b99dd40b86a3aa334ae798ef0103fe34fb5d9be6da","last_reissued_at":"2026-05-18T03:19:59.033907Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:19:59.033907Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Higher-Loop Calculations of the Ultraviolet to Infrared Evolution of a Vectorial Gauge Theory in the Limit $N_c \\to \\infty$, $N_f \\to \\infty$ with $N_f/N_c$ Fixed","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"hep-th","authors_text":"Robert Shrock","submitted_at":"2013-02-21T21:07:24Z","abstract_excerpt":"We consider an asymptotically free vectorial SU($N_c$) gauge theory with $N_f$ fermions in the fundamental representation and analyze higher-loop contributions to the evolution of the theory from the ultraviolet to the infrared in the limit where $N_c \\to \\infty$ and $N_f \\to \\infty$ with $r=N_f/N_c$ a fixed, finite constant. We focus on the case where the $n$-loop beta function has an infrared zero, at $\\xi=\\xi_{IR,n\\ell}$, where $\\xi=\\alpha N_c$. We give results on $\\xi_{IR,n\\ell}$, the anomalous dimension of the fermion bilinear evaluated at $\\xi_{IR,n\\ell}$, denoted $\\gamma_{IR,n\\ell}$, an"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.5434","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":""},"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":"1302.5434","created_at":"2026-05-18T03:19:59.033982+00:00"},{"alias_kind":"arxiv_version","alias_value":"1302.5434v1","created_at":"2026-05-18T03:19:59.033982+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1302.5434","created_at":"2026-05-18T03:19:59.033982+00:00"},{"alias_kind":"pith_short_12","alias_value":"MAI6DFNTD3XA","created_at":"2026-05-18T12:27:51.066281+00:00"},{"alias_kind":"pith_short_16","alias_value":"MAI6DFNTD3XAF4VK","created_at":"2026-05-18T12:27:51.066281+00:00"},{"alias_kind":"pith_short_8","alias_value":"MAI6DFNT","created_at":"2026-05-18T12:27:51.066281+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/MAI6DFNTD3XAF4VKSS4Z3VALQ2","json":"https://pith.science/pith/MAI6DFNTD3XAF4VKSS4Z3VALQ2.json","graph_json":"https://pith.science/api/pith-number/MAI6DFNTD3XAF4VKSS4Z3VALQ2/graph.json","events_json":"https://pith.science/api/pith-number/MAI6DFNTD3XAF4VKSS4Z3VALQ2/events.json","paper":"https://pith.science/paper/MAI6DFNT"},"agent_actions":{"view_html":"https://pith.science/pith/MAI6DFNTD3XAF4VKSS4Z3VALQ2","download_json":"https://pith.science/pith/MAI6DFNTD3XAF4VKSS4Z3VALQ2.json","view_paper":"https://pith.science/paper/MAI6DFNT","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1302.5434&json=true","fetch_graph":"https://pith.science/api/pith-number/MAI6DFNTD3XAF4VKSS4Z3VALQ2/graph.json","fetch_events":"https://pith.science/api/pith-number/MAI6DFNTD3XAF4VKSS4Z3VALQ2/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/MAI6DFNTD3XAF4VKSS4Z3VALQ2/action/timestamp_anchor","attest_storage":"https://pith.science/pith/MAI6DFNTD3XAF4VKSS4Z3VALQ2/action/storage_attestation","attest_author":"https://pith.science/pith/MAI6DFNTD3XAF4VKSS4Z3VALQ2/action/author_attestation","sign_citation":"https://pith.science/pith/MAI6DFNTD3XAF4VKSS4Z3VALQ2/action/citation_signature","submit_replication":"https://pith.science/pith/MAI6DFNTD3XAF4VKSS4Z3VALQ2/action/replication_record"}},"created_at":"2026-05-18T03:19:59.033982+00:00","updated_at":"2026-05-18T03:19:59.033982+00:00"}