{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:PFYPHTCL7OUYV7KMFXXNF7QHCF","short_pith_number":"pith:PFYPHTCL","schema_version":"1.0","canonical_sha256":"7970f3cc4bfba98afd4c2deed2fe07117eb5bbe4b8c31560a3e22dfcfaffb916","source":{"kind":"arxiv","id":"1606.08662","version":2},"attestation_state":"computed","paper":{"title":"Towards the five-loop Beta function for a general gauge group","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"hep-ph","authors_text":"Andreas Maier, Peter Marquard, Thomas Luthe, York Schroder","submitted_at":"2016-06-28T11:50:11Z","abstract_excerpt":"We present analytical results for the $N_f^4$ and $N_f^3$ terms of the five-loop Beta function, for a general gauge group. While the former term agrees with results available from large-$N_f$ studies, the latter is new and extends the value known for SU(3) from an independent calculation."},"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":"1606.08662","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-ph","submitted_at":"2016-06-28T11:50:11Z","cross_cats_sorted":[],"title_canon_sha256":"237c27bac469d3db2fff7c461908c8dd1faafeb06fa7932632b560ba9b768b4d","abstract_canon_sha256":"e3038411ef87e42fd2479b0bad2a25e85bb46a60ca980d7215a2e652345cfe0e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:10:28.780978Z","signature_b64":"KoKKEKCftN+rySG+eDiHBzK6CuvMxyK8VMKVW3gNfPDcwbQVXSt1ys1XHdc5usO8pcd1Nif6pRbrneukeZEWBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7970f3cc4bfba98afd4c2deed2fe07117eb5bbe4b8c31560a3e22dfcfaffb916","last_reissued_at":"2026-05-18T01:10:28.780454Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:10:28.780454Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Towards the five-loop Beta function for a general gauge group","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"hep-ph","authors_text":"Andreas Maier, Peter Marquard, Thomas Luthe, York Schroder","submitted_at":"2016-06-28T11:50:11Z","abstract_excerpt":"We present analytical results for the $N_f^4$ and $N_f^3$ terms of the five-loop Beta function, for a general gauge group. While the former term agrees with results available from large-$N_f$ studies, the latter is new and extends the value known for SU(3) from an independent calculation."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.08662","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1606.08662","created_at":"2026-05-18T01:10:28.780531+00:00"},{"alias_kind":"arxiv_version","alias_value":"1606.08662v2","created_at":"2026-05-18T01:10:28.780531+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1606.08662","created_at":"2026-05-18T01:10:28.780531+00:00"},{"alias_kind":"pith_short_12","alias_value":"PFYPHTCL7OUY","created_at":"2026-05-18T12:30:39.010887+00:00"},{"alias_kind":"pith_short_16","alias_value":"PFYPHTCL7OUYV7KM","created_at":"2026-05-18T12:30:39.010887+00:00"},{"alias_kind":"pith_short_8","alias_value":"PFYPHTCL","created_at":"2026-05-18T12:30:39.010887+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"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":23,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/PFYPHTCL7OUYV7KMFXXNF7QHCF","json":"https://pith.science/pith/PFYPHTCL7OUYV7KMFXXNF7QHCF.json","graph_json":"https://pith.science/api/pith-number/PFYPHTCL7OUYV7KMFXXNF7QHCF/graph.json","events_json":"https://pith.science/api/pith-number/PFYPHTCL7OUYV7KMFXXNF7QHCF/events.json","paper":"https://pith.science/paper/PFYPHTCL"},"agent_actions":{"view_html":"https://pith.science/pith/PFYPHTCL7OUYV7KMFXXNF7QHCF","download_json":"https://pith.science/pith/PFYPHTCL7OUYV7KMFXXNF7QHCF.json","view_paper":"https://pith.science/paper/PFYPHTCL","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1606.08662&json=true","fetch_graph":"https://pith.science/api/pith-number/PFYPHTCL7OUYV7KMFXXNF7QHCF/graph.json","fetch_events":"https://pith.science/api/pith-number/PFYPHTCL7OUYV7KMFXXNF7QHCF/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/PFYPHTCL7OUYV7KMFXXNF7QHCF/action/timestamp_anchor","attest_storage":"https://pith.science/pith/PFYPHTCL7OUYV7KMFXXNF7QHCF/action/storage_attestation","attest_author":"https://pith.science/pith/PFYPHTCL7OUYV7KMFXXNF7QHCF/action/author_attestation","sign_citation":"https://pith.science/pith/PFYPHTCL7OUYV7KMFXXNF7QHCF/action/citation_signature","submit_replication":"https://pith.science/pith/PFYPHTCL7OUYV7KMFXXNF7QHCF/action/replication_record"}},"created_at":"2026-05-18T01:10:28.780531+00:00","updated_at":"2026-05-18T01:10:28.780531+00:00"}