{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2022:B7YJB7WRXA7VQU4EJVFUTIFWGM","short_pith_number":"pith:B7YJB7WR","schema_version":"1.0","canonical_sha256":"0ff090fed1b83f5853844d4b49a0b6333e7c95acbeb6278b9657281dcaf36cf0","source":{"kind":"arxiv","id":"2208.04612","version":1},"attestation_state":"computed","paper":{"title":"Six-loop anomalous dimension of the $\\phi^Q$ operator in the $O(N)$ symmetric model","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cond-mat.stat-mech","hep-ph"],"primary_cat":"hep-th","authors_text":"Alexander Bednyakov, Andrey Pikelner","submitted_at":"2022-08-09T09:07:47Z","abstract_excerpt":"A technique of large-charge expansion provides a novel opportunity for calculation of critical dimensions of operators $\\phi^Q$ with fixed charge $Q$. In the small-coupling regime the polynomial structure of the anomalous dimensions can be fixed from a number of direct perturbative calculations for a fixed $Q$. At the six-loop level one needs to include new diagrams that correspond to operators with five or more legs. The latter never appeared before in scalar-theory calculations. Here we show how to compute the anomalous dimension of the operator $\\phi^{Q=5}$ at the six-loop order. In combina"},"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":"2208.04612","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"hep-th","submitted_at":"2022-08-09T09:07:47Z","cross_cats_sorted":["cond-mat.stat-mech","hep-ph"],"title_canon_sha256":"878550b44a45c8e873e05db05167ac35e6d9ffd04023773d23f98320b3bad0fe","abstract_canon_sha256":"fd5dff2898f7542ff3e4d8501291f4cb72903808f74392ce938d58c30ce32210"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T05:14:20.186160Z","signature_b64":"47Anlu2DpGHGENOB6Xj10GhxmnLSceBqspapcp9mFmNMvfEbgQMpqNRGyo82SlEn4vEHMR5zTniLqTvSS+D8DA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0ff090fed1b83f5853844d4b49a0b6333e7c95acbeb6278b9657281dcaf36cf0","last_reissued_at":"2026-07-05T05:14:20.184836Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T05:14:20.184836Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Six-loop anomalous dimension of the $\\phi^Q$ operator in the $O(N)$ symmetric model","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cond-mat.stat-mech","hep-ph"],"primary_cat":"hep-th","authors_text":"Alexander Bednyakov, Andrey Pikelner","submitted_at":"2022-08-09T09:07:47Z","abstract_excerpt":"A technique of large-charge expansion provides a novel opportunity for calculation of critical dimensions of operators $\\phi^Q$ with fixed charge $Q$. In the small-coupling regime the polynomial structure of the anomalous dimensions can be fixed from a number of direct perturbative calculations for a fixed $Q$. At the six-loop level one needs to include new diagrams that correspond to operators with five or more legs. The latter never appeared before in scalar-theory calculations. Here we show how to compute the anomalous dimension of the operator $\\phi^{Q=5}$ at the six-loop order. In combina"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2208.04612","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/2208.04612/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":"2208.04612","created_at":"2026-07-05T05:14:20.185634+00:00"},{"alias_kind":"arxiv_version","alias_value":"2208.04612v1","created_at":"2026-07-05T05:14:20.185634+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2208.04612","created_at":"2026-07-05T05:14:20.185634+00:00"},{"alias_kind":"pith_short_12","alias_value":"B7YJB7WRXA7V","created_at":"2026-07-05T05:14:20.185634+00:00"},{"alias_kind":"pith_short_16","alias_value":"B7YJB7WRXA7VQU4E","created_at":"2026-07-05T05:14:20.185634+00:00"},{"alias_kind":"pith_short_8","alias_value":"B7YJB7WR","created_at":"2026-07-05T05:14:20.185634+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2604.13464","citing_title":"Four-loop Anomalous Dimensions of Scalar-QED Theory from Operator Product Expansion","ref_index":51,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/B7YJB7WRXA7VQU4EJVFUTIFWGM","json":"https://pith.science/pith/B7YJB7WRXA7VQU4EJVFUTIFWGM.json","graph_json":"https://pith.science/api/pith-number/B7YJB7WRXA7VQU4EJVFUTIFWGM/graph.json","events_json":"https://pith.science/api/pith-number/B7YJB7WRXA7VQU4EJVFUTIFWGM/events.json","paper":"https://pith.science/paper/B7YJB7WR"},"agent_actions":{"view_html":"https://pith.science/pith/B7YJB7WRXA7VQU4EJVFUTIFWGM","download_json":"https://pith.science/pith/B7YJB7WRXA7VQU4EJVFUTIFWGM.json","view_paper":"https://pith.science/paper/B7YJB7WR","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2208.04612&json=true","fetch_graph":"https://pith.science/api/pith-number/B7YJB7WRXA7VQU4EJVFUTIFWGM/graph.json","fetch_events":"https://pith.science/api/pith-number/B7YJB7WRXA7VQU4EJVFUTIFWGM/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/B7YJB7WRXA7VQU4EJVFUTIFWGM/action/timestamp_anchor","attest_storage":"https://pith.science/pith/B7YJB7WRXA7VQU4EJVFUTIFWGM/action/storage_attestation","attest_author":"https://pith.science/pith/B7YJB7WRXA7VQU4EJVFUTIFWGM/action/author_attestation","sign_citation":"https://pith.science/pith/B7YJB7WRXA7VQU4EJVFUTIFWGM/action/citation_signature","submit_replication":"https://pith.science/pith/B7YJB7WRXA7VQU4EJVFUTIFWGM/action/replication_record"}},"created_at":"2026-07-05T05:14:20.185634+00:00","updated_at":"2026-07-05T05:14:20.185634+00:00"}