{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2007:KAKQ6TEMYAOW5MCM2URQQIPJ6I","short_pith_number":"pith:KAKQ6TEM","schema_version":"1.0","canonical_sha256":"50150f4c8cc01d6eb04cd5230821e9f212ea1062f3b642ebe526dcf7145739e0","source":{"kind":"arxiv","id":"0707.2936","version":2},"attestation_state":"computed","paper":{"title":"Anomalous dimensions of leading twist conformal operators","license":"","headline":"","cross_cats":[],"primary_cat":"hep-th","authors_text":"A. V. Belitsky, C. Jarczak, D. M\\\"uller, E. Sokatchev, J. Henn","submitted_at":"2007-07-19T16:33:56Z","abstract_excerpt":"We extend and develop a method for perturbative calculations of anomalous dimensions and mixing matrices of leading twist conformal primary operators in conformal field theories. Such operators lie on the unitarity bound and hence are conserved (irreducible) in the free theory. The technique relies on the known pattern of breaking of the irreducibility conditions in the interacting theory. We relate the divergence of the conformal operators via the field equations to their descendants involving an extra field and accompanied by an extra power of the coupling constant. The ratio of the two-poin"},"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":"0707.2936","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"hep-th","submitted_at":"2007-07-19T16:33:56Z","cross_cats_sorted":[],"title_canon_sha256":"f48df8b91807de2c910a38a6cb41986689b124974e2f120902bfea36cdc081ba","abstract_canon_sha256":"b84d9e9d56a8127f0d48d9030c52fe3adc7cde0ed2539d7f0cc038c9645d09e1"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T15:24:29.034529Z","signature_b64":"VMLOC8heFQNY2f7wVuD1ITH8/FvLKd8vd+oMlIdONBzFSxW6icfnEGvrRNmS8qOJatT/5NOvmceyRdkdGSOhAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"50150f4c8cc01d6eb04cd5230821e9f212ea1062f3b642ebe526dcf7145739e0","last_reissued_at":"2026-07-04T15:24:29.034054Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T15:24:29.034054Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Anomalous dimensions of leading twist conformal operators","license":"","headline":"","cross_cats":[],"primary_cat":"hep-th","authors_text":"A. V. Belitsky, C. Jarczak, D. M\\\"uller, E. Sokatchev, J. Henn","submitted_at":"2007-07-19T16:33:56Z","abstract_excerpt":"We extend and develop a method for perturbative calculations of anomalous dimensions and mixing matrices of leading twist conformal primary operators in conformal field theories. Such operators lie on the unitarity bound and hence are conserved (irreducible) in the free theory. The technique relies on the known pattern of breaking of the irreducibility conditions in the interacting theory. We relate the divergence of the conformal operators via the field equations to their descendants involving an extra field and accompanied by an extra power of the coupling constant. The ratio of the two-poin"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0707.2936","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/0707.2936/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":"0707.2936","created_at":"2026-07-04T15:24:29.034119+00:00"},{"alias_kind":"arxiv_version","alias_value":"0707.2936v2","created_at":"2026-07-04T15:24:29.034119+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0707.2936","created_at":"2026-07-04T15:24:29.034119+00:00"},{"alias_kind":"pith_short_12","alias_value":"KAKQ6TEMYAOW","created_at":"2026-07-04T15:24:29.034119+00:00"},{"alias_kind":"pith_short_16","alias_value":"KAKQ6TEMYAOW5MCM","created_at":"2026-07-04T15:24:29.034119+00:00"},{"alias_kind":"pith_short_8","alias_value":"KAKQ6TEM","created_at":"2026-07-04T15:24:29.034119+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2606.07738","citing_title":"New Exotic Operators in the Spectrum of Wilson Lines in General Representations","ref_index":64,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/KAKQ6TEMYAOW5MCM2URQQIPJ6I","json":"https://pith.science/pith/KAKQ6TEMYAOW5MCM2URQQIPJ6I.json","graph_json":"https://pith.science/api/pith-number/KAKQ6TEMYAOW5MCM2URQQIPJ6I/graph.json","events_json":"https://pith.science/api/pith-number/KAKQ6TEMYAOW5MCM2URQQIPJ6I/events.json","paper":"https://pith.science/paper/KAKQ6TEM"},"agent_actions":{"view_html":"https://pith.science/pith/KAKQ6TEMYAOW5MCM2URQQIPJ6I","download_json":"https://pith.science/pith/KAKQ6TEMYAOW5MCM2URQQIPJ6I.json","view_paper":"https://pith.science/paper/KAKQ6TEM","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=0707.2936&json=true","fetch_graph":"https://pith.science/api/pith-number/KAKQ6TEMYAOW5MCM2URQQIPJ6I/graph.json","fetch_events":"https://pith.science/api/pith-number/KAKQ6TEMYAOW5MCM2URQQIPJ6I/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/KAKQ6TEMYAOW5MCM2URQQIPJ6I/action/timestamp_anchor","attest_storage":"https://pith.science/pith/KAKQ6TEMYAOW5MCM2URQQIPJ6I/action/storage_attestation","attest_author":"https://pith.science/pith/KAKQ6TEMYAOW5MCM2URQQIPJ6I/action/author_attestation","sign_citation":"https://pith.science/pith/KAKQ6TEMYAOW5MCM2URQQIPJ6I/action/citation_signature","submit_replication":"https://pith.science/pith/KAKQ6TEMYAOW5MCM2URQQIPJ6I/action/replication_record"}},"created_at":"2026-07-04T15:24:29.034119+00:00","updated_at":"2026-07-04T15:24:29.034119+00:00"}