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We find that the sub-logarithmic contribution $\\gamma^{(n)}(g,L) $ is governed by a linear integral equation, depending on the solution of the linear integral equations appearing at the steps $n'\\leq n-3$. We work out this recursive procedure and determine explicitly $\\gamma^{(n)}(g,L) $ (in particular $\\gamma^{(1)}(g,L)=0$ and "},"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":"0911.2425","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2009-11-12T17:49:57Z","cross_cats_sorted":[],"title_canon_sha256":"a69411a6d90ffafbc7a2e92a3409a72c8f23862002a09510b9f31ced1123da3b","abstract_canon_sha256":"07a5e194052c7fd5f61be2e0125a53f59690288bc9c5c16dfef3e115902981b7"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:34:11.076127Z","signature_b64":"7NbCUCELu/uTruJxHnCZxkkb6/hUMyR3tBz1fxX4q0llPQz5NnDQILa8RAXbnPVioEvVPIXr4Kq7LShRkuGpDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d0073c0cd09ec8830c952905b1e0ac39feac3dd508f6b4416a5b57429c6d15cf","last_reissued_at":"2026-05-18T02:34:11.075672Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:34:11.075672Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the logarithmic powers of $sl(2)$ SYM$_4$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"hep-th","authors_text":"Davide Fioravanti, Marco Rossi, Paolo Grinza","submitted_at":"2009-11-12T17:49:57Z","abstract_excerpt":"In the high spin limit the minimal anomalous dimension of (fixed) twist operators in the $sl(2)$ sector of planar ${\\cal N}=4$ Super Yang-Mills theory expands as $\\gamma(g,s,L)=f(g) \\ln s + f_{sl}(g,L) + \\sum \\limits_{n=1}^\\infty \\gamma^{(n)}(g,L) (\\ln s)^{-n} + ... $. We find that the sub-logarithmic contribution $\\gamma^{(n)}(g,L) $ is governed by a linear integral equation, depending on the solution of the linear integral equations appearing at the steps $n'\\leq n-3$. We work out this recursive procedure and determine explicitly $\\gamma^{(n)}(g,L) $ (in particular $\\gamma^{(1)}(g,L)=0$ and "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0911.2425","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":"0911.2425","created_at":"2026-05-18T02:34:11.075752+00:00"},{"alias_kind":"arxiv_version","alias_value":"0911.2425v2","created_at":"2026-05-18T02:34:11.075752+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0911.2425","created_at":"2026-05-18T02:34:11.075752+00:00"},{"alias_kind":"pith_short_12","alias_value":"2ADTYDGQT3EI","created_at":"2026-05-18T12:25:58.018023+00:00"},{"alias_kind":"pith_short_16","alias_value":"2ADTYDGQT3EIGDEV","created_at":"2026-05-18T12:25:58.018023+00:00"},{"alias_kind":"pith_short_8","alias_value":"2ADTYDGQ","created_at":"2026-05-18T12:25:58.018023+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/2ADTYDGQT3EIGDEVFEC3DYFMHH","json":"https://pith.science/pith/2ADTYDGQT3EIGDEVFEC3DYFMHH.json","graph_json":"https://pith.science/api/pith-number/2ADTYDGQT3EIGDEVFEC3DYFMHH/graph.json","events_json":"https://pith.science/api/pith-number/2ADTYDGQT3EIGDEVFEC3DYFMHH/events.json","paper":"https://pith.science/paper/2ADTYDGQ"},"agent_actions":{"view_html":"https://pith.science/pith/2ADTYDGQT3EIGDEVFEC3DYFMHH","download_json":"https://pith.science/pith/2ADTYDGQT3EIGDEVFEC3DYFMHH.json","view_paper":"https://pith.science/paper/2ADTYDGQ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=0911.2425&json=true","fetch_graph":"https://pith.science/api/pith-number/2ADTYDGQT3EIGDEVFEC3DYFMHH/graph.json","fetch_events":"https://pith.science/api/pith-number/2ADTYDGQT3EIGDEVFEC3DYFMHH/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/2ADTYDGQT3EIGDEVFEC3DYFMHH/action/timestamp_anchor","attest_storage":"https://pith.science/pith/2ADTYDGQT3EIGDEVFEC3DYFMHH/action/storage_attestation","attest_author":"https://pith.science/pith/2ADTYDGQT3EIGDEVFEC3DYFMHH/action/author_attestation","sign_citation":"https://pith.science/pith/2ADTYDGQT3EIGDEVFEC3DYFMHH/action/citation_signature","submit_replication":"https://pith.science/pith/2ADTYDGQT3EIGDEVFEC3DYFMHH/action/replication_record"}},"created_at":"2026-05-18T02:34:11.075752+00:00","updated_at":"2026-05-18T02:34:11.075752+00:00"}