{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:5NRCNPBF6QYU57STX6EKZNTM26","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"36e942d1fdb64161b1cbaf116747b0a9c66169b5ea580b77f65079c1ffdaa49a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2017-03-16T19:11:22Z","title_canon_sha256":"c6b69f359cd714ef835b73ba7c20d45c8dcf7c1b835a579ecc505194cbb8422f"},"schema_version":"1.0","source":{"id":"1703.05798","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1703.05798","created_at":"2026-05-18T00:41:24Z"},{"alias_kind":"arxiv_version","alias_value":"1703.05798v3","created_at":"2026-05-18T00:41:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1703.05798","created_at":"2026-05-18T00:41:24Z"},{"alias_kind":"pith_short_12","alias_value":"5NRCNPBF6QYU","created_at":"2026-05-18T12:31:00Z"},{"alias_kind":"pith_short_16","alias_value":"5NRCNPBF6QYU57ST","created_at":"2026-05-18T12:31:00Z"},{"alias_kind":"pith_short_8","alias_value":"5NRCNPBF","created_at":"2026-05-18T12:31:00Z"}],"graph_snapshots":[{"event_id":"sha256:f63fb69c17c607a213da61f4b1b10bb2fe68003208c054173af468e4fd493c00","target":"graph","created_at":"2026-05-18T00:41:24Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"We compute the grand partition function of $\\mathcal{N}=4$ SYM at one-loop in the $SU(2)$ sector with general chemical potentials, extending the results of P\\'olya's theorem. We make use of finite group theory, applicable to all orders of $1/N_c$ expansion. We show that only the planar terms contribute to the grand partition function, which is therefore equal to the grand partition function of an ensemble of XXX$_\\frac12$ spin chains. We discuss how Hagedorn temperature changes on the complex plane of chemical potentials.","authors_text":"Ryo Suzuki","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2017-03-16T19:11:22Z","title":"Refined Counting of Necklaces in One-loop $\\mathcal{N}=4$ SYM"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.05798","kind":"arxiv","version":3},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:5c2562d9546691945dac5f002c6ff71d598cd7e34fe1360bade84265d1a3259b","target":"record","created_at":"2026-05-18T00:41:24Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"36e942d1fdb64161b1cbaf116747b0a9c66169b5ea580b77f65079c1ffdaa49a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2017-03-16T19:11:22Z","title_canon_sha256":"c6b69f359cd714ef835b73ba7c20d45c8dcf7c1b835a579ecc505194cbb8422f"},"schema_version":"1.0","source":{"id":"1703.05798","kind":"arxiv","version":3}},"canonical_sha256":"eb6226bc25f4314efe53bf88acb66cd780bde695461f46b4fdf36e769ce4e6bc","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"eb6226bc25f4314efe53bf88acb66cd780bde695461f46b4fdf36e769ce4e6bc","first_computed_at":"2026-05-18T00:41:24.511439Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:41:24.511439Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"6wULoQ9z0kgPGclieqVKqgY2wN4IhV4RJdBkzdi9qGBXkUiiyckTjKfo6BJXtAXYpXg0tI0TPu0jAdhTVFyTCw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:41:24.512016Z","signed_message":"canonical_sha256_bytes"},"source_id":"1703.05798","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5c2562d9546691945dac5f002c6ff71d598cd7e34fe1360bade84265d1a3259b","sha256:f63fb69c17c607a213da61f4b1b10bb2fe68003208c054173af468e4fd493c00"],"state_sha256":"9dce2a2a3b0616a3f790a6528a35a333beba36ea9d8cb10d7cd8743f2d0a39d5"}