{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2024:RAASA2SQYERQTS3FPXDN7UGP7V","short_pith_number":"pith:RAASA2SQ","schema_version":"1.0","canonical_sha256":"8801206a50c12309cb657dc6dfd0cffd7457fca7e0f22f09434b4ec1a9e0ec70","source":{"kind":"arxiv","id":"2410.18174","version":3},"attestation_state":"computed","paper":{"title":"A universal inequality on the unitary 2D CFT partition function","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.stat-mech","math-ph","math.MP"],"primary_cat":"hep-th","authors_text":"Indranil Dey, Jiaxin Qiao, Sridip Pal","submitted_at":"2024-10-23T18:00:01Z","abstract_excerpt":"We prove the conjecture proposed by Hartman, Keller and Stoica [HKS14]: the grand-canonical free energy of a unitary 2D CFT with a sparse spectrum below the scaling dimension $\\frac{c}{12}+\\epsilon$ and below the twist $\\frac{c}{12}$ is universal in the large $c$ limit for all $\\beta_L\\beta_R \\neq 4\\pi^2$.\n  The technique of the proof allows us to derive a one-parameter (with parameter $\\alpha\\in(0,1]$) family of universal inequalities on the unitary 2D CFT partition function with general central charge $c\\geqslant 0$, using analytical modular bootstrap. We derive an iterative equation for the"},"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":"2410.18174","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2024-10-23T18:00:01Z","cross_cats_sorted":["cond-mat.stat-mech","math-ph","math.MP"],"title_canon_sha256":"cb125bf4f9ec153fe9843b8b974f2ea8692ee7566f9d50d6425ead8e0d038974","abstract_canon_sha256":"03ef389858ff141bb5f0b0e2ba923da6c5c442f1868b2b0c441735d2f699bcd2"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:58:19.568464Z","signature_b64":"7pYkh6HsHntbMqVVtjKk5IVP2SGew+8B9RyUWbxvSnvIOMZnpTgA+Abou38UxBCK9ezGffQJ/I5qW90H0LvoBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8801206a50c12309cb657dc6dfd0cffd7457fca7e0f22f09434b4ec1a9e0ec70","last_reissued_at":"2026-07-05T10:58:19.567879Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:58:19.567879Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A universal inequality on the unitary 2D CFT partition function","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.stat-mech","math-ph","math.MP"],"primary_cat":"hep-th","authors_text":"Indranil Dey, Jiaxin Qiao, Sridip Pal","submitted_at":"2024-10-23T18:00:01Z","abstract_excerpt":"We prove the conjecture proposed by Hartman, Keller and Stoica [HKS14]: the grand-canonical free energy of a unitary 2D CFT with a sparse spectrum below the scaling dimension $\\frac{c}{12}+\\epsilon$ and below the twist $\\frac{c}{12}$ is universal in the large $c$ limit for all $\\beta_L\\beta_R \\neq 4\\pi^2$.\n  The technique of the proof allows us to derive a one-parameter (with parameter $\\alpha\\in(0,1]$) family of universal inequalities on the unitary 2D CFT partition function with general central charge $c\\geqslant 0$, using analytical modular bootstrap. We derive an iterative equation for the"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2410.18174","kind":"arxiv","version":3},"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/2410.18174/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":"2410.18174","created_at":"2026-07-05T10:58:19.567946+00:00"},{"alias_kind":"arxiv_version","alias_value":"2410.18174v3","created_at":"2026-07-05T10:58:19.567946+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2410.18174","created_at":"2026-07-05T10:58:19.567946+00:00"},{"alias_kind":"pith_short_12","alias_value":"RAASA2SQYERQ","created_at":"2026-07-05T10:58:19.567946+00:00"},{"alias_kind":"pith_short_16","alias_value":"RAASA2SQYERQTS3F","created_at":"2026-07-05T10:58:19.567946+00:00"},{"alias_kind":"pith_short_8","alias_value":"RAASA2SQ","created_at":"2026-07-05T10:58:19.567946+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2508.03236","citing_title":"Timelike Liouville theory and AdS$_3$ gravity at finite cutoff","ref_index":65,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/RAASA2SQYERQTS3FPXDN7UGP7V","json":"https://pith.science/pith/RAASA2SQYERQTS3FPXDN7UGP7V.json","graph_json":"https://pith.science/api/pith-number/RAASA2SQYERQTS3FPXDN7UGP7V/graph.json","events_json":"https://pith.science/api/pith-number/RAASA2SQYERQTS3FPXDN7UGP7V/events.json","paper":"https://pith.science/paper/RAASA2SQ"},"agent_actions":{"view_html":"https://pith.science/pith/RAASA2SQYERQTS3FPXDN7UGP7V","download_json":"https://pith.science/pith/RAASA2SQYERQTS3FPXDN7UGP7V.json","view_paper":"https://pith.science/paper/RAASA2SQ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2410.18174&json=true","fetch_graph":"https://pith.science/api/pith-number/RAASA2SQYERQTS3FPXDN7UGP7V/graph.json","fetch_events":"https://pith.science/api/pith-number/RAASA2SQYERQTS3FPXDN7UGP7V/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/RAASA2SQYERQTS3FPXDN7UGP7V/action/timestamp_anchor","attest_storage":"https://pith.science/pith/RAASA2SQYERQTS3FPXDN7UGP7V/action/storage_attestation","attest_author":"https://pith.science/pith/RAASA2SQYERQTS3FPXDN7UGP7V/action/author_attestation","sign_citation":"https://pith.science/pith/RAASA2SQYERQTS3FPXDN7UGP7V/action/citation_signature","submit_replication":"https://pith.science/pith/RAASA2SQYERQTS3FPXDN7UGP7V/action/replication_record"}},"created_at":"2026-07-05T10:58:19.567946+00:00","updated_at":"2026-07-05T10:58:19.567946+00:00"}