{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:RAASA2SQYERQTS3FPXDN7UGP7V","short_pith_number":"pith:RAASA2SQ","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"},"canonical_sha256":"8801206a50c12309cb657dc6dfd0cffd7457fca7e0f22f09434b4ec1a9e0ec70","source":{"kind":"arxiv","id":"2410.18174","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2410.18174","created_at":"2026-07-05T10:58:19Z"},{"alias_kind":"arxiv_version","alias_value":"2410.18174v3","created_at":"2026-07-05T10:58:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2410.18174","created_at":"2026-07-05T10:58:19Z"},{"alias_kind":"pith_short_12","alias_value":"RAASA2SQYERQ","created_at":"2026-07-05T10:58:19Z"},{"alias_kind":"pith_short_16","alias_value":"RAASA2SQYERQTS3F","created_at":"2026-07-05T10:58:19Z"},{"alias_kind":"pith_short_8","alias_value":"RAASA2SQ","created_at":"2026-07-05T10:58:19Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:RAASA2SQYERQTS3FPXDN7UGP7V","target":"record","payload":{"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"},"canonical_sha256":"8801206a50c12309cb657dc6dfd0cffd7457fca7e0f22f09434b4ec1a9e0ec70","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"},"source_kind":"arxiv","source_id":"2410.18174","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T10:58:19Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QzULYeim3mUYpPBlATnKjgFYfr+HrHj6nHjxOyx7mJ1t4TJmSEYt7m14aXPvJD6T13rh31X9b9U6IjM9+jV5Bw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-08T03:38:48.355230Z"},"content_sha256":"771ae348b6bf03cf02e74c11a48edff00d0be8c1a813790077039ac8c1ec84ea","schema_version":"1.0","event_id":"sha256:771ae348b6bf03cf02e74c11a48edff00d0be8c1a813790077039ac8c1ec84ea"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:RAASA2SQYERQTS3FPXDN7UGP7V","target":"graph","payload":{"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T10:58:19Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Y29hqLSlqEkGoIpeyHksy5jotRmgYkM/KdfWml+qOEKmEb4gUyPctz5+E3e3QzOk2qlkgyjaHFVSXc/W3Ir3CQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-08T03:38:48.355741Z"},"content_sha256":"c9b956fbf8eaf593aa2a3869175a397e49c202cf084f69e8ea72993db283fcc3","schema_version":"1.0","event_id":"sha256:c9b956fbf8eaf593aa2a3869175a397e49c202cf084f69e8ea72993db283fcc3"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/RAASA2SQYERQTS3FPXDN7UGP7V/bundle.json","state_url":"https://pith.science/pith/RAASA2SQYERQTS3FPXDN7UGP7V/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/RAASA2SQYERQTS3FPXDN7UGP7V/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-08-08T03:38:48Z","links":{"resolver":"https://pith.science/pith/RAASA2SQYERQTS3FPXDN7UGP7V","bundle":"https://pith.science/pith/RAASA2SQYERQTS3FPXDN7UGP7V/bundle.json","state":"https://pith.science/pith/RAASA2SQYERQTS3FPXDN7UGP7V/state.json","well_known_bundle":"https://pith.science/.well-known/pith/RAASA2SQYERQTS3FPXDN7UGP7V/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:RAASA2SQYERQTS3FPXDN7UGP7V","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":"03ef389858ff141bb5f0b0e2ba923da6c5c442f1868b2b0c441735d2f699bcd2","cross_cats_sorted":["cond-mat.stat-mech","math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2024-10-23T18:00:01Z","title_canon_sha256":"cb125bf4f9ec153fe9843b8b974f2ea8692ee7566f9d50d6425ead8e0d038974"},"schema_version":"1.0","source":{"id":"2410.18174","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2410.18174","created_at":"2026-07-05T10:58:19Z"},{"alias_kind":"arxiv_version","alias_value":"2410.18174v3","created_at":"2026-07-05T10:58:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2410.18174","created_at":"2026-07-05T10:58:19Z"},{"alias_kind":"pith_short_12","alias_value":"RAASA2SQYERQ","created_at":"2026-07-05T10:58:19Z"},{"alias_kind":"pith_short_16","alias_value":"RAASA2SQYERQTS3F","created_at":"2026-07-05T10:58:19Z"},{"alias_kind":"pith_short_8","alias_value":"RAASA2SQ","created_at":"2026-07-05T10:58:19Z"}],"graph_snapshots":[{"event_id":"sha256:c9b956fbf8eaf593aa2a3869175a397e49c202cf084f69e8ea72993db283fcc3","target":"graph","created_at":"2026-07-05T10:58:19Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2410.18174/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"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","authors_text":"Indranil Dey, Jiaxin Qiao, Sridip Pal","cross_cats":["cond-mat.stat-mech","math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2024-10-23T18:00:01Z","title":"A universal inequality on the unitary 2D CFT partition function"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2410.18174","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":"sha256:771ae348b6bf03cf02e74c11a48edff00d0be8c1a813790077039ac8c1ec84ea","target":"record","created_at":"2026-07-05T10:58:19Z","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":"03ef389858ff141bb5f0b0e2ba923da6c5c442f1868b2b0c441735d2f699bcd2","cross_cats_sorted":["cond-mat.stat-mech","math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2024-10-23T18:00:01Z","title_canon_sha256":"cb125bf4f9ec153fe9843b8b974f2ea8692ee7566f9d50d6425ead8e0d038974"},"schema_version":"1.0","source":{"id":"2410.18174","kind":"arxiv","version":3}},"canonical_sha256":"8801206a50c12309cb657dc6dfd0cffd7457fca7e0f22f09434b4ec1a9e0ec70","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8801206a50c12309cb657dc6dfd0cffd7457fca7e0f22f09434b4ec1a9e0ec70","first_computed_at":"2026-07-05T10:58:19.567879Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T10:58:19.567879Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"7pYkh6HsHntbMqVVtjKk5IVP2SGew+8B9RyUWbxvSnvIOMZnpTgA+Abou38UxBCK9ezGffQJ/I5qW90H0LvoBQ==","signature_status":"signed_v1","signed_at":"2026-07-05T10:58:19.568464Z","signed_message":"canonical_sha256_bytes"},"source_id":"2410.18174","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:771ae348b6bf03cf02e74c11a48edff00d0be8c1a813790077039ac8c1ec84ea","sha256:c9b956fbf8eaf593aa2a3869175a397e49c202cf084f69e8ea72993db283fcc3"],"state_sha256":"0be51e4cba0eee11a482175ddbbafa97bba782a518e3644db7b4b93d287f4b82"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FsGqT2sNGa4Ii4KeW4rSoJpFYCMkviIk76m4lW2i7S2OmQAIikilexpQVBBKtFq6suBetGKhhm8i2pPxD3h4Dg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-08T03:38:48.360028Z","bundle_sha256":"6cbd0d5f10c976534685db061f2759dec412bb00bb12b9dd101edb7926a42639"}}