{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:MNHEAVZVJ3XU66QQPVFLF3CSIN","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":"e21768c72b501a1315b9e3394a56b38182d52a67228b18ed47d2e63216cdfda0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2018-03-13T17:11:45Z","title_canon_sha256":"c2c2403958c1a96b3bd4192b3fbb531c64b1525b6d0490c8595bae4accb683db"},"schema_version":"1.0","source":{"id":"1803.04938","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1803.04938","created_at":"2026-05-18T00:05:57Z"},{"alias_kind":"arxiv_version","alias_value":"1803.04938v3","created_at":"2026-05-18T00:05:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1803.04938","created_at":"2026-05-18T00:05:57Z"},{"alias_kind":"pith_short_12","alias_value":"MNHEAVZVJ3XU","created_at":"2026-05-18T12:32:37Z"},{"alias_kind":"pith_short_16","alias_value":"MNHEAVZVJ3XU66QQ","created_at":"2026-05-18T12:32:37Z"},{"alias_kind":"pith_short_8","alias_value":"MNHEAVZV","created_at":"2026-05-18T12:32:37Z"}],"graph_snapshots":[{"event_id":"sha256:4324ce4f3a34be8037f048539763d6459b2159888aa88cde494d853f5da751e0","target":"graph","created_at":"2026-05-18T00:05:57Z","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 consider unitary, modular invariant, two-dimensional CFTs which are invariant under the parity transformation $P$. Combining $P$ with modular inversion $S$ leads to a continuous family of fixed points of the $SP$ transformation. A particular subset of this locus of fixed points exists along the line of positive left- and right-moving temperatures satisfying $\\beta_L \\beta_R = 4\\pi^2$. We use this fixed locus to prove a conjecture of Hartman, Keller, and Stoica that the free energy of a large-$c$ CFT$_2$ with a suitably sparse low-lying spectrum matches that of AdS$_3$ gravity at all tempera","authors_text":"Edgar Shaghoulian, Raghu Mahajan, Tarek Anous","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2018-03-13T17:11:45Z","title":"Parity and the modular bootstrap"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.04938","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:ea7785c310483915809fc7bfd507eb688d70e94ddaaf0ba7edb0dc54adfabb01","target":"record","created_at":"2026-05-18T00:05:57Z","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":"e21768c72b501a1315b9e3394a56b38182d52a67228b18ed47d2e63216cdfda0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2018-03-13T17:11:45Z","title_canon_sha256":"c2c2403958c1a96b3bd4192b3fbb531c64b1525b6d0490c8595bae4accb683db"},"schema_version":"1.0","source":{"id":"1803.04938","kind":"arxiv","version":3}},"canonical_sha256":"634e4057354eef4f7a107d4ab2ec52437c86e54a102142317408fdac44aec154","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"634e4057354eef4f7a107d4ab2ec52437c86e54a102142317408fdac44aec154","first_computed_at":"2026-05-18T00:05:57.314542Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:05:57.314542Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"C3Dkex5vAFzyERYyWzw77aqYTarFCLoTAPhhb7kS4hFX2X50FNO8wrRIGzOm3YxuYAYt2H9i5zlUtpNPX2gYDw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:05:57.315066Z","signed_message":"canonical_sha256_bytes"},"source_id":"1803.04938","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ea7785c310483915809fc7bfd507eb688d70e94ddaaf0ba7edb0dc54adfabb01","sha256:4324ce4f3a34be8037f048539763d6459b2159888aa88cde494d853f5da751e0"],"state_sha256":"9b729b7c5ad32303bfe44919cb9d8515055bc340e91d4ecebf9600a003b201ef"}