{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:MNHEAVZVJ3XU66QQPVFLF3CSIN","short_pith_number":"pith:MNHEAVZV","canonical_record":{"source":{"id":"1803.04938","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2018-03-13T17:11:45Z","cross_cats_sorted":[],"title_canon_sha256":"c2c2403958c1a96b3bd4192b3fbb531c64b1525b6d0490c8595bae4accb683db","abstract_canon_sha256":"e21768c72b501a1315b9e3394a56b38182d52a67228b18ed47d2e63216cdfda0"},"schema_version":"1.0"},"canonical_sha256":"634e4057354eef4f7a107d4ab2ec52437c86e54a102142317408fdac44aec154","source":{"kind":"arxiv","id":"1803.04938","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"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:MNHEAVZVJ3XU66QQPVFLF3CSIN","target":"record","payload":{"canonical_record":{"source":{"id":"1803.04938","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2018-03-13T17:11:45Z","cross_cats_sorted":[],"title_canon_sha256":"c2c2403958c1a96b3bd4192b3fbb531c64b1525b6d0490c8595bae4accb683db","abstract_canon_sha256":"e21768c72b501a1315b9e3394a56b38182d52a67228b18ed47d2e63216cdfda0"},"schema_version":"1.0"},"canonical_sha256":"634e4057354eef4f7a107d4ab2ec52437c86e54a102142317408fdac44aec154","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:05:57.315066Z","signature_b64":"C3Dkex5vAFzyERYyWzw77aqYTarFCLoTAPhhb7kS4hFX2X50FNO8wrRIGzOm3YxuYAYt2H9i5zlUtpNPX2gYDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"634e4057354eef4f7a107d4ab2ec52437c86e54a102142317408fdac44aec154","last_reissued_at":"2026-05-18T00:05:57.314542Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:05:57.314542Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1803.04938","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":"2026-05-18T00:05:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ex8Kg1Z6Cqko2/HyJ0JWH2ABL2Z4CwOmT+FPWGjae5aOu97+r/8TaN87699b+tGCtx/CTavtNjpXK9EyMrflCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-22T11:36:10.716357Z"},"content_sha256":"ea7785c310483915809fc7bfd507eb688d70e94ddaaf0ba7edb0dc54adfabb01","schema_version":"1.0","event_id":"sha256:ea7785c310483915809fc7bfd507eb688d70e94ddaaf0ba7edb0dc54adfabb01"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:MNHEAVZVJ3XU66QQPVFLF3CSIN","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Parity and the modular bootstrap","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"hep-th","authors_text":"Edgar Shaghoulian, Raghu Mahajan, Tarek Anous","submitted_at":"2018-03-13T17:11:45Z","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"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.04938","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":""},"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":"2026-05-18T00:05:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wJKRUFM7QhWzuj5C0h84LTtceCPnOyjFQTNnnl8mnHEo6+msveSkM3EZN2kKFRriR7Vql23KkZB8+Sb6W5o3Cg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-22T11:36:10.717014Z"},"content_sha256":"4324ce4f3a34be8037f048539763d6459b2159888aa88cde494d853f5da751e0","schema_version":"1.0","event_id":"sha256:4324ce4f3a34be8037f048539763d6459b2159888aa88cde494d853f5da751e0"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/MNHEAVZVJ3XU66QQPVFLF3CSIN/bundle.json","state_url":"https://pith.science/pith/MNHEAVZVJ3XU66QQPVFLF3CSIN/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/MNHEAVZVJ3XU66QQPVFLF3CSIN/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":"2026-05-22T11:36:10Z","links":{"resolver":"https://pith.science/pith/MNHEAVZVJ3XU66QQPVFLF3CSIN","bundle":"https://pith.science/pith/MNHEAVZVJ3XU66QQPVFLF3CSIN/bundle.json","state":"https://pith.science/pith/MNHEAVZVJ3XU66QQPVFLF3CSIN/state.json","well_known_bundle":"https://pith.science/.well-known/pith/MNHEAVZVJ3XU66QQPVFLF3CSIN/bundle.json"},"state":{"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"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Qu8m/V5oqZPG5+IYeK1Q0ToF25hkaPQ1jr+Kdfj9aTzKQeBhxdBHikI4lTL6m5KP0AVl5/V/2SUQ93gnIJ3gAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-22T11:36:10.720221Z","bundle_sha256":"ab9e342f01de78761ee5ea7c68bba6bc572b6c6b94674d52397f3e3897b489ce"}}