{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2023:L5NNGVRISPBKVOPQW7R6DZJSW5","short_pith_number":"pith:L5NNGVRI","canonical_record":{"source":{"id":"2310.07681","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NT","submitted_at":"2023-10-11T17:30:24Z","cross_cats_sorted":[],"title_canon_sha256":"ab413dfeee7bdb1aa0f9b7fcef435cee5b183b022c5e719e575ca9e03d51b709","abstract_canon_sha256":"2c1134de76cdab1e2dd3a178e855ad97ab66445c8e51362afe1a3c77e269ab95"},"schema_version":"1.0"},"canonical_sha256":"5f5ad3562893c2aab9f0b7e3e1e532b744c7003bd322b2c6db849f232d28e09e","source":{"kind":"arxiv","id":"2310.07681","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2310.07681","created_at":"2026-07-05T11:39:01Z"},{"alias_kind":"arxiv_version","alias_value":"2310.07681v2","created_at":"2026-07-05T11:39:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2310.07681","created_at":"2026-07-05T11:39:01Z"},{"alias_kind":"pith_short_12","alias_value":"L5NNGVRISPBK","created_at":"2026-07-05T11:39:01Z"},{"alias_kind":"pith_short_16","alias_value":"L5NNGVRISPBKVOPQ","created_at":"2026-07-05T11:39:01Z"},{"alias_kind":"pith_short_8","alias_value":"L5NNGVRI","created_at":"2026-07-05T11:39:01Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2023:L5NNGVRISPBKVOPQW7R6DZJSW5","target":"record","payload":{"canonical_record":{"source":{"id":"2310.07681","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NT","submitted_at":"2023-10-11T17:30:24Z","cross_cats_sorted":[],"title_canon_sha256":"ab413dfeee7bdb1aa0f9b7fcef435cee5b183b022c5e719e575ca9e03d51b709","abstract_canon_sha256":"2c1134de76cdab1e2dd3a178e855ad97ab66445c8e51362afe1a3c77e269ab95"},"schema_version":"1.0"},"canonical_sha256":"5f5ad3562893c2aab9f0b7e3e1e532b744c7003bd322b2c6db849f232d28e09e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:39:01.374467Z","signature_b64":"g9TxJ7IeJI8cFxoSQtk2LUybYAkzR1m87QVff/RR5JWx360JRHqBdAzeTpai6h4/P8gUdXc73qKiJ1kIHWiFBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5f5ad3562893c2aab9f0b7e3e1e532b744c7003bd322b2c6db849f232d28e09e","last_reissued_at":"2026-07-05T11:39:01.373984Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:39:01.373984Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2310.07681","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T11:39:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bZspe8aA2S9L2YP1G5PSKLk6nF/6gcBLwi+5gmjgmqaOVwaBvHbzHnbj7Zcfc0TMjYBULgVUHP60ta+/SanrCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-08T13:16:17.785652Z"},"content_sha256":"d505e204d6b4084a7df97d7b09dd4ed34c18287ccb3dfab846c970598f7766a8","schema_version":"1.0","event_id":"sha256:d505e204d6b4084a7df97d7b09dd4ed34c18287ccb3dfab846c970598f7766a8"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2023:L5NNGVRISPBKVOPQW7R6DZJSW5","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Murmurations","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Nina Zubrilina","submitted_at":"2023-10-11T17:30:24Z","abstract_excerpt":"We establish a case of the surprising correlation phenomenon observed in the recent works of He, Lee, Oliver, Pozdnyakov, and Sutherland between Fourier coefficients of families of modular forms and their root numbers."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2310.07681","kind":"arxiv","version":2},"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/2310.07681/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":"2026-07-05T11:39:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nNWosynK3JLVX2oHWhTpVuIskg1tUMWAYI796RnZuNfg9+FN2N26taVgJSOj0rmd2LcOKCi+Tx6udXaWiQtADA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-08T13:16:17.786133Z"},"content_sha256":"04c2b13e29618566c9962cec9d6848a0c82967c9c5da0b9a1750d6f2b1a46412","schema_version":"1.0","event_id":"sha256:04c2b13e29618566c9962cec9d6848a0c82967c9c5da0b9a1750d6f2b1a46412"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/L5NNGVRISPBKVOPQW7R6DZJSW5/bundle.json","state_url":"https://pith.science/pith/L5NNGVRISPBKVOPQW7R6DZJSW5/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/L5NNGVRISPBKVOPQW7R6DZJSW5/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":"2026-08-08T13:16:17Z","links":{"resolver":"https://pith.science/pith/L5NNGVRISPBKVOPQW7R6DZJSW5","bundle":"https://pith.science/pith/L5NNGVRISPBKVOPQW7R6DZJSW5/bundle.json","state":"https://pith.science/pith/L5NNGVRISPBKVOPQW7R6DZJSW5/state.json","well_known_bundle":"https://pith.science/.well-known/pith/L5NNGVRISPBKVOPQW7R6DZJSW5/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:L5NNGVRISPBKVOPQW7R6DZJSW5","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":"2c1134de76cdab1e2dd3a178e855ad97ab66445c8e51362afe1a3c77e269ab95","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NT","submitted_at":"2023-10-11T17:30:24Z","title_canon_sha256":"ab413dfeee7bdb1aa0f9b7fcef435cee5b183b022c5e719e575ca9e03d51b709"},"schema_version":"1.0","source":{"id":"2310.07681","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2310.07681","created_at":"2026-07-05T11:39:01Z"},{"alias_kind":"arxiv_version","alias_value":"2310.07681v2","created_at":"2026-07-05T11:39:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2310.07681","created_at":"2026-07-05T11:39:01Z"},{"alias_kind":"pith_short_12","alias_value":"L5NNGVRISPBK","created_at":"2026-07-05T11:39:01Z"},{"alias_kind":"pith_short_16","alias_value":"L5NNGVRISPBKVOPQ","created_at":"2026-07-05T11:39:01Z"},{"alias_kind":"pith_short_8","alias_value":"L5NNGVRI","created_at":"2026-07-05T11:39:01Z"}],"graph_snapshots":[{"event_id":"sha256:04c2b13e29618566c9962cec9d6848a0c82967c9c5da0b9a1750d6f2b1a46412","target":"graph","created_at":"2026-07-05T11:39:01Z","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/2310.07681/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We establish a case of the surprising correlation phenomenon observed in the recent works of He, Lee, Oliver, Pozdnyakov, and Sutherland between Fourier coefficients of families of modular forms and their root numbers.","authors_text":"Nina Zubrilina","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NT","submitted_at":"2023-10-11T17:30:24Z","title":"Murmurations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2310.07681","kind":"arxiv","version":2},"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:d505e204d6b4084a7df97d7b09dd4ed34c18287ccb3dfab846c970598f7766a8","target":"record","created_at":"2026-07-05T11:39:01Z","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":"2c1134de76cdab1e2dd3a178e855ad97ab66445c8e51362afe1a3c77e269ab95","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NT","submitted_at":"2023-10-11T17:30:24Z","title_canon_sha256":"ab413dfeee7bdb1aa0f9b7fcef435cee5b183b022c5e719e575ca9e03d51b709"},"schema_version":"1.0","source":{"id":"2310.07681","kind":"arxiv","version":2}},"canonical_sha256":"5f5ad3562893c2aab9f0b7e3e1e532b744c7003bd322b2c6db849f232d28e09e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5f5ad3562893c2aab9f0b7e3e1e532b744c7003bd322b2c6db849f232d28e09e","first_computed_at":"2026-07-05T11:39:01.373984Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:39:01.373984Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"g9TxJ7IeJI8cFxoSQtk2LUybYAkzR1m87QVff/RR5JWx360JRHqBdAzeTpai6h4/P8gUdXc73qKiJ1kIHWiFBA==","signature_status":"signed_v1","signed_at":"2026-07-05T11:39:01.374467Z","signed_message":"canonical_sha256_bytes"},"source_id":"2310.07681","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d505e204d6b4084a7df97d7b09dd4ed34c18287ccb3dfab846c970598f7766a8","sha256:04c2b13e29618566c9962cec9d6848a0c82967c9c5da0b9a1750d6f2b1a46412"],"state_sha256":"c290ac4020d3608084e92530264ccdad6287438ed5bbfb973ae4651c9a8ce569"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"uDITi+c6Wbg8mCjONrd+USR1XCDARtXN7Jkawtl53NzXgKZeZJsjFPPDcA747Wkyx7LrkqKoT/YypFyS2/KrCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-08T13:16:17.791328Z","bundle_sha256":"05e503a90d1479d3ed0b4bf766e87d7c46e92aeacff2523f5c4426185da214f0"}}