{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:AUC57XFT6TTYDGHV7Y73MODYWJ","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":"e3230e997c0f0aef9e71955fff80ede6dba685ffb18fc657df6c3d8beff05866","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NT","submitted_at":"2025-01-23T02:18:50Z","title_canon_sha256":"6ce1b0c4f6de7658f6ad3d23e103e73b8979adb1599c85e19f05678278cf6431"},"schema_version":"1.0","source":{"id":"2501.13330","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2501.13330","created_at":"2026-07-05T11:56:52Z"},{"alias_kind":"arxiv_version","alias_value":"2501.13330v2","created_at":"2026-07-05T11:56:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2501.13330","created_at":"2026-07-05T11:56:52Z"},{"alias_kind":"pith_short_12","alias_value":"AUC57XFT6TTY","created_at":"2026-07-05T11:56:52Z"},{"alias_kind":"pith_short_16","alias_value":"AUC57XFT6TTYDGHV","created_at":"2026-07-05T11:56:52Z"},{"alias_kind":"pith_short_8","alias_value":"AUC57XFT","created_at":"2026-07-05T11:56:52Z"}],"graph_snapshots":[{"event_id":"sha256:1585aa3b3a11fbc515d9e9a6a8cdaf59071e07f6d8c3ff4c34b4a0652b7cc7ec","target":"graph","created_at":"2026-07-05T11:56:52Z","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/2501.13330/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Recently, the first author as well as the second author with Ono, Pujahari, and Saikia determined the limiting distribution of values of certain finite field ${_2F_1}$ and ${_3F_2}$ hypergeometric functions. These hypergeometric values are related to Frobenius traces of elliptic curves and their limiting distribution is determined using connections to the theory of modular forms and harmonic Maass forms. Here we determine the limiting distribution of values of some ${_4F_3}$ hypergeometric functions which are sums of traces of Frobenius for a pair of elliptic curves. To obtain this result, we ","authors_text":"Brian Grove, Hasan Saad","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NT","submitted_at":"2025-01-23T02:18:50Z","title":"Hypergeometric Distributions and Joint Families of Elliptic Curves"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2501.13330","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:dc186aa1bda5239917a9e82613e8b6e76fac969ccc17a4f98df62ab55eec49f9","target":"record","created_at":"2026-07-05T11:56:52Z","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":"e3230e997c0f0aef9e71955fff80ede6dba685ffb18fc657df6c3d8beff05866","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NT","submitted_at":"2025-01-23T02:18:50Z","title_canon_sha256":"6ce1b0c4f6de7658f6ad3d23e103e73b8979adb1599c85e19f05678278cf6431"},"schema_version":"1.0","source":{"id":"2501.13330","kind":"arxiv","version":2}},"canonical_sha256":"0505dfdcb3f4e78198f5fe3fb63878b2495505bd04e5537504004143b8d33bdc","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0505dfdcb3f4e78198f5fe3fb63878b2495505bd04e5537504004143b8d33bdc","first_computed_at":"2026-07-05T11:56:52.321472Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:56:52.321472Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"iRLjg3j0vFEyLQTDlbb36j7mq/b9F2DxV+AvUHSSZ+b0YZUzE46rLpOD1mRvSp2Ms7cObQlhJe79br2xi3PlBA==","signature_status":"signed_v1","signed_at":"2026-07-05T11:56:52.321888Z","signed_message":"canonical_sha256_bytes"},"source_id":"2501.13330","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:dc186aa1bda5239917a9e82613e8b6e76fac969ccc17a4f98df62ab55eec49f9","sha256:1585aa3b3a11fbc515d9e9a6a8cdaf59071e07f6d8c3ff4c34b4a0652b7cc7ec"],"state_sha256":"34c8a4f9c5c99d6940ba7d294cfb825c0dde9363a78f0e9e14fc24b8eec99a05"}