{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:56HSWJKBMLMX5IC4VHXF7XRPJV","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":"cef91701186bb9dac619bf7380134d144783f8766e67e08d6b0e0f6c0ed86b30","cross_cats_sorted":["q-fin.CP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2009-12-15T07:50:33Z","title_canon_sha256":"e10824ffc3e2be167c158ebefc36099d4d5115dff8b15018d32a1b11747b9da4"},"schema_version":"1.0","source":{"id":"0912.2816","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0912.2816","created_at":"2026-05-18T00:05:34Z"},{"alias_kind":"arxiv_version","alias_value":"0912.2816v1","created_at":"2026-05-18T00:05:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0912.2816","created_at":"2026-05-18T00:05:34Z"},{"alias_kind":"pith_short_12","alias_value":"56HSWJKBMLMX","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_16","alias_value":"56HSWJKBMLMX5IC4","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_8","alias_value":"56HSWJKB","created_at":"2026-05-18T12:25:58Z"}],"graph_snapshots":[{"event_id":"sha256:94e1db76a27d9580eeb07e48703dac26c09890e50711263a8113b34f001b1c79","target":"graph","created_at":"2026-05-18T00:05:34Z","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 collect well known and less known facts about the bivariate normal distribution and translate them into copula language. In addition, we prove a very general formula for the bivariate normal copula, we compute Gini's gamma, and we provide improved bounds and approximations on the diagonal.","authors_text":"Christian Meyer","cross_cats":["q-fin.CP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2009-12-15T07:50:33Z","title":"The Bivariate Normal Copula"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0912.2816","kind":"arxiv","version":1},"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":"sha256:76648708811e5a6cbc4cd74163a5e498cf40d14fb1bbc8a2c87ec7212a2ae111","target":"record","created_at":"2026-05-18T00:05:34Z","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":"cef91701186bb9dac619bf7380134d144783f8766e67e08d6b0e0f6c0ed86b30","cross_cats_sorted":["q-fin.CP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2009-12-15T07:50:33Z","title_canon_sha256":"e10824ffc3e2be167c158ebefc36099d4d5115dff8b15018d32a1b11747b9da4"},"schema_version":"1.0","source":{"id":"0912.2816","kind":"arxiv","version":1}},"canonical_sha256":"ef8f2b254162d97ea05ca9ee5fde2f4d509786c96a149cf190a3b3cf486ace82","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ef8f2b254162d97ea05ca9ee5fde2f4d509786c96a149cf190a3b3cf486ace82","first_computed_at":"2026-05-18T00:05:34.891660Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:05:34.891660Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"GuXjq/DIcLZa1N6Twc5gRbOQRLp2nwxp9zv6W7GbxTNMFwhnMOSGlsyIDCmGRN8+S+tw1F8zhWarZvYqSpDQBw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:05:34.892270Z","signed_message":"canonical_sha256_bytes"},"source_id":"0912.2816","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:76648708811e5a6cbc4cd74163a5e498cf40d14fb1bbc8a2c87ec7212a2ae111","sha256:94e1db76a27d9580eeb07e48703dac26c09890e50711263a8113b34f001b1c79"],"state_sha256":"92def854ff2f5b12ce2f81ae05532682e173997a1a125c40aff07b7aecab1973"}