{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:IA6ORD7EQLQ6Z72NTSJKTRKPY6","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":"4003c52b0185e16b4052d492f889691de950e62ab87a2665b3169d1a4001f5a3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-09-07T22:21:22Z","title_canon_sha256":"a788502433e2bd6c6fa068477b1d49d80d55ff394c2c5aa4d26aa83f267e51d3"},"schema_version":"1.0","source":{"id":"1709.02472","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1709.02472","created_at":"2026-05-18T00:35:45Z"},{"alias_kind":"arxiv_version","alias_value":"1709.02472v1","created_at":"2026-05-18T00:35:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1709.02472","created_at":"2026-05-18T00:35:45Z"},{"alias_kind":"pith_short_12","alias_value":"IA6ORD7EQLQ6","created_at":"2026-05-18T12:31:21Z"},{"alias_kind":"pith_short_16","alias_value":"IA6ORD7EQLQ6Z72N","created_at":"2026-05-18T12:31:21Z"},{"alias_kind":"pith_short_8","alias_value":"IA6ORD7E","created_at":"2026-05-18T12:31:21Z"}],"graph_snapshots":[{"event_id":"sha256:49402159c352b912789fd9850eaae4a7ea465e7e211d39e30d48b3472fa47c0a","target":"graph","created_at":"2026-05-18T00:35:45Z","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":"In this paper our aim is to characterize the set of extreme points of the set of all n-dimensional copulas (n > 1). We have shown that a copula must induce a singular measure with respect to Lebesgue measure in order to be an extreme point in the set of n-dimensional copulas. We also have discovered some sufficient conditions for a copula to be an extreme copula. We have presented a construction of a small subset of n-dimensional extreme copulas such that any n-dimensional copula is a limit point of that subset with respect to weak convergence. The applications of such a theory are widespread,","authors_text":"Partha Pratim Ghosh, Subir Kumar Bhandari","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-09-07T22:21:22Z","title":"Characterization of Extreme Copulas"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.02472","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:ea8844e468075228f59754527f570c8d3e3c219aec58757c42df72d1ce8cc486","target":"record","created_at":"2026-05-18T00:35:45Z","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":"4003c52b0185e16b4052d492f889691de950e62ab87a2665b3169d1a4001f5a3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-09-07T22:21:22Z","title_canon_sha256":"a788502433e2bd6c6fa068477b1d49d80d55ff394c2c5aa4d26aa83f267e51d3"},"schema_version":"1.0","source":{"id":"1709.02472","kind":"arxiv","version":1}},"canonical_sha256":"403ce88fe482e1ecff4d9c92a9c54fc78f4f063e2ddcd6d26e750679b86c546c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"403ce88fe482e1ecff4d9c92a9c54fc78f4f063e2ddcd6d26e750679b86c546c","first_computed_at":"2026-05-18T00:35:45.695945Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:35:45.695945Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"kmcApgbh4jkHxP6IkLiLcL+C19zY/XNfDm3IABCQj0dHTEqp9iHS2m3rdPOBtGJT2GvDLRvYW40TCtTDr2TwAA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:35:45.696444Z","signed_message":"canonical_sha256_bytes"},"source_id":"1709.02472","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ea8844e468075228f59754527f570c8d3e3c219aec58757c42df72d1ce8cc486","sha256:49402159c352b912789fd9850eaae4a7ea465e7e211d39e30d48b3472fa47c0a"],"state_sha256":"4681c2cfdee7b06585c4bd64394909499b283a3a7da619dbf30684ce4265aca5"}