{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:XS5GKWYY4SEIG367TKAXUIJV2S","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":"004d702b052642869bf36dbac07b8275d8d5120866a4e2d0827e66fba451b99c","cross_cats_sorted":["math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-fin.RM","submitted_at":"2014-11-17T11:44:12Z","title_canon_sha256":"72b0b302cb6bafbf9597cd50a2c9ac2450f9d1f777e35935dd20b71262c6994b"},"schema_version":"1.0","source":{"id":"1411.4441","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1411.4441","created_at":"2026-05-18T02:30:33Z"},{"alias_kind":"arxiv_version","alias_value":"1411.4441v4","created_at":"2026-05-18T02:30:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1411.4441","created_at":"2026-05-18T02:30:33Z"},{"alias_kind":"pith_short_12","alias_value":"XS5GKWYY4SEI","created_at":"2026-05-18T12:28:57Z"},{"alias_kind":"pith_short_16","alias_value":"XS5GKWYY4SEIG367","created_at":"2026-05-18T12:28:57Z"},{"alias_kind":"pith_short_8","alias_value":"XS5GKWYY","created_at":"2026-05-18T12:28:57Z"}],"graph_snapshots":[{"event_id":"sha256:96a785e62717527e14ff991048ab146910cafc2da5f266f45cd22750310649a3","target":"graph","created_at":"2026-05-18T02:30:33Z","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 give a complete characterization of both comonotone and not comonotone coherent risk measures in the discrete finite probability space, where each outcome is equally likely. To the best of our knowledge, this is the first work that characterizes \\textit{and} distinguishes comonotone and not comonotone coherent risk measures via a simplified AVaR representation in this probability space, which is crucial in applications and simulations.","authors_text":"Kerem Ugurlu","cross_cats":["math.PR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-fin.RM","submitted_at":"2014-11-17T11:44:12Z","title":"On the Coherent Risk Measure Representations in the Discrete Probability Spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.4441","kind":"arxiv","version":4},"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:ae342e77146d6cd843c723adbfd34a34c7f5636f652d446f1d1c740eaa3f13bf","target":"record","created_at":"2026-05-18T02:30:33Z","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":"004d702b052642869bf36dbac07b8275d8d5120866a4e2d0827e66fba451b99c","cross_cats_sorted":["math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-fin.RM","submitted_at":"2014-11-17T11:44:12Z","title_canon_sha256":"72b0b302cb6bafbf9597cd50a2c9ac2450f9d1f777e35935dd20b71262c6994b"},"schema_version":"1.0","source":{"id":"1411.4441","kind":"arxiv","version":4}},"canonical_sha256":"bcba655b18e488836fdf9a817a2135d4bce74f667e536ad9ad9eee37b650b784","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"bcba655b18e488836fdf9a817a2135d4bce74f667e536ad9ad9eee37b650b784","first_computed_at":"2026-05-18T02:30:33.670136Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:30:33.670136Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"/3lV0/JkZFioxZuFluNuqnHBC22uZ7iof0BORrbCZrHaQE+o6aS/3m4bhrSr8sCcH5fRbtQ51DfrKbdEeiY7Bg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:30:33.670523Z","signed_message":"canonical_sha256_bytes"},"source_id":"1411.4441","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ae342e77146d6cd843c723adbfd34a34c7f5636f652d446f1d1c740eaa3f13bf","sha256:96a785e62717527e14ff991048ab146910cafc2da5f266f45cd22750310649a3"],"state_sha256":"1a5f013738ae1fdb7d2d8399520dbbdc8dfba86dfa2029ab7afc3b78cd3435c0"}