{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:4BIEB4F6P37QPVLC33A742GAAU","short_pith_number":"pith:4BIEB4F6","canonical_record":{"source":{"id":"1401.3121","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-fin.RM","submitted_at":"2014-01-14T10:05:28Z","cross_cats_sorted":["math.ST","stat.TH"],"title_canon_sha256":"3aac3424bed909791e1b3c324ca6865af07eabf365f4dc90727a9ae5a0f0abf4","abstract_canon_sha256":"51d0bd64e64ac86089621a3225f9971b3a7692afc210d50e787650b929ab00fd"},"schema_version":"1.0"},"canonical_sha256":"e05040f0be7eff07d562dec1fe68c00512373051ce5f3ffdaeb6dadb66b9edde","source":{"kind":"arxiv","id":"1401.3121","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1401.3121","created_at":"2026-05-18T03:02:19Z"},{"alias_kind":"arxiv_version","alias_value":"1401.3121v1","created_at":"2026-05-18T03:02:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1401.3121","created_at":"2026-05-18T03:02:19Z"},{"alias_kind":"pith_short_12","alias_value":"4BIEB4F6P37Q","created_at":"2026-05-18T12:28:14Z"},{"alias_kind":"pith_short_16","alias_value":"4BIEB4F6P37QPVLC","created_at":"2026-05-18T12:28:14Z"},{"alias_kind":"pith_short_8","alias_value":"4BIEB4F6","created_at":"2026-05-18T12:28:14Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:4BIEB4F6P37QPVLC33A742GAAU","target":"record","payload":{"canonical_record":{"source":{"id":"1401.3121","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-fin.RM","submitted_at":"2014-01-14T10:05:28Z","cross_cats_sorted":["math.ST","stat.TH"],"title_canon_sha256":"3aac3424bed909791e1b3c324ca6865af07eabf365f4dc90727a9ae5a0f0abf4","abstract_canon_sha256":"51d0bd64e64ac86089621a3225f9971b3a7692afc210d50e787650b929ab00fd"},"schema_version":"1.0"},"canonical_sha256":"e05040f0be7eff07d562dec1fe68c00512373051ce5f3ffdaeb6dadb66b9edde","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:02:19.591569Z","signature_b64":"CS2t4mO7tKHwaoa6uJESIdOmCQES/Yy04fT59smyVDTzdT9zzsm2ByuWUt3nepEhV7l1aRBc+XsQEmO+bxBVCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e05040f0be7eff07d562dec1fe68c00512373051ce5f3ffdaeb6dadb66b9edde","last_reissued_at":"2026-05-18T03:02:19.590915Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:02:19.590915Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1401.3121","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:02:19Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xywhRIwTYD8e+pgK1Bi1t6BbTfTFVj4BqqP37VUy9OqjQjrh+VnnCKkvEZO01omhc1jKOazFg2czR+YnJqq+DQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T00:56:47.934899Z"},"content_sha256":"45bae49a6b0f0a4c5e6173aed274692c5fd9f6fa3e4eec135e827242e4b79ce8","schema_version":"1.0","event_id":"sha256:45bae49a6b0f0a4c5e6173aed274692c5fd9f6fa3e4eec135e827242e4b79ce8"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:4BIEB4F6P37QPVLC33A742GAAU","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Law-invariant risk measures: extension properties and qualitative robustness","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.ST","stat.TH"],"primary_cat":"q-fin.RM","authors_text":"Cosimo Munari, Pablo Koch-Medina","submitted_at":"2014-01-14T10:05:28Z","abstract_excerpt":"We characterize when a convex risk measure associated to a law-invariant acceptance set in $L^\\infty$ can be extended to $L^p$, $1\\leq p<\\infty$, preserving finiteness and continuity. This problem is strongly connected to the statistical robustness of the corresponding risk measures. Special attention is paid to concrete examples including risk measures based on expected utility, max-correlation risk measures, and distortion risk measures."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.3121","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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":"2026-05-18T03:02:19Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"oP3ipKbVzhH9XzZiD3kQvURtOHLB3Z7LazckOLiHVWPjgyH3HhYkavjzAqa6XEeDTYL0BGrlOcEyyQ2gRcwUAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T00:56:47.935621Z"},"content_sha256":"05b7640b18b1cde83f1cd5185628b696b93a04779c6d2e5880d68219193dac48","schema_version":"1.0","event_id":"sha256:05b7640b18b1cde83f1cd5185628b696b93a04779c6d2e5880d68219193dac48"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/4BIEB4F6P37QPVLC33A742GAAU/bundle.json","state_url":"https://pith.science/pith/4BIEB4F6P37QPVLC33A742GAAU/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/4BIEB4F6P37QPVLC33A742GAAU/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":"2026-06-01T00:56:47Z","links":{"resolver":"https://pith.science/pith/4BIEB4F6P37QPVLC33A742GAAU","bundle":"https://pith.science/pith/4BIEB4F6P37QPVLC33A742GAAU/bundle.json","state":"https://pith.science/pith/4BIEB4F6P37QPVLC33A742GAAU/state.json","well_known_bundle":"https://pith.science/.well-known/pith/4BIEB4F6P37QPVLC33A742GAAU/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:4BIEB4F6P37QPVLC33A742GAAU","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":"51d0bd64e64ac86089621a3225f9971b3a7692afc210d50e787650b929ab00fd","cross_cats_sorted":["math.ST","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-fin.RM","submitted_at":"2014-01-14T10:05:28Z","title_canon_sha256":"3aac3424bed909791e1b3c324ca6865af07eabf365f4dc90727a9ae5a0f0abf4"},"schema_version":"1.0","source":{"id":"1401.3121","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1401.3121","created_at":"2026-05-18T03:02:19Z"},{"alias_kind":"arxiv_version","alias_value":"1401.3121v1","created_at":"2026-05-18T03:02:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1401.3121","created_at":"2026-05-18T03:02:19Z"},{"alias_kind":"pith_short_12","alias_value":"4BIEB4F6P37Q","created_at":"2026-05-18T12:28:14Z"},{"alias_kind":"pith_short_16","alias_value":"4BIEB4F6P37QPVLC","created_at":"2026-05-18T12:28:14Z"},{"alias_kind":"pith_short_8","alias_value":"4BIEB4F6","created_at":"2026-05-18T12:28:14Z"}],"graph_snapshots":[{"event_id":"sha256:05b7640b18b1cde83f1cd5185628b696b93a04779c6d2e5880d68219193dac48","target":"graph","created_at":"2026-05-18T03:02:19Z","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 characterize when a convex risk measure associated to a law-invariant acceptance set in $L^\\infty$ can be extended to $L^p$, $1\\leq p<\\infty$, preserving finiteness and continuity. This problem is strongly connected to the statistical robustness of the corresponding risk measures. Special attention is paid to concrete examples including risk measures based on expected utility, max-correlation risk measures, and distortion risk measures.","authors_text":"Cosimo Munari, Pablo Koch-Medina","cross_cats":["math.ST","stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-fin.RM","submitted_at":"2014-01-14T10:05:28Z","title":"Law-invariant risk measures: extension properties and qualitative robustness"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.3121","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":"sha256:45bae49a6b0f0a4c5e6173aed274692c5fd9f6fa3e4eec135e827242e4b79ce8","target":"record","created_at":"2026-05-18T03:02:19Z","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":"51d0bd64e64ac86089621a3225f9971b3a7692afc210d50e787650b929ab00fd","cross_cats_sorted":["math.ST","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-fin.RM","submitted_at":"2014-01-14T10:05:28Z","title_canon_sha256":"3aac3424bed909791e1b3c324ca6865af07eabf365f4dc90727a9ae5a0f0abf4"},"schema_version":"1.0","source":{"id":"1401.3121","kind":"arxiv","version":1}},"canonical_sha256":"e05040f0be7eff07d562dec1fe68c00512373051ce5f3ffdaeb6dadb66b9edde","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e05040f0be7eff07d562dec1fe68c00512373051ce5f3ffdaeb6dadb66b9edde","first_computed_at":"2026-05-18T03:02:19.590915Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:02:19.590915Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"CS2t4mO7tKHwaoa6uJESIdOmCQES/Yy04fT59smyVDTzdT9zzsm2ByuWUt3nepEhV7l1aRBc+XsQEmO+bxBVCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:02:19.591569Z","signed_message":"canonical_sha256_bytes"},"source_id":"1401.3121","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:45bae49a6b0f0a4c5e6173aed274692c5fd9f6fa3e4eec135e827242e4b79ce8","sha256:05b7640b18b1cde83f1cd5185628b696b93a04779c6d2e5880d68219193dac48"],"state_sha256":"a0994a97a5adcb38d1f924b7a82bb91d90692a3f6741176e1da91f5ebf3a7cf1"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Uinl8HvOd5Twh1KIwuUk5eEVWxnmhBXnkQwCAda0yHky5ge4lsdik0NZbJSY4r1+o83B4zher4z9gbkmydHfAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T00:56:47.939694Z","bundle_sha256":"cc7062e96581f03f6d84f26109513f4ffce6acc8a713119f772a1c7be2d64a18"}}