{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:MUV2DYUS7TQZ2RRAZFSDEF33FX","short_pith_number":"pith:MUV2DYUS","canonical_record":{"source":{"id":"1205.3827","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-05-16T22:28:07Z","cross_cats_sorted":[],"title_canon_sha256":"00a34b9199adb560d66cba391c7eb8593a99fbcbcd3373b52c0027b7081a043b","abstract_canon_sha256":"a55b9e2eee0406daf7997d1cb68f715ec23a356a515058de7f897a13709eba88"},"schema_version":"1.0"},"canonical_sha256":"652ba1e292fce19d4620c96432177b2de8a2738e10cd30dadd3f5416b99dcee7","source":{"kind":"arxiv","id":"1205.3827","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1205.3827","created_at":"2026-05-18T03:00:39Z"},{"alias_kind":"arxiv_version","alias_value":"1205.3827v2","created_at":"2026-05-18T03:00:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1205.3827","created_at":"2026-05-18T03:00:39Z"},{"alias_kind":"pith_short_12","alias_value":"MUV2DYUS7TQZ","created_at":"2026-05-18T12:27:14Z"},{"alias_kind":"pith_short_16","alias_value":"MUV2DYUS7TQZ2RRA","created_at":"2026-05-18T12:27:14Z"},{"alias_kind":"pith_short_8","alias_value":"MUV2DYUS","created_at":"2026-05-18T12:27:14Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:MUV2DYUS7TQZ2RRAZFSDEF33FX","target":"record","payload":{"canonical_record":{"source":{"id":"1205.3827","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-05-16T22:28:07Z","cross_cats_sorted":[],"title_canon_sha256":"00a34b9199adb560d66cba391c7eb8593a99fbcbcd3373b52c0027b7081a043b","abstract_canon_sha256":"a55b9e2eee0406daf7997d1cb68f715ec23a356a515058de7f897a13709eba88"},"schema_version":"1.0"},"canonical_sha256":"652ba1e292fce19d4620c96432177b2de8a2738e10cd30dadd3f5416b99dcee7","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:00:39.909511Z","signature_b64":"R1Y4zsMz8WAQyiddIreIEExNqAn0wENOwsmNgGyBOlYH6eFGY6835f0m+bwSXm29iFS62Kvm0h8CdBEK7ZmaDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"652ba1e292fce19d4620c96432177b2de8a2738e10cd30dadd3f5416b99dcee7","last_reissued_at":"2026-05-18T03:00:39.908869Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:00:39.908869Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1205.3827","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:00:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/BUwH+/wZVcrgsWChAkBlopY9IwHwX8uVMiTiVSFtdPxJ016iA0UBLD0A8jYCHdF4bZOClrIHgvMEjZHcyPEDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T19:50:55.470012Z"},"content_sha256":"0c495a44130ee814b326e6d809bab56e0a65450c4a3644dc955e0b4ddcc7c86e","schema_version":"1.0","event_id":"sha256:0c495a44130ee814b326e6d809bab56e0a65450c4a3644dc955e0b4ddcc7c86e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:MUV2DYUS7TQZ2RRAZFSDEF33FX","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Characterization of the minimal penalty of a convex risk measure with applications to Levy processes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Daniel Hern\\'andez-Hern\\'andez, Leonel P\\'erez-Hern\\'andez","submitted_at":"2012-05-16T22:28:07Z","abstract_excerpt":"The minimality of the penalization function associated with a convex risk measure is analyzed in this paper. First, in a general static framework, we provide necessary and sufficient conditions for a penalty function defined in a convex and closed subset of the absolutely continuous measures with respect to some reference measure $\\mathbb{P}$ to be minimal. When the probability space supports a L\\'{e}vy process, we establish results that guarantee the minimality property of a penalty function described in terms of the coefficients associated with the density processes. The set of densities pro"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.3827","kind":"arxiv","version":2},"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":"2026-05-18T03:00:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"L4XCQ0qW/moQGiIG8U8afN/jCH+Y1e4stQ7Wj15Hyz4lOysfeK8domS6GzpT82RIcQvVGnj69X/NaaKoh95fCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T19:50:55.470371Z"},"content_sha256":"fcb747a43315652eebe39624d87579a6ef8c1a1210a813c5f3b369cf7c9d8e7d","schema_version":"1.0","event_id":"sha256:fcb747a43315652eebe39624d87579a6ef8c1a1210a813c5f3b369cf7c9d8e7d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/MUV2DYUS7TQZ2RRAZFSDEF33FX/bundle.json","state_url":"https://pith.science/pith/MUV2DYUS7TQZ2RRAZFSDEF33FX/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/MUV2DYUS7TQZ2RRAZFSDEF33FX/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":"2026-05-28T19:50:55Z","links":{"resolver":"https://pith.science/pith/MUV2DYUS7TQZ2RRAZFSDEF33FX","bundle":"https://pith.science/pith/MUV2DYUS7TQZ2RRAZFSDEF33FX/bundle.json","state":"https://pith.science/pith/MUV2DYUS7TQZ2RRAZFSDEF33FX/state.json","well_known_bundle":"https://pith.science/.well-known/pith/MUV2DYUS7TQZ2RRAZFSDEF33FX/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:MUV2DYUS7TQZ2RRAZFSDEF33FX","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":"a55b9e2eee0406daf7997d1cb68f715ec23a356a515058de7f897a13709eba88","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-05-16T22:28:07Z","title_canon_sha256":"00a34b9199adb560d66cba391c7eb8593a99fbcbcd3373b52c0027b7081a043b"},"schema_version":"1.0","source":{"id":"1205.3827","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1205.3827","created_at":"2026-05-18T03:00:39Z"},{"alias_kind":"arxiv_version","alias_value":"1205.3827v2","created_at":"2026-05-18T03:00:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1205.3827","created_at":"2026-05-18T03:00:39Z"},{"alias_kind":"pith_short_12","alias_value":"MUV2DYUS7TQZ","created_at":"2026-05-18T12:27:14Z"},{"alias_kind":"pith_short_16","alias_value":"MUV2DYUS7TQZ2RRA","created_at":"2026-05-18T12:27:14Z"},{"alias_kind":"pith_short_8","alias_value":"MUV2DYUS","created_at":"2026-05-18T12:27:14Z"}],"graph_snapshots":[{"event_id":"sha256:fcb747a43315652eebe39624d87579a6ef8c1a1210a813c5f3b369cf7c9d8e7d","target":"graph","created_at":"2026-05-18T03:00:39Z","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":"The minimality of the penalization function associated with a convex risk measure is analyzed in this paper. First, in a general static framework, we provide necessary and sufficient conditions for a penalty function defined in a convex and closed subset of the absolutely continuous measures with respect to some reference measure $\\mathbb{P}$ to be minimal. When the probability space supports a L\\'{e}vy process, we establish results that guarantee the minimality property of a penalty function described in terms of the coefficients associated with the density processes. The set of densities pro","authors_text":"Daniel Hern\\'andez-Hern\\'andez, Leonel P\\'erez-Hern\\'andez","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-05-16T22:28:07Z","title":"Characterization of the minimal penalty of a convex risk measure with applications to Levy processes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.3827","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":"sha256:0c495a44130ee814b326e6d809bab56e0a65450c4a3644dc955e0b4ddcc7c86e","target":"record","created_at":"2026-05-18T03:00:39Z","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":"a55b9e2eee0406daf7997d1cb68f715ec23a356a515058de7f897a13709eba88","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-05-16T22:28:07Z","title_canon_sha256":"00a34b9199adb560d66cba391c7eb8593a99fbcbcd3373b52c0027b7081a043b"},"schema_version":"1.0","source":{"id":"1205.3827","kind":"arxiv","version":2}},"canonical_sha256":"652ba1e292fce19d4620c96432177b2de8a2738e10cd30dadd3f5416b99dcee7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"652ba1e292fce19d4620c96432177b2de8a2738e10cd30dadd3f5416b99dcee7","first_computed_at":"2026-05-18T03:00:39.908869Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:00:39.908869Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"R1Y4zsMz8WAQyiddIreIEExNqAn0wENOwsmNgGyBOlYH6eFGY6835f0m+bwSXm29iFS62Kvm0h8CdBEK7ZmaDg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:00:39.909511Z","signed_message":"canonical_sha256_bytes"},"source_id":"1205.3827","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0c495a44130ee814b326e6d809bab56e0a65450c4a3644dc955e0b4ddcc7c86e","sha256:fcb747a43315652eebe39624d87579a6ef8c1a1210a813c5f3b369cf7c9d8e7d"],"state_sha256":"6d8346eb8762e9af843f189384e9cca2ec2175328848a904e8d698cf5ad5f9c3"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Xa2ZmpfNIA1Q1iGlQCJBAwfW2HzisZfAvb7qS5Gfpoz1oWmhpSum/iP1/rFXwAZbk4kf7CSwLIUXwAVRNIc6CQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T19:50:55.472614Z","bundle_sha256":"2daecf34b76482b201127d4bb6f8bef34f7dd6da89e49c18a20d94be55d038eb"}}