{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2021:OVJZ5K7EWQVAQ23CIHYKYTTO62","short_pith_number":"pith:OVJZ5K7E","canonical_record":{"source":{"id":"2106.04218","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"econ.EM","submitted_at":"2021-06-08T09:57:46Z","cross_cats_sorted":["q-fin.PM"],"title_canon_sha256":"902124f58b99a449193cefca3ddcc8ad4a5e92e8d607043b0f4a1846c6e7d231","abstract_canon_sha256":"ff17023caff890e5120223276727cca87f5f14a6b62d782b83f573db899a2bf0"},"schema_version":"1.0"},"canonical_sha256":"75539eabe4b42a086b6241f0ac4e6ef69b7ca0b7668ea03142aba5289171e9a2","source":{"kind":"arxiv","id":"2106.04218","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2106.04218","created_at":"2026-07-05T02:47:13Z"},{"alias_kind":"arxiv_version","alias_value":"2106.04218v1","created_at":"2026-07-05T02:47:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2106.04218","created_at":"2026-07-05T02:47:13Z"},{"alias_kind":"pith_short_12","alias_value":"OVJZ5K7EWQVA","created_at":"2026-07-05T02:47:13Z"},{"alias_kind":"pith_short_16","alias_value":"OVJZ5K7EWQVAQ23C","created_at":"2026-07-05T02:47:13Z"},{"alias_kind":"pith_short_8","alias_value":"OVJZ5K7E","created_at":"2026-07-05T02:47:13Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2021:OVJZ5K7EWQVAQ23CIHYKYTTO62","target":"record","payload":{"canonical_record":{"source":{"id":"2106.04218","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"econ.EM","submitted_at":"2021-06-08T09:57:46Z","cross_cats_sorted":["q-fin.PM"],"title_canon_sha256":"902124f58b99a449193cefca3ddcc8ad4a5e92e8d607043b0f4a1846c6e7d231","abstract_canon_sha256":"ff17023caff890e5120223276727cca87f5f14a6b62d782b83f573db899a2bf0"},"schema_version":"1.0"},"canonical_sha256":"75539eabe4b42a086b6241f0ac4e6ef69b7ca0b7668ea03142aba5289171e9a2","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T02:47:13.450861Z","signature_b64":"jFzIQ1pB1iIK+ZCdATQ4UWUm9QlHyXZp5HmubqA3/gqkhLwiRHX1KOmftmw9WdXgKKFzEUgUXhSXv6n67GRmDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"75539eabe4b42a086b6241f0ac4e6ef69b7ca0b7668ea03142aba5289171e9a2","last_reissued_at":"2026-07-05T02:47:13.450366Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T02:47:13.450366Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2106.04218","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":"2026-07-05T02:47:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"A44fVqml0nd4BebfiMDWVJOX31e0j8GCTcom2dpCT+1aNntk4LryGBSLlQDeAKA+WqXD8+cu1QgRYLyjj/wmCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-07T14:11:10.907881Z"},"content_sha256":"28f92768b161926f6550a59f67ad6146f91a8e5176d3961057c37d28ec799d9a","schema_version":"1.0","event_id":"sha256:28f92768b161926f6550a59f67ad6146f91a8e5176d3961057c37d28ec799d9a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2021:OVJZ5K7EWQVAQ23CIHYKYTTO62","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Modeling Portfolios with Leptokurtic and Dependent Risk Factors","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","headline":"","cross_cats":["q-fin.PM"],"primary_cat":"econ.EM","authors_text":"Gianmarco Vacca, Maria Grazia Zoia, Piero Quatto","submitted_at":"2021-06-08T09:57:46Z","abstract_excerpt":"Recently, an approach to modeling portfolio distribution with risk factors distributed as Gram-Charlier (GC) expansions of the Gaussian law, has been conceived. GC expansions prove effective when dealing with moderately leptokurtic data. In order to cover the case of possibly severe leptokurtosis, the so-called GC-like expansions have been devised by reshaping parent leptokurtic distributions by means of orthogonal polynomials specific to them. In this paper, we focus on the hyperbolic-secant (HS) law as parent distribution whose GC-like expansions fit with kurtosis levels up to 19.4. A portfo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2106.04218","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2106.04218/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T02:47:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mH+9U14K9FlR/s34FDvt7LzhxThHr11Po1ycT8LgAllEDriRJMn+09DSl82fs1D8tGw5VVfyblczeTwWd84+Bw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-07T14:11:10.908266Z"},"content_sha256":"7ae53d2b25efe20fde3f1faa0bb98f73ba1cdfd630f07cd7823a863fe7e8b641","schema_version":"1.0","event_id":"sha256:7ae53d2b25efe20fde3f1faa0bb98f73ba1cdfd630f07cd7823a863fe7e8b641"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/OVJZ5K7EWQVAQ23CIHYKYTTO62/bundle.json","state_url":"https://pith.science/pith/OVJZ5K7EWQVAQ23CIHYKYTTO62/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/OVJZ5K7EWQVAQ23CIHYKYTTO62/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":"2026-08-07T14:11:10Z","links":{"resolver":"https://pith.science/pith/OVJZ5K7EWQVAQ23CIHYKYTTO62","bundle":"https://pith.science/pith/OVJZ5K7EWQVAQ23CIHYKYTTO62/bundle.json","state":"https://pith.science/pith/OVJZ5K7EWQVAQ23CIHYKYTTO62/state.json","well_known_bundle":"https://pith.science/.well-known/pith/OVJZ5K7EWQVAQ23CIHYKYTTO62/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:OVJZ5K7EWQVAQ23CIHYKYTTO62","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":"ff17023caff890e5120223276727cca87f5f14a6b62d782b83f573db899a2bf0","cross_cats_sorted":["q-fin.PM"],"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"econ.EM","submitted_at":"2021-06-08T09:57:46Z","title_canon_sha256":"902124f58b99a449193cefca3ddcc8ad4a5e92e8d607043b0f4a1846c6e7d231"},"schema_version":"1.0","source":{"id":"2106.04218","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2106.04218","created_at":"2026-07-05T02:47:13Z"},{"alias_kind":"arxiv_version","alias_value":"2106.04218v1","created_at":"2026-07-05T02:47:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2106.04218","created_at":"2026-07-05T02:47:13Z"},{"alias_kind":"pith_short_12","alias_value":"OVJZ5K7EWQVA","created_at":"2026-07-05T02:47:13Z"},{"alias_kind":"pith_short_16","alias_value":"OVJZ5K7EWQVAQ23C","created_at":"2026-07-05T02:47:13Z"},{"alias_kind":"pith_short_8","alias_value":"OVJZ5K7E","created_at":"2026-07-05T02:47:13Z"}],"graph_snapshots":[{"event_id":"sha256:7ae53d2b25efe20fde3f1faa0bb98f73ba1cdfd630f07cd7823a863fe7e8b641","target":"graph","created_at":"2026-07-05T02:47:13Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2106.04218/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Recently, an approach to modeling portfolio distribution with risk factors distributed as Gram-Charlier (GC) expansions of the Gaussian law, has been conceived. GC expansions prove effective when dealing with moderately leptokurtic data. In order to cover the case of possibly severe leptokurtosis, the so-called GC-like expansions have been devised by reshaping parent leptokurtic distributions by means of orthogonal polynomials specific to them. In this paper, we focus on the hyperbolic-secant (HS) law as parent distribution whose GC-like expansions fit with kurtosis levels up to 19.4. A portfo","authors_text":"Gianmarco Vacca, Maria Grazia Zoia, Piero Quatto","cross_cats":["q-fin.PM"],"headline":"","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"econ.EM","submitted_at":"2021-06-08T09:57:46Z","title":"Modeling Portfolios with Leptokurtic and Dependent Risk Factors"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2106.04218","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":"sha256:28f92768b161926f6550a59f67ad6146f91a8e5176d3961057c37d28ec799d9a","target":"record","created_at":"2026-07-05T02:47:13Z","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":"ff17023caff890e5120223276727cca87f5f14a6b62d782b83f573db899a2bf0","cross_cats_sorted":["q-fin.PM"],"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"econ.EM","submitted_at":"2021-06-08T09:57:46Z","title_canon_sha256":"902124f58b99a449193cefca3ddcc8ad4a5e92e8d607043b0f4a1846c6e7d231"},"schema_version":"1.0","source":{"id":"2106.04218","kind":"arxiv","version":1}},"canonical_sha256":"75539eabe4b42a086b6241f0ac4e6ef69b7ca0b7668ea03142aba5289171e9a2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"75539eabe4b42a086b6241f0ac4e6ef69b7ca0b7668ea03142aba5289171e9a2","first_computed_at":"2026-07-05T02:47:13.450366Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T02:47:13.450366Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"jFzIQ1pB1iIK+ZCdATQ4UWUm9QlHyXZp5HmubqA3/gqkhLwiRHX1KOmftmw9WdXgKKFzEUgUXhSXv6n67GRmDw==","signature_status":"signed_v1","signed_at":"2026-07-05T02:47:13.450861Z","signed_message":"canonical_sha256_bytes"},"source_id":"2106.04218","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:28f92768b161926f6550a59f67ad6146f91a8e5176d3961057c37d28ec799d9a","sha256:7ae53d2b25efe20fde3f1faa0bb98f73ba1cdfd630f07cd7823a863fe7e8b641"],"state_sha256":"1ff3b91abebf1b292dd8cee9d5cb7c75bf81c63f24f2ceec5ebb0b60f07dc548"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"83oCfBGp9ycqNQEpjAzbQ/oAOJa4MAXbwynsjjFb21dfYhg4A2t5apfWL2AccD3MZqnCHn/qjv0s+AAwMzdLDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-07T14:11:10.910994Z","bundle_sha256":"71fe922fc1aed177d6e96f83e8ecd6e5690fecdfc3371a69bd2fb2fd2eb7c193"}}