{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2009:WX2GNP4ZMCVFA54AMMZNA5I2KV","short_pith_number":"pith:WX2GNP4Z","canonical_record":{"source":{"id":"0901.0434","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-fin.ST","submitted_at":"2009-01-05T08:49:18Z","cross_cats_sorted":["q-fin.CP"],"title_canon_sha256":"cfd00883ec2542abb43c63083bd4be4ee93b343c4a3a158663b6aa95bdc9b705","abstract_canon_sha256":"e8c2196a89b82792622dad155561d88a20b54548919d8e68aa673829ac9d4b21"},"schema_version":"1.0"},"canonical_sha256":"b5f466bf9960aa5077806332d0751a556e7d7e83ab897e1b5758f1378ac30bbf","source":{"kind":"arxiv","id":"0901.0434","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0901.0434","created_at":"2026-07-04T15:35:29Z"},{"alias_kind":"arxiv_version","alias_value":"0901.0434v1","created_at":"2026-07-04T15:35:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0901.0434","created_at":"2026-07-04T15:35:29Z"},{"alias_kind":"pith_short_12","alias_value":"WX2GNP4ZMCVF","created_at":"2026-07-04T15:35:29Z"},{"alias_kind":"pith_short_16","alias_value":"WX2GNP4ZMCVFA54A","created_at":"2026-07-04T15:35:29Z"},{"alias_kind":"pith_short_8","alias_value":"WX2GNP4Z","created_at":"2026-07-04T15:35:29Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2009:WX2GNP4ZMCVFA54AMMZNA5I2KV","target":"record","payload":{"canonical_record":{"source":{"id":"0901.0434","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-fin.ST","submitted_at":"2009-01-05T08:49:18Z","cross_cats_sorted":["q-fin.CP"],"title_canon_sha256":"cfd00883ec2542abb43c63083bd4be4ee93b343c4a3a158663b6aa95bdc9b705","abstract_canon_sha256":"e8c2196a89b82792622dad155561d88a20b54548919d8e68aa673829ac9d4b21"},"schema_version":"1.0"},"canonical_sha256":"b5f466bf9960aa5077806332d0751a556e7d7e83ab897e1b5758f1378ac30bbf","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T15:35:29.312878Z","signature_b64":"aO6xI0N2hYpRjC5m95bprMe5p76kBXKGbBkQQfc8CNdW79VMAceOlvWHONZXzXdz5lCcmwb1SdcU8N05Gp/4AA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b5f466bf9960aa5077806332d0751a556e7d7e83ab897e1b5758f1378ac30bbf","last_reissued_at":"2026-07-04T15:35:29.312469Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T15:35:29.312469Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0901.0434","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":"2026-07-04T15:35:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1AUYHmkYdflm/D9ohhgoU6aOTzDp6GJB7s81UVYIzn91d+ahCasHUGSUN4w+i9VTyPzyj62MhDk2N2nYA3dHCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-08T12:55:20.371454Z"},"content_sha256":"f45bdee21035e8695525f16d4317adb1ef02a3968c430575c72fe5159487fc28","schema_version":"1.0","event_id":"sha256:f45bdee21035e8695525f16d4317adb1ef02a3968c430575c72fe5159487fc28"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2009:WX2GNP4ZMCVFA54AMMZNA5I2KV","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The alchemy of probability distributions: beyond Gram-Charlier expansions, and a skew-kurtotic-normal distribution from a rank transmutation map","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["q-fin.CP"],"primary_cat":"q-fin.ST","authors_text":"Ian R.C. Buckley, William T. Shaw","submitted_at":"2009-01-05T08:49:18Z","abstract_excerpt":"Motivated by the need for parametric families of rich and yet tractable distributions in financial mathematics, both in pricing and risk management settings, but also considering wider statistical applications, we investigate a novel technique for introducing skewness or kurtosis into a symmetric or other distribution. We use a \"transmutation\" map, which is the functional composition of the cumulative distribution function of one distribution with the inverse cumulative distribution (quantile) function of another. In contrast to the Gram-Charlier approach, this is done without resorting to an "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0901.0434","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/0901.0434/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":"2026-07-04T15:35:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"H9apQecHntWAa3+/pZ1j31aBgeqdOQFKYv7PeBzagOSO1D9hK9M/UW8JaYbm5/qSDHJHgSzmV1YKD92sRgd8Dw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-08T12:55:20.371971Z"},"content_sha256":"0c7cdea146e1b7f9ca49daef222342f50024675f8675214249dd6d1eaf5a7494","schema_version":"1.0","event_id":"sha256:0c7cdea146e1b7f9ca49daef222342f50024675f8675214249dd6d1eaf5a7494"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/WX2GNP4ZMCVFA54AMMZNA5I2KV/bundle.json","state_url":"https://pith.science/pith/WX2GNP4ZMCVFA54AMMZNA5I2KV/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/WX2GNP4ZMCVFA54AMMZNA5I2KV/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":"2026-08-08T12:55:20Z","links":{"resolver":"https://pith.science/pith/WX2GNP4ZMCVFA54AMMZNA5I2KV","bundle":"https://pith.science/pith/WX2GNP4ZMCVFA54AMMZNA5I2KV/bundle.json","state":"https://pith.science/pith/WX2GNP4ZMCVFA54AMMZNA5I2KV/state.json","well_known_bundle":"https://pith.science/.well-known/pith/WX2GNP4ZMCVFA54AMMZNA5I2KV/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:WX2GNP4ZMCVFA54AMMZNA5I2KV","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":"e8c2196a89b82792622dad155561d88a20b54548919d8e68aa673829ac9d4b21","cross_cats_sorted":["q-fin.CP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-fin.ST","submitted_at":"2009-01-05T08:49:18Z","title_canon_sha256":"cfd00883ec2542abb43c63083bd4be4ee93b343c4a3a158663b6aa95bdc9b705"},"schema_version":"1.0","source":{"id":"0901.0434","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0901.0434","created_at":"2026-07-04T15:35:29Z"},{"alias_kind":"arxiv_version","alias_value":"0901.0434v1","created_at":"2026-07-04T15:35:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0901.0434","created_at":"2026-07-04T15:35:29Z"},{"alias_kind":"pith_short_12","alias_value":"WX2GNP4ZMCVF","created_at":"2026-07-04T15:35:29Z"},{"alias_kind":"pith_short_16","alias_value":"WX2GNP4ZMCVFA54A","created_at":"2026-07-04T15:35:29Z"},{"alias_kind":"pith_short_8","alias_value":"WX2GNP4Z","created_at":"2026-07-04T15:35:29Z"}],"graph_snapshots":[{"event_id":"sha256:0c7cdea146e1b7f9ca49daef222342f50024675f8675214249dd6d1eaf5a7494","target":"graph","created_at":"2026-07-04T15:35:29Z","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/0901.0434/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Motivated by the need for parametric families of rich and yet tractable distributions in financial mathematics, both in pricing and risk management settings, but also considering wider statistical applications, we investigate a novel technique for introducing skewness or kurtosis into a symmetric or other distribution. We use a \"transmutation\" map, which is the functional composition of the cumulative distribution function of one distribution with the inverse cumulative distribution (quantile) function of another. In contrast to the Gram-Charlier approach, this is done without resorting to an ","authors_text":"Ian R.C. Buckley, William T. Shaw","cross_cats":["q-fin.CP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-fin.ST","submitted_at":"2009-01-05T08:49:18Z","title":"The alchemy of probability distributions: beyond Gram-Charlier expansions, and a skew-kurtotic-normal distribution from a rank transmutation map"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0901.0434","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:f45bdee21035e8695525f16d4317adb1ef02a3968c430575c72fe5159487fc28","target":"record","created_at":"2026-07-04T15:35:29Z","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":"e8c2196a89b82792622dad155561d88a20b54548919d8e68aa673829ac9d4b21","cross_cats_sorted":["q-fin.CP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-fin.ST","submitted_at":"2009-01-05T08:49:18Z","title_canon_sha256":"cfd00883ec2542abb43c63083bd4be4ee93b343c4a3a158663b6aa95bdc9b705"},"schema_version":"1.0","source":{"id":"0901.0434","kind":"arxiv","version":1}},"canonical_sha256":"b5f466bf9960aa5077806332d0751a556e7d7e83ab897e1b5758f1378ac30bbf","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b5f466bf9960aa5077806332d0751a556e7d7e83ab897e1b5758f1378ac30bbf","first_computed_at":"2026-07-04T15:35:29.312469Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T15:35:29.312469Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"aO6xI0N2hYpRjC5m95bprMe5p76kBXKGbBkQQfc8CNdW79VMAceOlvWHONZXzXdz5lCcmwb1SdcU8N05Gp/4AA==","signature_status":"signed_v1","signed_at":"2026-07-04T15:35:29.312878Z","signed_message":"canonical_sha256_bytes"},"source_id":"0901.0434","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f45bdee21035e8695525f16d4317adb1ef02a3968c430575c72fe5159487fc28","sha256:0c7cdea146e1b7f9ca49daef222342f50024675f8675214249dd6d1eaf5a7494"],"state_sha256":"0cb1f54f79dcaad3d905e48c999cc2ba93db692446ac8435d1bf5ff312e86570"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"yX+ubWgpw11ueMmc1B2d1SjGlT3q7t0yiU+RNlxEmznlLSlixmzWKE00Kwh/Zc3TXyBSOVv3LrXl5j3FUykVDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-08T12:55:20.377320Z","bundle_sha256":"1308f2386af7d6358123d7a32742ef5a04cd7245eb8fd3318002406261b67453"}}