{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:ZMGZXPN3PEH76A3HHECNTNOZIT","short_pith_number":"pith:ZMGZXPN3","canonical_record":{"source":{"id":"1403.0089","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-03-01T14:41:52Z","cross_cats_sorted":[],"title_canon_sha256":"067c272b9334ba51d51031f0b324a8f5acf47201fe74aba44b6d48a786c24922","abstract_canon_sha256":"ea4fe5b5dfae104e5b799446efc9b415951fff05e6409d202cd99b6dd5592784"},"schema_version":"1.0"},"canonical_sha256":"cb0d9bbdbb790fff03673904d9b5d944ffbf2aef01ce4102b9aaa66ffaae84aa","source":{"kind":"arxiv","id":"1403.0089","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1403.0089","created_at":"2026-05-18T02:57:25Z"},{"alias_kind":"arxiv_version","alias_value":"1403.0089v1","created_at":"2026-05-18T02:57:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1403.0089","created_at":"2026-05-18T02:57:25Z"},{"alias_kind":"pith_short_12","alias_value":"ZMGZXPN3PEH7","created_at":"2026-05-18T12:28:59Z"},{"alias_kind":"pith_short_16","alias_value":"ZMGZXPN3PEH76A3H","created_at":"2026-05-18T12:28:59Z"},{"alias_kind":"pith_short_8","alias_value":"ZMGZXPN3","created_at":"2026-05-18T12:28:59Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:ZMGZXPN3PEH76A3HHECNTNOZIT","target":"record","payload":{"canonical_record":{"source":{"id":"1403.0089","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-03-01T14:41:52Z","cross_cats_sorted":[],"title_canon_sha256":"067c272b9334ba51d51031f0b324a8f5acf47201fe74aba44b6d48a786c24922","abstract_canon_sha256":"ea4fe5b5dfae104e5b799446efc9b415951fff05e6409d202cd99b6dd5592784"},"schema_version":"1.0"},"canonical_sha256":"cb0d9bbdbb790fff03673904d9b5d944ffbf2aef01ce4102b9aaa66ffaae84aa","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:57:25.785498Z","signature_b64":"Sv7rD3yx8I+5kFWGDPssHMeXGCM+r8FJnbVO+xF7T1T2H+ZBP+HaZtz/OyWamCRAwDpatM26jrR0nUfVGfbNAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cb0d9bbdbb790fff03673904d9b5d944ffbf2aef01ce4102b9aaa66ffaae84aa","last_reissued_at":"2026-05-18T02:57:25.784881Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:57:25.784881Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1403.0089","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":"2026-05-18T02:57:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pNbPPQ2lkT/0X7vP/Ls/pbCq2P0HE85jM54YMpU6MeXoti9T84UeFUa8l1ipDZ2FbMfLpovVFDxeLVafvE5MCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T20:30:50.539568Z"},"content_sha256":"891a4b10ee81e129db4e10d4bbbd524b0fe0eb436881dcf15bc7a615efb657bf","schema_version":"1.0","event_id":"sha256:891a4b10ee81e129db4e10d4bbbd524b0fe0eb436881dcf15bc7a615efb657bf"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:ZMGZXPN3PEH76A3HHECNTNOZIT","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Factorization Property of Generalized s-self-decomposable measures and class $L^f$ distributions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"A. Czyzewska-Jankowska, Zbigniew J. Jurek","submitted_at":"2014-03-01T14:41:52Z","abstract_excerpt":"The method of \\emph{random integral representation}, that is, the method of representing a given probability measure as the probability distribution of some random integral, was quite successful in the past few decades. In this note we will find such a representation for generalized s-selfdecomposable and selfdecomposable distributions that have the \\emph{factorization property}. These are the classes $\\mathcal{U}^f_{\\be}$ and $L^f$, respectively."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.0089","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":"2026-05-18T02:57:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WicU/nKzxMfHzH6vXPrL/uPk3N8ue3Ak5z1rtp4TOdtbYh7ILcgn6PI2jBSdpdWwnqXZDXaf2RnD8k4kBLOgBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T20:30:50.539905Z"},"content_sha256":"dfd4ec50ea0eff71c53c244851989d0e79a5e51b7f64217e48e6bd280adf0442","schema_version":"1.0","event_id":"sha256:dfd4ec50ea0eff71c53c244851989d0e79a5e51b7f64217e48e6bd280adf0442"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ZMGZXPN3PEH76A3HHECNTNOZIT/bundle.json","state_url":"https://pith.science/pith/ZMGZXPN3PEH76A3HHECNTNOZIT/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ZMGZXPN3PEH76A3HHECNTNOZIT/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":"2026-06-25T20:30:50Z","links":{"resolver":"https://pith.science/pith/ZMGZXPN3PEH76A3HHECNTNOZIT","bundle":"https://pith.science/pith/ZMGZXPN3PEH76A3HHECNTNOZIT/bundle.json","state":"https://pith.science/pith/ZMGZXPN3PEH76A3HHECNTNOZIT/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ZMGZXPN3PEH76A3HHECNTNOZIT/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:ZMGZXPN3PEH76A3HHECNTNOZIT","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":"ea4fe5b5dfae104e5b799446efc9b415951fff05e6409d202cd99b6dd5592784","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-03-01T14:41:52Z","title_canon_sha256":"067c272b9334ba51d51031f0b324a8f5acf47201fe74aba44b6d48a786c24922"},"schema_version":"1.0","source":{"id":"1403.0089","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1403.0089","created_at":"2026-05-18T02:57:25Z"},{"alias_kind":"arxiv_version","alias_value":"1403.0089v1","created_at":"2026-05-18T02:57:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1403.0089","created_at":"2026-05-18T02:57:25Z"},{"alias_kind":"pith_short_12","alias_value":"ZMGZXPN3PEH7","created_at":"2026-05-18T12:28:59Z"},{"alias_kind":"pith_short_16","alias_value":"ZMGZXPN3PEH76A3H","created_at":"2026-05-18T12:28:59Z"},{"alias_kind":"pith_short_8","alias_value":"ZMGZXPN3","created_at":"2026-05-18T12:28:59Z"}],"graph_snapshots":[{"event_id":"sha256:dfd4ec50ea0eff71c53c244851989d0e79a5e51b7f64217e48e6bd280adf0442","target":"graph","created_at":"2026-05-18T02:57:25Z","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 method of \\emph{random integral representation}, that is, the method of representing a given probability measure as the probability distribution of some random integral, was quite successful in the past few decades. In this note we will find such a representation for generalized s-selfdecomposable and selfdecomposable distributions that have the \\emph{factorization property}. These are the classes $\\mathcal{U}^f_{\\be}$ and $L^f$, respectively.","authors_text":"A. Czyzewska-Jankowska, Zbigniew J. Jurek","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-03-01T14:41:52Z","title":"Factorization Property of Generalized s-self-decomposable measures and class $L^f$ distributions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.0089","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":"sha256:891a4b10ee81e129db4e10d4bbbd524b0fe0eb436881dcf15bc7a615efb657bf","target":"record","created_at":"2026-05-18T02:57:25Z","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":"ea4fe5b5dfae104e5b799446efc9b415951fff05e6409d202cd99b6dd5592784","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-03-01T14:41:52Z","title_canon_sha256":"067c272b9334ba51d51031f0b324a8f5acf47201fe74aba44b6d48a786c24922"},"schema_version":"1.0","source":{"id":"1403.0089","kind":"arxiv","version":1}},"canonical_sha256":"cb0d9bbdbb790fff03673904d9b5d944ffbf2aef01ce4102b9aaa66ffaae84aa","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"cb0d9bbdbb790fff03673904d9b5d944ffbf2aef01ce4102b9aaa66ffaae84aa","first_computed_at":"2026-05-18T02:57:25.784881Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:57:25.784881Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Sv7rD3yx8I+5kFWGDPssHMeXGCM+r8FJnbVO+xF7T1T2H+ZBP+HaZtz/OyWamCRAwDpatM26jrR0nUfVGfbNAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:57:25.785498Z","signed_message":"canonical_sha256_bytes"},"source_id":"1403.0089","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:891a4b10ee81e129db4e10d4bbbd524b0fe0eb436881dcf15bc7a615efb657bf","sha256:dfd4ec50ea0eff71c53c244851989d0e79a5e51b7f64217e48e6bd280adf0442"],"state_sha256":"0b46607ea14c271248ab4a0e4a06aa2f32aa0b2272050050e19cf3ef55683606"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Kawn7BqYoq2qz8gi/5Ceya/5XPvBApzVUqPachU5ZaJ4l4/vuIxLVNz4yAtcrvS2ctRKeqTOmM348ikL9NxIAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-25T20:30:50.541760Z","bundle_sha256":"eb7744660c7e615a793af99a080440076abdc284a109637da442708700c74e69"}}