{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:CN4LZP3MPJBAFPA2T7DZY5URCZ","short_pith_number":"pith:CN4LZP3M","schema_version":"1.0","canonical_sha256":"1378bcbf6c7a4202bc1a9fc79c76911651a7df7c4a248abcd533c5ed941d28c0","source":{"kind":"arxiv","id":"1207.4983","version":3},"attestation_state":"computed","paper":{"title":"Stochastic integral representations and classification of sum- and max-infinitely divisible processes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"math.PR","authors_text":"Stilian Stoev, Zakhar Kabluchko","submitted_at":"2012-07-20T15:40:22Z","abstract_excerpt":"Introduced is the notion of minimality for spectral representations of sum- and max-infinitely divisible processes and it is shown that the minimal spectral representation on a Borel space exists and is unique. This fact is used to show that a stationary, stochastically continuous, sum- or max-i.d. random process on $\\mathbb{R}^d$ can be generated by a measure-preserving flow on a $\\sigma$-finite Borel measure space and that this flow is unique. This development makes it possible to extend the classification program of Rosi\\'{n}ski (Ann. Probab. 23 (1995) 1163-1187) with a unified treatment of"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1207.4983","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-07-20T15:40:22Z","cross_cats_sorted":["math.DS"],"title_canon_sha256":"0bc9cce92b0fe43442a50ea352402eabd06400eb7004f3d947d11d2d83580326","abstract_canon_sha256":"95ca682aacb225ab16f71ec87d7aed788877ab93102f82c063d396820ef8d572"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:22:52.629967Z","signature_b64":"GNvY7BSTVbF3f+v2IYGbsUKT3mq3U07xzy6HV1cB5ZJHh0LxUjp2p/e1J70QlT6jLIEwhaXYTqS5BSNwjxi4Cw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1378bcbf6c7a4202bc1a9fc79c76911651a7df7c4a248abcd533c5ed941d28c0","last_reissued_at":"2026-05-18T01:22:52.629279Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:22:52.629279Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Stochastic integral representations and classification of sum- and max-infinitely divisible processes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"math.PR","authors_text":"Stilian Stoev, Zakhar Kabluchko","submitted_at":"2012-07-20T15:40:22Z","abstract_excerpt":"Introduced is the notion of minimality for spectral representations of sum- and max-infinitely divisible processes and it is shown that the minimal spectral representation on a Borel space exists and is unique. This fact is used to show that a stationary, stochastically continuous, sum- or max-i.d. random process on $\\mathbb{R}^d$ can be generated by a measure-preserving flow on a $\\sigma$-finite Borel measure space and that this flow is unique. This development makes it possible to extend the classification program of Rosi\\'{n}ski (Ann. Probab. 23 (1995) 1163-1187) with a unified treatment of"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1207.4983","kind":"arxiv","version":3},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1207.4983","created_at":"2026-05-18T01:22:52.629411+00:00"},{"alias_kind":"arxiv_version","alias_value":"1207.4983v3","created_at":"2026-05-18T01:22:52.629411+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1207.4983","created_at":"2026-05-18T01:22:52.629411+00:00"},{"alias_kind":"pith_short_12","alias_value":"CN4LZP3MPJBA","created_at":"2026-05-18T12:27:01.376967+00:00"},{"alias_kind":"pith_short_16","alias_value":"CN4LZP3MPJBAFPA2","created_at":"2026-05-18T12:27:01.376967+00:00"},{"alias_kind":"pith_short_8","alias_value":"CN4LZP3M","created_at":"2026-05-18T12:27:01.376967+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/CN4LZP3MPJBAFPA2T7DZY5URCZ","json":"https://pith.science/pith/CN4LZP3MPJBAFPA2T7DZY5URCZ.json","graph_json":"https://pith.science/api/pith-number/CN4LZP3MPJBAFPA2T7DZY5URCZ/graph.json","events_json":"https://pith.science/api/pith-number/CN4LZP3MPJBAFPA2T7DZY5URCZ/events.json","paper":"https://pith.science/paper/CN4LZP3M"},"agent_actions":{"view_html":"https://pith.science/pith/CN4LZP3MPJBAFPA2T7DZY5URCZ","download_json":"https://pith.science/pith/CN4LZP3MPJBAFPA2T7DZY5URCZ.json","view_paper":"https://pith.science/paper/CN4LZP3M","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1207.4983&json=true","fetch_graph":"https://pith.science/api/pith-number/CN4LZP3MPJBAFPA2T7DZY5URCZ/graph.json","fetch_events":"https://pith.science/api/pith-number/CN4LZP3MPJBAFPA2T7DZY5URCZ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/CN4LZP3MPJBAFPA2T7DZY5URCZ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/CN4LZP3MPJBAFPA2T7DZY5URCZ/action/storage_attestation","attest_author":"https://pith.science/pith/CN4LZP3MPJBAFPA2T7DZY5URCZ/action/author_attestation","sign_citation":"https://pith.science/pith/CN4LZP3MPJBAFPA2T7DZY5URCZ/action/citation_signature","submit_replication":"https://pith.science/pith/CN4LZP3MPJBAFPA2T7DZY5URCZ/action/replication_record"}},"created_at":"2026-05-18T01:22:52.629411+00:00","updated_at":"2026-05-18T01:22:52.629411+00:00"}