{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:NX4IB2MNAL3RDOW7ZCI7VZJDXY","short_pith_number":"pith:NX4IB2MN","schema_version":"1.0","canonical_sha256":"6df880e98d02f711badfc891fae523be1b7ef7abee0ba4d089781281c9818f11","source":{"kind":"arxiv","id":"1304.0189","version":1},"attestation_state":"computed","paper":{"title":"Fractional Non-Linear, Linear and Sublinear Death Processes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Enzo Orsingher, Federico Polito, Ludmila Sakhno","submitted_at":"2013-03-31T11:20:40Z","abstract_excerpt":"This paper is devoted to the study of a fractional version of non-linear $\\mathpzc{M}^\\nu(t)$, $t>0$, linear $M^\\nu (t)$, $t>0$ and sublinear $\\mathfrak{M}^\\nu (t)$, $t>0$ death processes. Fractionality is introduced by replacing the usual integer-order derivative in the difference-differential equations governing the state probabilities, with the fractional derivative understood in the sense of Dzhrbashyan--Caputo. We derive explicitly the state probabilities of the three death processes and examine the related probability generating functions and mean values. A useful subordination relation "},"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":"1304.0189","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-03-31T11:20:40Z","cross_cats_sorted":[],"title_canon_sha256":"4128a7ab4f014b46b9aeb2a3ef8aa5342b8822810ca6eda9a787b6fd36e9eb08","abstract_canon_sha256":"2a3e43bb37102f915b87b4491c7dfb785cd31be08a5d8c62d0b6c19517d0e451"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:29:25.775695Z","signature_b64":"CwF3IzyfD2lmMNeoEa9byz0qWuIllsVroRceOZz+wLwHPtGoQXjLsrHbYhBKhl58dVe9NXsEA47WXSgAW+JZDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6df880e98d02f711badfc891fae523be1b7ef7abee0ba4d089781281c9818f11","last_reissued_at":"2026-05-18T03:29:25.775024Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:29:25.775024Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Fractional Non-Linear, Linear and Sublinear Death Processes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Enzo Orsingher, Federico Polito, Ludmila Sakhno","submitted_at":"2013-03-31T11:20:40Z","abstract_excerpt":"This paper is devoted to the study of a fractional version of non-linear $\\mathpzc{M}^\\nu(t)$, $t>0$, linear $M^\\nu (t)$, $t>0$ and sublinear $\\mathfrak{M}^\\nu (t)$, $t>0$ death processes. Fractionality is introduced by replacing the usual integer-order derivative in the difference-differential equations governing the state probabilities, with the fractional derivative understood in the sense of Dzhrbashyan--Caputo. We derive explicitly the state probabilities of the three death processes and examine the related probability generating functions and mean values. A useful subordination relation "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.0189","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1304.0189","created_at":"2026-05-18T03:29:25.775124+00:00"},{"alias_kind":"arxiv_version","alias_value":"1304.0189v1","created_at":"2026-05-18T03:29:25.775124+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1304.0189","created_at":"2026-05-18T03:29:25.775124+00:00"},{"alias_kind":"pith_short_12","alias_value":"NX4IB2MNAL3R","created_at":"2026-05-18T12:27:52.871228+00:00"},{"alias_kind":"pith_short_16","alias_value":"NX4IB2MNAL3RDOW7","created_at":"2026-05-18T12:27:52.871228+00:00"},{"alias_kind":"pith_short_8","alias_value":"NX4IB2MN","created_at":"2026-05-18T12:27:52.871228+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/NX4IB2MNAL3RDOW7ZCI7VZJDXY","json":"https://pith.science/pith/NX4IB2MNAL3RDOW7ZCI7VZJDXY.json","graph_json":"https://pith.science/api/pith-number/NX4IB2MNAL3RDOW7ZCI7VZJDXY/graph.json","events_json":"https://pith.science/api/pith-number/NX4IB2MNAL3RDOW7ZCI7VZJDXY/events.json","paper":"https://pith.science/paper/NX4IB2MN"},"agent_actions":{"view_html":"https://pith.science/pith/NX4IB2MNAL3RDOW7ZCI7VZJDXY","download_json":"https://pith.science/pith/NX4IB2MNAL3RDOW7ZCI7VZJDXY.json","view_paper":"https://pith.science/paper/NX4IB2MN","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1304.0189&json=true","fetch_graph":"https://pith.science/api/pith-number/NX4IB2MNAL3RDOW7ZCI7VZJDXY/graph.json","fetch_events":"https://pith.science/api/pith-number/NX4IB2MNAL3RDOW7ZCI7VZJDXY/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/NX4IB2MNAL3RDOW7ZCI7VZJDXY/action/timestamp_anchor","attest_storage":"https://pith.science/pith/NX4IB2MNAL3RDOW7ZCI7VZJDXY/action/storage_attestation","attest_author":"https://pith.science/pith/NX4IB2MNAL3RDOW7ZCI7VZJDXY/action/author_attestation","sign_citation":"https://pith.science/pith/NX4IB2MNAL3RDOW7ZCI7VZJDXY/action/citation_signature","submit_replication":"https://pith.science/pith/NX4IB2MNAL3RDOW7ZCI7VZJDXY/action/replication_record"}},"created_at":"2026-05-18T03:29:25.775124+00:00","updated_at":"2026-05-18T03:29:25.775124+00:00"}