{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:OZYRXKZCTJO3QMFSQGERUREEIS","short_pith_number":"pith:OZYRXKZC","schema_version":"1.0","canonical_sha256":"76711bab229a5db830b281891a44844496becb4c0af0778824353a0991ee304f","source":{"kind":"arxiv","id":"1604.00864","version":1},"attestation_state":"computed","paper":{"title":"Recurrence and transience of near-critical multivariate growth models: criteria and examples","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"G\\\"otz Kersting","submitted_at":"2016-04-04T14:05:54Z","abstract_excerpt":"We discuss complementary recurrence and transience criteria for stochastic processes $(X_n)_{n \\ge 0}$ with values in the $d$-dimensional orthant $\\mathbb R^d_+$ fulfilling a non-linear stochastic equation of the form $X_{n+1}=MX_n+g(X_n)+ \\xi_n$ with a primitive matrix $M$ and random noise $\\xi_n$ and obeying a weak Markov property. As examples we discuss bisexual Galton-Watson processes and multivariate Galton-Watson processes, which both may be population size dependent."},"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":"1604.00864","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-04-04T14:05:54Z","cross_cats_sorted":[],"title_canon_sha256":"bace00709fed6ea0e62fc7357cb06d212667a5e20147d326111a6137ed73ea3c","abstract_canon_sha256":"54e28c4b6e1e8654b7558c426630d79bb1a14934b54c298d12c1debe425e9533"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:17:47.975686Z","signature_b64":"km4MKcj2Ih58Ts/N+rbiKpVM7Q5C4pcqGNZILgV5kdl1KMi1FIFCNHDwA3Oo+3wyDSXlj3H+qCy+pdgg+oSwCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"76711bab229a5db830b281891a44844496becb4c0af0778824353a0991ee304f","last_reissued_at":"2026-05-18T01:17:47.974928Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:17:47.974928Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Recurrence and transience of near-critical multivariate growth models: criteria and examples","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"G\\\"otz Kersting","submitted_at":"2016-04-04T14:05:54Z","abstract_excerpt":"We discuss complementary recurrence and transience criteria for stochastic processes $(X_n)_{n \\ge 0}$ with values in the $d$-dimensional orthant $\\mathbb R^d_+$ fulfilling a non-linear stochastic equation of the form $X_{n+1}=MX_n+g(X_n)+ \\xi_n$ with a primitive matrix $M$ and random noise $\\xi_n$ and obeying a weak Markov property. As examples we discuss bisexual Galton-Watson processes and multivariate Galton-Watson processes, which both may be population size dependent."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.00864","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":"1604.00864","created_at":"2026-05-18T01:17:47.975039+00:00"},{"alias_kind":"arxiv_version","alias_value":"1604.00864v1","created_at":"2026-05-18T01:17:47.975039+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1604.00864","created_at":"2026-05-18T01:17:47.975039+00:00"},{"alias_kind":"pith_short_12","alias_value":"OZYRXKZCTJO3","created_at":"2026-05-18T12:30:36.002864+00:00"},{"alias_kind":"pith_short_16","alias_value":"OZYRXKZCTJO3QMFS","created_at":"2026-05-18T12:30:36.002864+00:00"},{"alias_kind":"pith_short_8","alias_value":"OZYRXKZC","created_at":"2026-05-18T12:30:36.002864+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/OZYRXKZCTJO3QMFSQGERUREEIS","json":"https://pith.science/pith/OZYRXKZCTJO3QMFSQGERUREEIS.json","graph_json":"https://pith.science/api/pith-number/OZYRXKZCTJO3QMFSQGERUREEIS/graph.json","events_json":"https://pith.science/api/pith-number/OZYRXKZCTJO3QMFSQGERUREEIS/events.json","paper":"https://pith.science/paper/OZYRXKZC"},"agent_actions":{"view_html":"https://pith.science/pith/OZYRXKZCTJO3QMFSQGERUREEIS","download_json":"https://pith.science/pith/OZYRXKZCTJO3QMFSQGERUREEIS.json","view_paper":"https://pith.science/paper/OZYRXKZC","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1604.00864&json=true","fetch_graph":"https://pith.science/api/pith-number/OZYRXKZCTJO3QMFSQGERUREEIS/graph.json","fetch_events":"https://pith.science/api/pith-number/OZYRXKZCTJO3QMFSQGERUREEIS/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/OZYRXKZCTJO3QMFSQGERUREEIS/action/timestamp_anchor","attest_storage":"https://pith.science/pith/OZYRXKZCTJO3QMFSQGERUREEIS/action/storage_attestation","attest_author":"https://pith.science/pith/OZYRXKZCTJO3QMFSQGERUREEIS/action/author_attestation","sign_citation":"https://pith.science/pith/OZYRXKZCTJO3QMFSQGERUREEIS/action/citation_signature","submit_replication":"https://pith.science/pith/OZYRXKZCTJO3QMFSQGERUREEIS/action/replication_record"}},"created_at":"2026-05-18T01:17:47.975039+00:00","updated_at":"2026-05-18T01:17:47.975039+00:00"}