{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:ZFHV4KN3J6ZQQ7AUHI2QOMF2PC","short_pith_number":"pith:ZFHV4KN3","schema_version":"1.0","canonical_sha256":"c94f5e29bb4fb3087c143a350730ba78a7e32795e80411f2317f9b9bc1dda00b","source":{"kind":"arxiv","id":"1803.02973","version":2},"attestation_state":"computed","paper":{"title":"On properties of a class of strong limits for supercritical superprocesses","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Renming Song, Rui Zhang, Yan-Xia Ren","submitted_at":"2018-03-08T05:26:29Z","abstract_excerpt":"Suppose that $X=\\{X_t, t\\ge 0; \\mathbb{P}_{\\mu}\\}$ is a supercritical superprocess in a locally compact separable metric space $E$. Let $\\phi_0$ be a positive\n  eigenfunction corresponding to the first eigenvalue $\\lambda_0$ of the generator of the mean semigroup of $X$. Then $M_t:=e^{-\\lambda_0t}\\langle\\phi_0, X_t\\rangle$ is a positive martingale. Let $M_\\infty$ be the limit of $M_t$. It is known that $M_\\infty$ is non-degenerate iff the $L\\log L$ condition is satisfied. When the $L\\log L$ condition may not be satisfied, we recently proved in (arXiv:1708.04422) that there exist a non-negative"},"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":"1803.02973","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-03-08T05:26:29Z","cross_cats_sorted":[],"title_canon_sha256":"e3a8095385b4f481238e9b8fbf983a8fe24d0ffd8f6603f1243cf5788cdb276c","abstract_canon_sha256":"25e69c6d4862ff891e32aa41b000e28d5483e4a5d1d636d10ce815623412f0e8"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:06:56.238279Z","signature_b64":"uW024/65sTSih61o2UfYjXCL+6ZEGQQGeCMSbACKbwoeGpCsJoPnu05OtOqmAX4rV7+f3/jNvxVQFO8LJUK7DA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c94f5e29bb4fb3087c143a350730ba78a7e32795e80411f2317f9b9bc1dda00b","last_reissued_at":"2026-05-18T00:06:56.237522Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:06:56.237522Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On properties of a class of strong limits for supercritical superprocesses","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Renming Song, Rui Zhang, Yan-Xia Ren","submitted_at":"2018-03-08T05:26:29Z","abstract_excerpt":"Suppose that $X=\\{X_t, t\\ge 0; \\mathbb{P}_{\\mu}\\}$ is a supercritical superprocess in a locally compact separable metric space $E$. Let $\\phi_0$ be a positive\n  eigenfunction corresponding to the first eigenvalue $\\lambda_0$ of the generator of the mean semigroup of $X$. Then $M_t:=e^{-\\lambda_0t}\\langle\\phi_0, X_t\\rangle$ is a positive martingale. Let $M_\\infty$ be the limit of $M_t$. It is known that $M_\\infty$ is non-degenerate iff the $L\\log L$ condition is satisfied. When the $L\\log L$ condition may not be satisfied, we recently proved in (arXiv:1708.04422) that there exist a non-negative"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.02973","kind":"arxiv","version":2},"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":"1803.02973","created_at":"2026-05-18T00:06:56.237652+00:00"},{"alias_kind":"arxiv_version","alias_value":"1803.02973v2","created_at":"2026-05-18T00:06:56.237652+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1803.02973","created_at":"2026-05-18T00:06:56.237652+00:00"},{"alias_kind":"pith_short_12","alias_value":"ZFHV4KN3J6ZQ","created_at":"2026-05-18T12:33:07.085635+00:00"},{"alias_kind":"pith_short_16","alias_value":"ZFHV4KN3J6ZQQ7AU","created_at":"2026-05-18T12:33:07.085635+00:00"},{"alias_kind":"pith_short_8","alias_value":"ZFHV4KN3","created_at":"2026-05-18T12:33:07.085635+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/ZFHV4KN3J6ZQQ7AUHI2QOMF2PC","json":"https://pith.science/pith/ZFHV4KN3J6ZQQ7AUHI2QOMF2PC.json","graph_json":"https://pith.science/api/pith-number/ZFHV4KN3J6ZQQ7AUHI2QOMF2PC/graph.json","events_json":"https://pith.science/api/pith-number/ZFHV4KN3J6ZQQ7AUHI2QOMF2PC/events.json","paper":"https://pith.science/paper/ZFHV4KN3"},"agent_actions":{"view_html":"https://pith.science/pith/ZFHV4KN3J6ZQQ7AUHI2QOMF2PC","download_json":"https://pith.science/pith/ZFHV4KN3J6ZQQ7AUHI2QOMF2PC.json","view_paper":"https://pith.science/paper/ZFHV4KN3","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1803.02973&json=true","fetch_graph":"https://pith.science/api/pith-number/ZFHV4KN3J6ZQQ7AUHI2QOMF2PC/graph.json","fetch_events":"https://pith.science/api/pith-number/ZFHV4KN3J6ZQQ7AUHI2QOMF2PC/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ZFHV4KN3J6ZQQ7AUHI2QOMF2PC/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ZFHV4KN3J6ZQQ7AUHI2QOMF2PC/action/storage_attestation","attest_author":"https://pith.science/pith/ZFHV4KN3J6ZQQ7AUHI2QOMF2PC/action/author_attestation","sign_citation":"https://pith.science/pith/ZFHV4KN3J6ZQQ7AUHI2QOMF2PC/action/citation_signature","submit_replication":"https://pith.science/pith/ZFHV4KN3J6ZQQ7AUHI2QOMF2PC/action/replication_record"}},"created_at":"2026-05-18T00:06:56.237652+00:00","updated_at":"2026-05-18T00:06:56.237652+00:00"}