{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:EWZ5XYHQ4XPU4WERSLPQLNORA3","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":"f97baf3cbfde52566630ce46e472daef2e3e10b204e41e87d97bcf9c79dfc7e4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-02-17T19:34:10Z","title_canon_sha256":"9ad6c81ab318fd1704f267061c97f93ef81525fa1651b3b65f871cabccf4d48b"},"schema_version":"1.0","source":{"id":"1102.3668","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1102.3668","created_at":"2026-05-18T04:28:28Z"},{"alias_kind":"arxiv_version","alias_value":"1102.3668v1","created_at":"2026-05-18T04:28:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1102.3668","created_at":"2026-05-18T04:28:28Z"},{"alias_kind":"pith_short_12","alias_value":"EWZ5XYHQ4XPU","created_at":"2026-05-18T12:26:28Z"},{"alias_kind":"pith_short_16","alias_value":"EWZ5XYHQ4XPU4WER","created_at":"2026-05-18T12:26:28Z"},{"alias_kind":"pith_short_8","alias_value":"EWZ5XYHQ","created_at":"2026-05-18T12:26:28Z"}],"graph_snapshots":[{"event_id":"sha256:2557956b9bacf6ce8a2db8dbb2ee4aa351ace87c64b3543fb56a680133723b28","target":"graph","created_at":"2026-05-18T04:28:28Z","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":"In this paper we prove that, under certain conditions, a strong law of large numbers holds for a class of super-diffusions $X$ corresponding to the evolution equation $\\partial_t u_t=L u_t+\\beta u_t-\\psi(u_t)$ on a bounded domain $D$ in $\\R^d$, where $L$ is the generator of the underlying diffusion and the branching mechanism\n  $\\psi(x,\\lambda)=1/2\\alpha(x)\\lambda^2+\\int_0^\\infty (e^{-\\lambda r}-1+\\lambda r)n(x, {\\rm d}r)$ satisfies $\\sup_{x\\in D}\\int_0^\\infty (r\\wedge r^2) n(x,{\\rm d}r)<\\infty$.","authors_text":"Renming Song, Rong-Li Liu, Yan-Xia Ren","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-02-17T19:34:10Z","title":"Strong law of large number of a class of super-diffusions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1102.3668","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":"sha256:55efc18ec802ad855d21f32a0693cb9f54dde53b1270cc156fcda85e16708ba2","target":"record","created_at":"2026-05-18T04:28:28Z","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":"f97baf3cbfde52566630ce46e472daef2e3e10b204e41e87d97bcf9c79dfc7e4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-02-17T19:34:10Z","title_canon_sha256":"9ad6c81ab318fd1704f267061c97f93ef81525fa1651b3b65f871cabccf4d48b"},"schema_version":"1.0","source":{"id":"1102.3668","kind":"arxiv","version":1}},"canonical_sha256":"25b3dbe0f0e5df4e589192df05b5d106e83418defe7ef5f4823a06b0654dc756","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"25b3dbe0f0e5df4e589192df05b5d106e83418defe7ef5f4823a06b0654dc756","first_computed_at":"2026-05-18T04:28:28.683812Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:28:28.683812Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"R/Fx5muaP1UQVNOkoL+xKRjJ4UUJSgADpQii2r+RroPRrA4VrPh5uDC5UnBsvaU4b5nfD+NdmDWykEXy8ULCBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:28:28.684391Z","signed_message":"canonical_sha256_bytes"},"source_id":"1102.3668","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:55efc18ec802ad855d21f32a0693cb9f54dde53b1270cc156fcda85e16708ba2","sha256:2557956b9bacf6ce8a2db8dbb2ee4aa351ace87c64b3543fb56a680133723b28"],"state_sha256":"d860073e4965ed5bb621d92885303f975f4e0314aeecfb2aad28b3003fd627de"}