{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:Y6TWV6ZQ3KDJOK3QVMGCVXBK2W","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":"5fd449a4990d95c6ec882af67a7b49787b16981a988bd3fa967e793cc71277c2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-10-08T10:26:51Z","title_canon_sha256":"3d6ae018aa4dfd672dc556bb0eecac29f6d6e25218d0c86f052f049d36d7e3c8"},"schema_version":"1.0","source":{"id":"1210.2218","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1210.2218","created_at":"2026-05-18T00:30:09Z"},{"alias_kind":"arxiv_version","alias_value":"1210.2218v2","created_at":"2026-05-18T00:30:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1210.2218","created_at":"2026-05-18T00:30:09Z"},{"alias_kind":"pith_short_12","alias_value":"Y6TWV6ZQ3KDJ","created_at":"2026-05-18T12:27:27Z"},{"alias_kind":"pith_short_16","alias_value":"Y6TWV6ZQ3KDJOK3Q","created_at":"2026-05-18T12:27:27Z"},{"alias_kind":"pith_short_8","alias_value":"Y6TWV6ZQ","created_at":"2026-05-18T12:27:27Z"}],"graph_snapshots":[{"event_id":"sha256:ead66899a1f1fbaf042f20fa9ff3a5487b8e95968230d90a64032fd0cfede99f","target":"graph","created_at":"2026-05-18T00:30:09Z","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":"For certain subordinators $(X_t)_{t\\ge 0}$ it is shown that the process $(-t\\log X_{ts})_{s>0}$ tends to an extremal process $(\\hat\\eta_s)_{s>0}$ in the sense of convergence of the finite dimensional distributions. Additionally it is also shown that $(z\\wedge(-t\\log X_{ts}))_{s\\ge 0}$ converges weakly to $(z\\wedge\\hat\\eta_s)_{s\\ge0}$ in $\\mathcal{D}[0,\\infty)$, the space of c\\`{a}dl\\`{a}g functions equipped with Skorohod's $J_1$ metric.","authors_text":"Andreas L\\\"opker, Offer Kella","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-10-08T10:26:51Z","title":"Weak Convergence of Subordinators to Extremal Processes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.2218","kind":"arxiv","version":2},"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":"sha256:995cf2376343646a49938e4cf575534ee7b5b408f89336185ffec69df26dab4d","target":"record","created_at":"2026-05-18T00:30:09Z","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":"5fd449a4990d95c6ec882af67a7b49787b16981a988bd3fa967e793cc71277c2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-10-08T10:26:51Z","title_canon_sha256":"3d6ae018aa4dfd672dc556bb0eecac29f6d6e25218d0c86f052f049d36d7e3c8"},"schema_version":"1.0","source":{"id":"1210.2218","kind":"arxiv","version":2}},"canonical_sha256":"c7a76afb30da86972b70ab0c2adc2ad585c0c2a03efb860da3e19ac0b0bacea7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c7a76afb30da86972b70ab0c2adc2ad585c0c2a03efb860da3e19ac0b0bacea7","first_computed_at":"2026-05-18T00:30:09.879728Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:30:09.879728Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"9zfzmRENoRPmqDJ+8g6y/BNZ+/UN9zQoNxPUW24l2CtrbF1M5VSQX7EhNjo9OvRbpLBGTxoeNS/xK/gbnXSOAg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:30:09.880283Z","signed_message":"canonical_sha256_bytes"},"source_id":"1210.2218","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:995cf2376343646a49938e4cf575534ee7b5b408f89336185ffec69df26dab4d","sha256:ead66899a1f1fbaf042f20fa9ff3a5487b8e95968230d90a64032fd0cfede99f"],"state_sha256":"c80f6ac544c5f88c6d946191b054f45a9f3bcb2bf2a883e3dbbcef68f6984405"}