{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:W4P2ADL26MYDRP5ZK53423J5YQ","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":"abe584ae7c3dbab91890b6bd8cf10a1a93afd00d3763c532e8fa6ef0a33c04e6","cross_cats_sorted":["math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2019-04-25T08:47:58Z","title_canon_sha256":"3ef0a7c706f56520ebc9cc84337b1ffee4cb32a358d8e8a9c6685df19c5b13d5"},"schema_version":"1.0","source":{"id":"1904.11213","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1904.11213","created_at":"2026-05-17T23:46:40Z"},{"alias_kind":"arxiv_version","alias_value":"1904.11213v2","created_at":"2026-05-17T23:46:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1904.11213","created_at":"2026-05-17T23:46:40Z"},{"alias_kind":"pith_short_12","alias_value":"W4P2ADL26MYD","created_at":"2026-05-18T12:33:30Z"},{"alias_kind":"pith_short_16","alias_value":"W4P2ADL26MYDRP5Z","created_at":"2026-05-18T12:33:30Z"},{"alias_kind":"pith_short_8","alias_value":"W4P2ADL2","created_at":"2026-05-18T12:33:30Z"}],"graph_snapshots":[{"event_id":"sha256:fd5251e88682726c27e8a7339eb53bc63baf1ec879c454dd53acc5ac1eb7c6e7","target":"graph","created_at":"2026-05-17T23:46:40Z","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":"We revisit the problem of maximising the expected length of increasing subsequence that can be selected from a marked Poisson process by an online strategy. Resorting to a natural size variable, the problem is represented in terms of a controlled partially deterministic Markov process with decreasing paths. Refining known estimates we obtain fairly complete asymptotic expansions for the moments, and using a renewal approximation give a novel proof of the central limit theorem for the length of selected subsequence under the optimal strategy.","authors_text":"Alexander Gnedin, Amirlan Seksenbayev","cross_cats":["math.OC"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2019-04-25T08:47:58Z","title":"Asymptotics and Renewal Approximation in the Online Selection of Increasing Subsequence"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.11213","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:e7d9866f2f6ee5ec2f30e335759797033e9345d03cdb9e7b4e1292b2e5ac7908","target":"record","created_at":"2026-05-17T23:46:40Z","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":"abe584ae7c3dbab91890b6bd8cf10a1a93afd00d3763c532e8fa6ef0a33c04e6","cross_cats_sorted":["math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2019-04-25T08:47:58Z","title_canon_sha256":"3ef0a7c706f56520ebc9cc84337b1ffee4cb32a358d8e8a9c6685df19c5b13d5"},"schema_version":"1.0","source":{"id":"1904.11213","kind":"arxiv","version":2}},"canonical_sha256":"b71fa00d7af33038bfb95777cd6d3dc40de86aa3471c56e6a1acd4729206dd99","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b71fa00d7af33038bfb95777cd6d3dc40de86aa3471c56e6a1acd4729206dd99","first_computed_at":"2026-05-17T23:46:40.770993Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:46:40.770993Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"kuqEN/XIPJeJHzyOYVFXoAYBZsqtQp6wjzXUNSqMBQlwg/pCIV2DShw6Jdry21nbvdfsUGiGE+5GS1TKCdptCg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:46:40.771765Z","signed_message":"canonical_sha256_bytes"},"source_id":"1904.11213","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e7d9866f2f6ee5ec2f30e335759797033e9345d03cdb9e7b4e1292b2e5ac7908","sha256:fd5251e88682726c27e8a7339eb53bc63baf1ec879c454dd53acc5ac1eb7c6e7"],"state_sha256":"e62515bdd95d6cb9cd916e5649facda987c0be97370409e463579bb951b5bfcb"}