{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:KM2NCJO4W4ZXTSAHJ3VCDLTJGQ","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":"bf60ad2d1710fec7cd0ab3511932f712a52841cc461a7e8d9e0e6928e9bfbd87","cross_cats_sorted":["math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2018-12-10T21:46:46Z","title_canon_sha256":"12cee814e69356dd2d01aea137d0feb053697732e020f0f0aa425a49cf4c8ebb"},"schema_version":"1.0","source":{"id":"1812.04112","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1812.04112","created_at":"2026-05-17T23:49:22Z"},{"alias_kind":"arxiv_version","alias_value":"1812.04112v2","created_at":"2026-05-17T23:49:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1812.04112","created_at":"2026-05-17T23:49:22Z"},{"alias_kind":"pith_short_12","alias_value":"KM2NCJO4W4ZX","created_at":"2026-05-18T12:32:33Z"},{"alias_kind":"pith_short_16","alias_value":"KM2NCJO4W4ZXTSAH","created_at":"2026-05-18T12:32:33Z"},{"alias_kind":"pith_short_8","alias_value":"KM2NCJO4","created_at":"2026-05-18T12:32:33Z"}],"graph_snapshots":[{"event_id":"sha256:0de9f08c62f745087d8f1f6be7d80a8cd5aded092fd174eaedb8835e3f221b98","target":"graph","created_at":"2026-05-17T23:49:22Z","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":"This paper proves the existence of optimal stopping times via elementary functional analytic arguments. The problem is first relaxed into a convex optimization problem over a closed convex subset of the unit ball of the dual of a Banach space. The existence of optimal solutions then follows from the Banach--Alaoglu compactness theorem and the Krein--Millman theorem on extreme points of convex sets. This approach seems to give the most general existence results known to date. Applying convex duality to the relaxed problem gives a dual problem and optimality conditions in terms of martingales th","authors_text":"Ari-Pekka Perkki\\\"o, Teemu Pennanen","cross_cats":["math.PR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2018-12-10T21:46:46Z","title":"Optimal stopping without Snell envelopes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.04112","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":"sha256:0f37c0fe87a112698319fdb6222170fbd22ed9dbac8e5f5af486a9e2480de32e","target":"record","created_at":"2026-05-17T23:49:22Z","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":"bf60ad2d1710fec7cd0ab3511932f712a52841cc461a7e8d9e0e6928e9bfbd87","cross_cats_sorted":["math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2018-12-10T21:46:46Z","title_canon_sha256":"12cee814e69356dd2d01aea137d0feb053697732e020f0f0aa425a49cf4c8ebb"},"schema_version":"1.0","source":{"id":"1812.04112","kind":"arxiv","version":2}},"canonical_sha256":"5334d125dcb73379c8074eea21ae693411374f038c417bd614661e54637fcfe6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5334d125dcb73379c8074eea21ae693411374f038c417bd614661e54637fcfe6","first_computed_at":"2026-05-17T23:49:22.022926Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:49:22.022926Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"YeCGemq3qeEUypM1lHGUX+GyMT2EONcUI/vnh/2ztqbmSAcb7BWR92o7jkmzKvndhbMawXd+T64G/Cf9Vw8uDQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:49:22.023349Z","signed_message":"canonical_sha256_bytes"},"source_id":"1812.04112","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0f37c0fe87a112698319fdb6222170fbd22ed9dbac8e5f5af486a9e2480de32e","sha256:0de9f08c62f745087d8f1f6be7d80a8cd5aded092fd174eaedb8835e3f221b98"],"state_sha256":"3d22777d610d2120e3edc6e866fc6e4a5be236a8b15180c569bf030112a0a345"}