{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:MXPKVJIVQDY7GRGF4TUBEOH6G2","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":"17e4e009dacf2f06308839f28ca57119db9769165b4c4c58814da2883c04a3d0","cross_cats_sorted":["math.ST","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-07-16T17:19:06Z","title_canon_sha256":"1b874fe4614001641971179dc9d2eb0c3cac937ed9dcdec161302a674c5ac76c"},"schema_version":"1.0","source":{"id":"1207.3733","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1207.3733","created_at":"2026-05-18T03:49:46Z"},{"alias_kind":"arxiv_version","alias_value":"1207.3733v2","created_at":"2026-05-18T03:49:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1207.3733","created_at":"2026-05-18T03:49:46Z"},{"alias_kind":"pith_short_12","alias_value":"MXPKVJIVQDY7","created_at":"2026-05-18T12:27:14Z"},{"alias_kind":"pith_short_16","alias_value":"MXPKVJIVQDY7GRGF","created_at":"2026-05-18T12:27:14Z"},{"alias_kind":"pith_short_8","alias_value":"MXPKVJIV","created_at":"2026-05-18T12:27:14Z"}],"graph_snapshots":[{"event_id":"sha256:4158ed85da1c222de2d998f74507bb0985aecd635df9435061c91df1d198f242","target":"graph","created_at":"2026-05-18T03:49:46Z","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 develop new optional stopping theorems for scenarios where the stopping rules are defined by bounded continuity regions. Moreover, we establish a wide variety of inequalities on the supremums and infimums of functions of stochastic processes over the whole range of time indexes.","authors_text":"Xinjia Chen","cross_cats":["math.ST","stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-07-16T17:19:06Z","title":"New Optional Stopping Theorems and Maximal Inequalities on Stochastic Processes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1207.3733","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:d4bf19a8823a7b1c6e0938f42087557bd5c371ffd28f1dc8f2b16e34248cec99","target":"record","created_at":"2026-05-18T03:49:46Z","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":"17e4e009dacf2f06308839f28ca57119db9769165b4c4c58814da2883c04a3d0","cross_cats_sorted":["math.ST","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-07-16T17:19:06Z","title_canon_sha256":"1b874fe4614001641971179dc9d2eb0c3cac937ed9dcdec161302a674c5ac76c"},"schema_version":"1.0","source":{"id":"1207.3733","kind":"arxiv","version":2}},"canonical_sha256":"65deaaa51580f1f344c5e4e81238fe369c008b07ad512522bf96c76acfe35638","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"65deaaa51580f1f344c5e4e81238fe369c008b07ad512522bf96c76acfe35638","first_computed_at":"2026-05-18T03:49:46.927561Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:49:46.927561Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Fjart9tt6FW1xgY3/RODl/BhZv1K5rwt91KsEXEAY9P0YIMMWdMuOpMoGRouAwrThU3iK81b5hInhjPnFeGnBA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:49:46.928124Z","signed_message":"canonical_sha256_bytes"},"source_id":"1207.3733","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d4bf19a8823a7b1c6e0938f42087557bd5c371ffd28f1dc8f2b16e34248cec99","sha256:4158ed85da1c222de2d998f74507bb0985aecd635df9435061c91df1d198f242"],"state_sha256":"4916c9cd46aa1b1f23444ed6613d949479d1a8bbdb24db8d39a20977fee70edd"}