{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:4AUNDOPY2AZAUEHIV7NLAAPGWY","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":"83f7197f04f72b63d9832126273deb48605d874222e564b13563b818d8efee1d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-10-03T16:16:52Z","title_canon_sha256":"7498ddc5dbfe8cd5f5c6a511d0540a6a4e8baeb01affba8b4cbd61d549765a29"},"schema_version":"1.0","source":{"id":"1510.00843","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1510.00843","created_at":"2026-05-18T01:31:05Z"},{"alias_kind":"arxiv_version","alias_value":"1510.00843v1","created_at":"2026-05-18T01:31:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1510.00843","created_at":"2026-05-18T01:31:05Z"},{"alias_kind":"pith_short_12","alias_value":"4AUNDOPY2AZA","created_at":"2026-05-18T12:29:05Z"},{"alias_kind":"pith_short_16","alias_value":"4AUNDOPY2AZAUEHI","created_at":"2026-05-18T12:29:05Z"},{"alias_kind":"pith_short_8","alias_value":"4AUNDOPY","created_at":"2026-05-18T12:29:05Z"}],"graph_snapshots":[{"event_id":"sha256:7ce84b947a7af4f46569ef3e0df713bd0c8da049d3ac8994bb8dd66b700c9d27","target":"graph","created_at":"2026-05-18T01:31:05Z","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":"The Bruss-Robertson inequality gives a bound on the maximal number of elements of a random sample whose sum is less than a specified value, and the extension of that inequality which is given here neither requires the independence of the summands nor requires the equality of their marginal distributions. A review is also given of the applications of the Bruss-Robertson inequality, especially the applications to problems of combinatorial optimization such as the sequential knapsack problem and the sequential monotone subsequence selection problem.","authors_text":"J. Michael Steele","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-10-03T16:16:52Z","title":"The Bruss-Robertson Inequality: Elaborations, Extensions, and Applications"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.00843","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":"sha256:041e6bea78c8c833613539ffcfe5b695fdc368aa2d2d9abe32ba6b6e3113c37e","target":"record","created_at":"2026-05-18T01:31:05Z","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":"83f7197f04f72b63d9832126273deb48605d874222e564b13563b818d8efee1d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-10-03T16:16:52Z","title_canon_sha256":"7498ddc5dbfe8cd5f5c6a511d0540a6a4e8baeb01affba8b4cbd61d549765a29"},"schema_version":"1.0","source":{"id":"1510.00843","kind":"arxiv","version":1}},"canonical_sha256":"e028d1b9f8d0320a10e8afdab001e6b61419007b50f778cd6862087345dc8bc0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e028d1b9f8d0320a10e8afdab001e6b61419007b50f778cd6862087345dc8bc0","first_computed_at":"2026-05-18T01:31:05.490620Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:31:05.490620Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"5QpIY2h9JaoG2mnQ+pCSc5js1NNRdqmgdcLD/6hAJRWmjXi2HeNpxOQv3T/sjXDXwamtjZ41EHIUFtEPIVQWCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:31:05.491360Z","signed_message":"canonical_sha256_bytes"},"source_id":"1510.00843","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:041e6bea78c8c833613539ffcfe5b695fdc368aa2d2d9abe32ba6b6e3113c37e","sha256:7ce84b947a7af4f46569ef3e0df713bd0c8da049d3ac8994bb8dd66b700c9d27"],"state_sha256":"4f876c606b17ff06cd7f7f60c0e54617ed38f8a170c311bd7c406e8e1d6e2d55"}