{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:ONMAVVM2CZCG23SUGHQNPAQ65C","short_pith_number":"pith:ONMAVVM2","canonical_record":{"source":{"id":"1611.00665","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2016-11-02T16:09:26Z","cross_cats_sorted":[],"title_canon_sha256":"d7488f240b82be0a418cc819aa8257ffdfb803a3844e637f3d3b3174875e6bfb","abstract_canon_sha256":"4ac19badc16026d197941501d5db2c782896f061cddbe295b02d717b3c8e0086"},"schema_version":"1.0"},"canonical_sha256":"73580ad59a16446d6e5431e0d7821ee8887d3ffd3a5df34696021a8b0ee019c7","source":{"kind":"arxiv","id":"1611.00665","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1611.00665","created_at":"2026-05-18T01:00:32Z"},{"alias_kind":"arxiv_version","alias_value":"1611.00665v1","created_at":"2026-05-18T01:00:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1611.00665","created_at":"2026-05-18T01:00:32Z"},{"alias_kind":"pith_short_12","alias_value":"ONMAVVM2CZCG","created_at":"2026-05-18T12:30:36Z"},{"alias_kind":"pith_short_16","alias_value":"ONMAVVM2CZCG23SU","created_at":"2026-05-18T12:30:36Z"},{"alias_kind":"pith_short_8","alias_value":"ONMAVVM2","created_at":"2026-05-18T12:30:36Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:ONMAVVM2CZCG23SUGHQNPAQ65C","target":"record","payload":{"canonical_record":{"source":{"id":"1611.00665","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2016-11-02T16:09:26Z","cross_cats_sorted":[],"title_canon_sha256":"d7488f240b82be0a418cc819aa8257ffdfb803a3844e637f3d3b3174875e6bfb","abstract_canon_sha256":"4ac19badc16026d197941501d5db2c782896f061cddbe295b02d717b3c8e0086"},"schema_version":"1.0"},"canonical_sha256":"73580ad59a16446d6e5431e0d7821ee8887d3ffd3a5df34696021a8b0ee019c7","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:00:32.180894Z","signature_b64":"2nTrmT5e4B5TwfFUoguvjBkWYKFpL/f2Gus7zq/VVXCwYm64hcbjpYakkK+M8EdDnqPqvfbqGjkOw5vdJiy4Dw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"73580ad59a16446d6e5431e0d7821ee8887d3ffd3a5df34696021a8b0ee019c7","last_reissued_at":"2026-05-18T01:00:32.180242Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:00:32.180242Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1611.00665","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:00:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"R2vpJ8lw5NMa8k5aS1kdlOUbnau4bhfiPHEjCXzo7/7RCypdfPrKuW/un0imX3KHJ5/byrFbtDvKxJ1yPVX7Ag==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T21:09:48.211248Z"},"content_sha256":"6eb34dd58229c83a5b0074dc5580e76d7098e7676e38ccc328ae5c2d0a6df8ee","schema_version":"1.0","event_id":"sha256:6eb34dd58229c83a5b0074dc5580e76d7098e7676e38ccc328ae5c2d0a6df8ee"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:ONMAVVM2CZCG23SUGHQNPAQ65C","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Combinatorial Prophet Inequalities","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Aviad Rubinstein, Sahil Singla","submitted_at":"2016-11-02T16:09:26Z","abstract_excerpt":"We introduce a novel framework of Prophet Inequalities for combinatorial valuation functions. For a (non-monotone) submodular objective function over an arbitrary matroid feasibility constraint, we give an $O(1)$-competitive algorithm. For a monotone subadditive objective function over an arbitrary downward-closed feasibility constraint, we give an $O(\\log n \\log^2 r)$-competitive algorithm (where $r$ is the cardinality of the largest feasible subset).\n  Inspired by the proof of our subadditive prophet inequality, we also obtain an $O(\\log n \\cdot \\log^2 r)$-competitive algorithm for the Secre"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.00665","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:00:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XOIeZsO6I2M6xH36KUhWL9yfQ4F/7N/loT8AF1mcp2554Ci3SpeiGL7nC2/CXBNYc340FINDD8Li+05N3m8KBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T21:09:48.211619Z"},"content_sha256":"e46fcb88ab8e3dc51d337834cdb36c785330e935d97d2052650a5ae10487457f","schema_version":"1.0","event_id":"sha256:e46fcb88ab8e3dc51d337834cdb36c785330e935d97d2052650a5ae10487457f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ONMAVVM2CZCG23SUGHQNPAQ65C/bundle.json","state_url":"https://pith.science/pith/ONMAVVM2CZCG23SUGHQNPAQ65C/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ONMAVVM2CZCG23SUGHQNPAQ65C/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-10T21:09:48Z","links":{"resolver":"https://pith.science/pith/ONMAVVM2CZCG23SUGHQNPAQ65C","bundle":"https://pith.science/pith/ONMAVVM2CZCG23SUGHQNPAQ65C/bundle.json","state":"https://pith.science/pith/ONMAVVM2CZCG23SUGHQNPAQ65C/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ONMAVVM2CZCG23SUGHQNPAQ65C/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:ONMAVVM2CZCG23SUGHQNPAQ65C","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":"4ac19badc16026d197941501d5db2c782896f061cddbe295b02d717b3c8e0086","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2016-11-02T16:09:26Z","title_canon_sha256":"d7488f240b82be0a418cc819aa8257ffdfb803a3844e637f3d3b3174875e6bfb"},"schema_version":"1.0","source":{"id":"1611.00665","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1611.00665","created_at":"2026-05-18T01:00:32Z"},{"alias_kind":"arxiv_version","alias_value":"1611.00665v1","created_at":"2026-05-18T01:00:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1611.00665","created_at":"2026-05-18T01:00:32Z"},{"alias_kind":"pith_short_12","alias_value":"ONMAVVM2CZCG","created_at":"2026-05-18T12:30:36Z"},{"alias_kind":"pith_short_16","alias_value":"ONMAVVM2CZCG23SU","created_at":"2026-05-18T12:30:36Z"},{"alias_kind":"pith_short_8","alias_value":"ONMAVVM2","created_at":"2026-05-18T12:30:36Z"}],"graph_snapshots":[{"event_id":"sha256:e46fcb88ab8e3dc51d337834cdb36c785330e935d97d2052650a5ae10487457f","target":"graph","created_at":"2026-05-18T01:00:32Z","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 introduce a novel framework of Prophet Inequalities for combinatorial valuation functions. For a (non-monotone) submodular objective function over an arbitrary matroid feasibility constraint, we give an $O(1)$-competitive algorithm. For a monotone subadditive objective function over an arbitrary downward-closed feasibility constraint, we give an $O(\\log n \\log^2 r)$-competitive algorithm (where $r$ is the cardinality of the largest feasible subset).\n  Inspired by the proof of our subadditive prophet inequality, we also obtain an $O(\\log n \\cdot \\log^2 r)$-competitive algorithm for the Secre","authors_text":"Aviad Rubinstein, Sahil Singla","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2016-11-02T16:09:26Z","title":"Combinatorial Prophet Inequalities"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.00665","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":"sha256:6eb34dd58229c83a5b0074dc5580e76d7098e7676e38ccc328ae5c2d0a6df8ee","target":"record","created_at":"2026-05-18T01:00:32Z","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":"4ac19badc16026d197941501d5db2c782896f061cddbe295b02d717b3c8e0086","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2016-11-02T16:09:26Z","title_canon_sha256":"d7488f240b82be0a418cc819aa8257ffdfb803a3844e637f3d3b3174875e6bfb"},"schema_version":"1.0","source":{"id":"1611.00665","kind":"arxiv","version":1}},"canonical_sha256":"73580ad59a16446d6e5431e0d7821ee8887d3ffd3a5df34696021a8b0ee019c7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"73580ad59a16446d6e5431e0d7821ee8887d3ffd3a5df34696021a8b0ee019c7","first_computed_at":"2026-05-18T01:00:32.180242Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:00:32.180242Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"2nTrmT5e4B5TwfFUoguvjBkWYKFpL/f2Gus7zq/VVXCwYm64hcbjpYakkK+M8EdDnqPqvfbqGjkOw5vdJiy4Dw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:00:32.180894Z","signed_message":"canonical_sha256_bytes"},"source_id":"1611.00665","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6eb34dd58229c83a5b0074dc5580e76d7098e7676e38ccc328ae5c2d0a6df8ee","sha256:e46fcb88ab8e3dc51d337834cdb36c785330e935d97d2052650a5ae10487457f"],"state_sha256":"f13a7dcf70f366a47ac408076814ca48d77fb22888048d82eed32d7f9688fcd6"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TB8OiDSWU+hOJpRtdGrdBafiwlShY4RB11SAoSdFnMkiRYc8IKPA6EwXuNzK+fsb8jgVnpVnPLLEYvczNyEUBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-10T21:09:48.213704Z","bundle_sha256":"b9672826e8bb0a30c1a92f1207bd661ad0efe07645dbc58d3910368c2bf73dc7"}}