{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:M6NKCZO3HBWU4CS5SEFHS3QDIR","short_pith_number":"pith:M6NKCZO3","canonical_record":{"source":{"id":"1807.05532","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2018-07-15T11:57:00Z","cross_cats_sorted":[],"title_canon_sha256":"5ed379ce696d811abcdf75ea1f65df2d26876942a0a751f31cff7c30e8f61bbc","abstract_canon_sha256":"c4a456c0d076cc0c000eb52b63fcbb1d22bd6d5752eeb2bc1296068b49b55323"},"schema_version":"1.0"},"canonical_sha256":"679aa165db386d4e0a5d910a796e03446fdad3a0399a47319724089933cd2768","source":{"kind":"arxiv","id":"1807.05532","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1807.05532","created_at":"2026-05-18T00:10:43Z"},{"alias_kind":"arxiv_version","alias_value":"1807.05532v1","created_at":"2026-05-18T00:10:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1807.05532","created_at":"2026-05-18T00:10:43Z"},{"alias_kind":"pith_short_12","alias_value":"M6NKCZO3HBWU","created_at":"2026-05-18T12:32:37Z"},{"alias_kind":"pith_short_16","alias_value":"M6NKCZO3HBWU4CS5","created_at":"2026-05-18T12:32:37Z"},{"alias_kind":"pith_short_8","alias_value":"M6NKCZO3","created_at":"2026-05-18T12:32:37Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:M6NKCZO3HBWU4CS5SEFHS3QDIR","target":"record","payload":{"canonical_record":{"source":{"id":"1807.05532","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2018-07-15T11:57:00Z","cross_cats_sorted":[],"title_canon_sha256":"5ed379ce696d811abcdf75ea1f65df2d26876942a0a751f31cff7c30e8f61bbc","abstract_canon_sha256":"c4a456c0d076cc0c000eb52b63fcbb1d22bd6d5752eeb2bc1296068b49b55323"},"schema_version":"1.0"},"canonical_sha256":"679aa165db386d4e0a5d910a796e03446fdad3a0399a47319724089933cd2768","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:10:43.291445Z","signature_b64":"R7oczrDglJ5IfU++xiBwlUazAg8Toyg6AjPo5Zg+aA8ZkQMPUsOj0gBL1oLyB/gi0Mzo1DjDUVlxUjUmX2ZZDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"679aa165db386d4e0a5d910a796e03446fdad3a0399a47319724089933cd2768","last_reissued_at":"2026-05-18T00:10:43.290841Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:10:43.290841Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1807.05532","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":"2026-05-18T00:10:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7GK3VbbcmvtU74/8tsn9YjlWnZ5I3+4vLeXIf88KP/OY7YN+FgJhlWn1T38YttvOC9m6MUXBfbTEJzSCkNEbDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T22:16:14.179983Z"},"content_sha256":"4c872f43f4b20c02a18ed5b88cf3ff99d8da34ce386589b7c91c2e57580c0cc3","schema_version":"1.0","event_id":"sha256:4c872f43f4b20c02a18ed5b88cf3ff99d8da34ce386589b7c91c2e57580c0cc3"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:M6NKCZO3HBWU4CS5SEFHS3QDIR","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Deterministic (1/2 + {\\epsilon})-Approximation for Submodular Maximization over a Matroid","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Mohit Garg, Moran Feldman, Niv Buchbinder","submitted_at":"2018-07-15T11:57:00Z","abstract_excerpt":"We study the problem of maximizing a monotone submodular function subject to a matroid constraint and present a deterministic algorithm that achieves (1/2 + {\\epsilon})-approximation for the problem. This algorithm is the first deterministic algorithm known to improve over the 1/2-approximation ratio of the classical greedy algorithm proved by Nemhauser, Wolsely and Fisher in 1978."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.05532","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":"2026-05-18T00:10:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9192d8yb/D9aK5ym/Mm29zKuGe4rI2vxhJF58da/hp5EX7weZ0ZUdqoPCVqL16+/gbfoVmPy2KtuGe45dAS0AQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T22:16:14.180654Z"},"content_sha256":"115d21f8e7e5303c12ba55da19957f075b3c9559e74a4fd3e78a982f84634d0b","schema_version":"1.0","event_id":"sha256:115d21f8e7e5303c12ba55da19957f075b3c9559e74a4fd3e78a982f84634d0b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/M6NKCZO3HBWU4CS5SEFHS3QDIR/bundle.json","state_url":"https://pith.science/pith/M6NKCZO3HBWU4CS5SEFHS3QDIR/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/M6NKCZO3HBWU4CS5SEFHS3QDIR/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":"2026-05-27T22:16:14Z","links":{"resolver":"https://pith.science/pith/M6NKCZO3HBWU4CS5SEFHS3QDIR","bundle":"https://pith.science/pith/M6NKCZO3HBWU4CS5SEFHS3QDIR/bundle.json","state":"https://pith.science/pith/M6NKCZO3HBWU4CS5SEFHS3QDIR/state.json","well_known_bundle":"https://pith.science/.well-known/pith/M6NKCZO3HBWU4CS5SEFHS3QDIR/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:M6NKCZO3HBWU4CS5SEFHS3QDIR","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":"c4a456c0d076cc0c000eb52b63fcbb1d22bd6d5752eeb2bc1296068b49b55323","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2018-07-15T11:57:00Z","title_canon_sha256":"5ed379ce696d811abcdf75ea1f65df2d26876942a0a751f31cff7c30e8f61bbc"},"schema_version":"1.0","source":{"id":"1807.05532","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1807.05532","created_at":"2026-05-18T00:10:43Z"},{"alias_kind":"arxiv_version","alias_value":"1807.05532v1","created_at":"2026-05-18T00:10:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1807.05532","created_at":"2026-05-18T00:10:43Z"},{"alias_kind":"pith_short_12","alias_value":"M6NKCZO3HBWU","created_at":"2026-05-18T12:32:37Z"},{"alias_kind":"pith_short_16","alias_value":"M6NKCZO3HBWU4CS5","created_at":"2026-05-18T12:32:37Z"},{"alias_kind":"pith_short_8","alias_value":"M6NKCZO3","created_at":"2026-05-18T12:32:37Z"}],"graph_snapshots":[{"event_id":"sha256:115d21f8e7e5303c12ba55da19957f075b3c9559e74a4fd3e78a982f84634d0b","target":"graph","created_at":"2026-05-18T00:10:43Z","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 study the problem of maximizing a monotone submodular function subject to a matroid constraint and present a deterministic algorithm that achieves (1/2 + {\\epsilon})-approximation for the problem. This algorithm is the first deterministic algorithm known to improve over the 1/2-approximation ratio of the classical greedy algorithm proved by Nemhauser, Wolsely and Fisher in 1978.","authors_text":"Mohit Garg, Moran Feldman, Niv Buchbinder","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2018-07-15T11:57:00Z","title":"Deterministic (1/2 + {\\epsilon})-Approximation for Submodular Maximization over a Matroid"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.05532","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":"sha256:4c872f43f4b20c02a18ed5b88cf3ff99d8da34ce386589b7c91c2e57580c0cc3","target":"record","created_at":"2026-05-18T00:10:43Z","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":"c4a456c0d076cc0c000eb52b63fcbb1d22bd6d5752eeb2bc1296068b49b55323","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2018-07-15T11:57:00Z","title_canon_sha256":"5ed379ce696d811abcdf75ea1f65df2d26876942a0a751f31cff7c30e8f61bbc"},"schema_version":"1.0","source":{"id":"1807.05532","kind":"arxiv","version":1}},"canonical_sha256":"679aa165db386d4e0a5d910a796e03446fdad3a0399a47319724089933cd2768","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"679aa165db386d4e0a5d910a796e03446fdad3a0399a47319724089933cd2768","first_computed_at":"2026-05-18T00:10:43.290841Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:10:43.290841Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"R7oczrDglJ5IfU++xiBwlUazAg8Toyg6AjPo5Zg+aA8ZkQMPUsOj0gBL1oLyB/gi0Mzo1DjDUVlxUjUmX2ZZDA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:10:43.291445Z","signed_message":"canonical_sha256_bytes"},"source_id":"1807.05532","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4c872f43f4b20c02a18ed5b88cf3ff99d8da34ce386589b7c91c2e57580c0cc3","sha256:115d21f8e7e5303c12ba55da19957f075b3c9559e74a4fd3e78a982f84634d0b"],"state_sha256":"bf6930fd631a9aaf2b515fcc1dbc89ecdf3132ae0d64227fc07076e5dd7c6802"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dVHefz30/ZJyAaHCH3Akvklh7FNds6adLSJu1JXs1JHCrBqW2tMstbISixalf9F+Xe/5DmWA96e5sVxiKhf9Ag==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T22:16:14.184465Z","bundle_sha256":"08cd001e9c459981a8d188cc8f87ab3cdc5a79a00306e57ecd0a952b26877c0b"}}