{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:TNSHXYDJPAHWW4GFS3GWW5T2S3","short_pith_number":"pith:TNSHXYDJ","canonical_record":{"source":{"id":"1511.07642","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2015-11-24T10:53:03Z","cross_cats_sorted":[],"title_canon_sha256":"362ba53008a72f9ce5fc1ffd41675f438f8e4f926d1346c655b16ab9c67182b9","abstract_canon_sha256":"22fa88f03b39e1dcc4d5647b33fa533222a907080345df3e8bec5c6bf01b1cad"},"schema_version":"1.0"},"canonical_sha256":"9b647be069780f6b70c596cd6b767a96cb1496ebf5974d800c1a2700f1e22435","source":{"kind":"arxiv","id":"1511.07642","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1511.07642","created_at":"2026-05-18T01:26:02Z"},{"alias_kind":"arxiv_version","alias_value":"1511.07642v2","created_at":"2026-05-18T01:26:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1511.07642","created_at":"2026-05-18T01:26:02Z"},{"alias_kind":"pith_short_12","alias_value":"TNSHXYDJPAHW","created_at":"2026-05-18T12:29:42Z"},{"alias_kind":"pith_short_16","alias_value":"TNSHXYDJPAHWW4GF","created_at":"2026-05-18T12:29:42Z"},{"alias_kind":"pith_short_8","alias_value":"TNSHXYDJ","created_at":"2026-05-18T12:29:42Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:TNSHXYDJPAHWW4GFS3GWW5T2S3","target":"record","payload":{"canonical_record":{"source":{"id":"1511.07642","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2015-11-24T10:53:03Z","cross_cats_sorted":[],"title_canon_sha256":"362ba53008a72f9ce5fc1ffd41675f438f8e4f926d1346c655b16ab9c67182b9","abstract_canon_sha256":"22fa88f03b39e1dcc4d5647b33fa533222a907080345df3e8bec5c6bf01b1cad"},"schema_version":"1.0"},"canonical_sha256":"9b647be069780f6b70c596cd6b767a96cb1496ebf5974d800c1a2700f1e22435","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:26:02.348423Z","signature_b64":"RS5AI6KY5qZDsYINDGoqW0c0d0QddPRp3Y/sE3j+cEG67t/e8Nrrsr6X+DurxtLd4HpHk7G6gcP7QqPY0Z81CQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9b647be069780f6b70c596cd6b767a96cb1496ebf5974d800c1a2700f1e22435","last_reissued_at":"2026-05-18T01:26:02.347982Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:26:02.347982Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1511.07642","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:26:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"AlR1G+QY3khXC53fuS9ToRh6I0oQettgmKG7OugIv4UfuMspdYMdPav4e3LvPnJpO5sUMXvd7Xs/Y0tFfN14Ag==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T11:45:31.302768Z"},"content_sha256":"7e29bc256a5c7e1337ccf5344554ce4633e94801f207b8273cf9d54cd4de0dab","schema_version":"1.0","event_id":"sha256:7e29bc256a5c7e1337ccf5344554ce4633e94801f207b8273cf9d54cd4de0dab"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:TNSHXYDJPAHWW4GFS3GWW5T2S3","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Multivariate Complexity Analysis of Geometric {\\sc Red Blue Set Cover}","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Pradeesha Ashok, Saket Saurabh, Sudeshna Kolay","submitted_at":"2015-11-24T10:53:03Z","abstract_excerpt":"We investigate the parameterized complexity of GENERALIZED RED BLUE SET COVER (Gen-RBSC), a generalization of the classic SET COVER problem and the more recently studied RED BLUE SET COVER problem. Given a universe $U$ containing $b$ blue elements and $r$ red elements, positive integers $k_\\ell$ and $k_r$, and a family $\\F$ of $\\ell$ sets over $U$, the \\srbsc\\ problem is to decide whether there is a subfamily $\\F'\\subseteq \\F$ of size at most $k_\\ell$ that covers all blue elements, but at most $k_r$ of the red elements. This generalizes SET COVER and thus in full generality it is intractable i"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.07642","kind":"arxiv","version":2},"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":"2026-05-18T01:26:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0L/7zvZiJhA2rllxCOzwT/2ByuuNxv8aIe8DOaronfdgKopF9LFhzUIsyNMWEp9REZidk8AypbQgjzJ5BWwdAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T11:45:31.303106Z"},"content_sha256":"246f5579c66fb7bb12eb59646eecae9b058c0861a31ee5e4647315fdc659c82e","schema_version":"1.0","event_id":"sha256:246f5579c66fb7bb12eb59646eecae9b058c0861a31ee5e4647315fdc659c82e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/TNSHXYDJPAHWW4GFS3GWW5T2S3/bundle.json","state_url":"https://pith.science/pith/TNSHXYDJPAHWW4GFS3GWW5T2S3/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/TNSHXYDJPAHWW4GFS3GWW5T2S3/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":"2026-06-22T11:45:31Z","links":{"resolver":"https://pith.science/pith/TNSHXYDJPAHWW4GFS3GWW5T2S3","bundle":"https://pith.science/pith/TNSHXYDJPAHWW4GFS3GWW5T2S3/bundle.json","state":"https://pith.science/pith/TNSHXYDJPAHWW4GFS3GWW5T2S3/state.json","well_known_bundle":"https://pith.science/.well-known/pith/TNSHXYDJPAHWW4GFS3GWW5T2S3/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:TNSHXYDJPAHWW4GFS3GWW5T2S3","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":"22fa88f03b39e1dcc4d5647b33fa533222a907080345df3e8bec5c6bf01b1cad","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2015-11-24T10:53:03Z","title_canon_sha256":"362ba53008a72f9ce5fc1ffd41675f438f8e4f926d1346c655b16ab9c67182b9"},"schema_version":"1.0","source":{"id":"1511.07642","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1511.07642","created_at":"2026-05-18T01:26:02Z"},{"alias_kind":"arxiv_version","alias_value":"1511.07642v2","created_at":"2026-05-18T01:26:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1511.07642","created_at":"2026-05-18T01:26:02Z"},{"alias_kind":"pith_short_12","alias_value":"TNSHXYDJPAHW","created_at":"2026-05-18T12:29:42Z"},{"alias_kind":"pith_short_16","alias_value":"TNSHXYDJPAHWW4GF","created_at":"2026-05-18T12:29:42Z"},{"alias_kind":"pith_short_8","alias_value":"TNSHXYDJ","created_at":"2026-05-18T12:29:42Z"}],"graph_snapshots":[{"event_id":"sha256:246f5579c66fb7bb12eb59646eecae9b058c0861a31ee5e4647315fdc659c82e","target":"graph","created_at":"2026-05-18T01:26:02Z","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 investigate the parameterized complexity of GENERALIZED RED BLUE SET COVER (Gen-RBSC), a generalization of the classic SET COVER problem and the more recently studied RED BLUE SET COVER problem. Given a universe $U$ containing $b$ blue elements and $r$ red elements, positive integers $k_\\ell$ and $k_r$, and a family $\\F$ of $\\ell$ sets over $U$, the \\srbsc\\ problem is to decide whether there is a subfamily $\\F'\\subseteq \\F$ of size at most $k_\\ell$ that covers all blue elements, but at most $k_r$ of the red elements. This generalizes SET COVER and thus in full generality it is intractable i","authors_text":"Pradeesha Ashok, Saket Saurabh, Sudeshna Kolay","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2015-11-24T10:53:03Z","title":"Multivariate Complexity Analysis of Geometric {\\sc Red Blue Set Cover}"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.07642","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":"sha256:7e29bc256a5c7e1337ccf5344554ce4633e94801f207b8273cf9d54cd4de0dab","target":"record","created_at":"2026-05-18T01:26:02Z","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":"22fa88f03b39e1dcc4d5647b33fa533222a907080345df3e8bec5c6bf01b1cad","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2015-11-24T10:53:03Z","title_canon_sha256":"362ba53008a72f9ce5fc1ffd41675f438f8e4f926d1346c655b16ab9c67182b9"},"schema_version":"1.0","source":{"id":"1511.07642","kind":"arxiv","version":2}},"canonical_sha256":"9b647be069780f6b70c596cd6b767a96cb1496ebf5974d800c1a2700f1e22435","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9b647be069780f6b70c596cd6b767a96cb1496ebf5974d800c1a2700f1e22435","first_computed_at":"2026-05-18T01:26:02.347982Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:26:02.347982Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"RS5AI6KY5qZDsYINDGoqW0c0d0QddPRp3Y/sE3j+cEG67t/e8Nrrsr6X+DurxtLd4HpHk7G6gcP7QqPY0Z81CQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:26:02.348423Z","signed_message":"canonical_sha256_bytes"},"source_id":"1511.07642","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7e29bc256a5c7e1337ccf5344554ce4633e94801f207b8273cf9d54cd4de0dab","sha256:246f5579c66fb7bb12eb59646eecae9b058c0861a31ee5e4647315fdc659c82e"],"state_sha256":"42a45ef2cefdc2a2b51f46c96d064dfbd55a6c80db9771d2a3bb1265b3640ccf"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Osa+8iRsmhME0XD/cFoG8ZtQTHGtmdjGuxnYRsDsxySQ1FYj/mOeNZYAzgljo5aoeH6YVsvyfD7AkEiwu2zICw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-22T11:45:31.305030Z","bundle_sha256":"9f0eafc89ab126ce2fa606a86f99cd7832ea72bf077cd2480efe250b7055d637"}}