{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:RWQLO7ZZ7SCSVQ5VOJORNRCTRK","short_pith_number":"pith:RWQLO7ZZ","canonical_record":{"source":{"id":"1404.5566","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2014-04-21T19:16:51Z","cross_cats_sorted":[],"title_canon_sha256":"db8399e714adda114fbd138f53e6ea58a5b2bb5de4a3a0c8178fcb3871af6ded","abstract_canon_sha256":"b5f517e2dc55e8fb0ad769ea4e0a67fbc2f94b42c47ab3b06a85443b6c1d0e4e"},"schema_version":"1.0"},"canonical_sha256":"8da0b77f39fc852ac3b5725d16c4538a99f8e3d2ef8d206ef4c53ba6b864a2a8","source":{"kind":"arxiv","id":"1404.5566","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1404.5566","created_at":"2026-05-18T02:53:28Z"},{"alias_kind":"arxiv_version","alias_value":"1404.5566v2","created_at":"2026-05-18T02:53:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1404.5566","created_at":"2026-05-18T02:53:28Z"},{"alias_kind":"pith_short_12","alias_value":"RWQLO7ZZ7SCS","created_at":"2026-05-18T12:28:46Z"},{"alias_kind":"pith_short_16","alias_value":"RWQLO7ZZ7SCSVQ5V","created_at":"2026-05-18T12:28:46Z"},{"alias_kind":"pith_short_8","alias_value":"RWQLO7ZZ","created_at":"2026-05-18T12:28:46Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:RWQLO7ZZ7SCSVQ5VOJORNRCTRK","target":"record","payload":{"canonical_record":{"source":{"id":"1404.5566","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2014-04-21T19:16:51Z","cross_cats_sorted":[],"title_canon_sha256":"db8399e714adda114fbd138f53e6ea58a5b2bb5de4a3a0c8178fcb3871af6ded","abstract_canon_sha256":"b5f517e2dc55e8fb0ad769ea4e0a67fbc2f94b42c47ab3b06a85443b6c1d0e4e"},"schema_version":"1.0"},"canonical_sha256":"8da0b77f39fc852ac3b5725d16c4538a99f8e3d2ef8d206ef4c53ba6b864a2a8","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:53:28.358791Z","signature_b64":"0Ym9c5Ll9UIYAoMVsdwoBOkV5e1m73bw1tCF+36hC/LNgAy5r6h99kjOy0O2px0XsYjQIJqgQGkNSlnwH6etAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8da0b77f39fc852ac3b5725d16c4538a99f8e3d2ef8d206ef4c53ba6b864a2a8","last_reissued_at":"2026-05-18T02:53:28.357992Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:53:28.357992Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1404.5566","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":"2026-05-18T02:53:28Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7t0RfHUfu2uT6IWGrdG1Tv8MwEtpY7bqTsIfcquL9pJZ606/tIfG3p/vzUVLxZMwDtGFgwtlaVPhHbGT3TfpDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T20:07:32.531368Z"},"content_sha256":"f997518766bdf099b4449e0226a2a2f6301bc1db235ecc6e4cda8281ce68ed32","schema_version":"1.0","event_id":"sha256:f997518766bdf099b4449e0226a2a2f6301bc1db235ecc6e4cda8281ce68ed32"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:RWQLO7ZZ7SCSVQ5VOJORNRCTRK","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Vertex Cover Gets Faster and Harder on Low Degree Graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Akanksha Agrawal, Neeldhara Misra, Sathish Govindarajan","submitted_at":"2014-04-21T19:16:51Z","abstract_excerpt":"The problem of finding an optimal vertex cover in a graph is a classic NP-complete problem, and is a special case of the hitting set question. On the other hand, the hitting set problem, when asked in the context of induced geometric objects, often turns out to be exactly the vertex cover problem on restricted classes of graphs. In this work we explore a particular instance of such a phenomenon. We consider the problem of hitting all axis-parallel slabs induced by a point set P, and show that it is equivalent to the problem of finding a vertex cover on a graph whose edge set is the union of tw"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.5566","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":"2026-05-18T02:53:28Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"EHLdiI/iiZqC9cw+GzuMdp/Ot4AxDeOHNx5coF2nCTBSedmup6h33ZiHr8XYYYz+aDL0XWeFAUEAeVkV7imJCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T20:07:32.531768Z"},"content_sha256":"d1521bc5d7cd6137a845d941c0ef57c8d778f330ef1426275d28648e44d5c836","schema_version":"1.0","event_id":"sha256:d1521bc5d7cd6137a845d941c0ef57c8d778f330ef1426275d28648e44d5c836"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/RWQLO7ZZ7SCSVQ5VOJORNRCTRK/bundle.json","state_url":"https://pith.science/pith/RWQLO7ZZ7SCSVQ5VOJORNRCTRK/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/RWQLO7ZZ7SCSVQ5VOJORNRCTRK/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":"2026-05-31T20:07:32Z","links":{"resolver":"https://pith.science/pith/RWQLO7ZZ7SCSVQ5VOJORNRCTRK","bundle":"https://pith.science/pith/RWQLO7ZZ7SCSVQ5VOJORNRCTRK/bundle.json","state":"https://pith.science/pith/RWQLO7ZZ7SCSVQ5VOJORNRCTRK/state.json","well_known_bundle":"https://pith.science/.well-known/pith/RWQLO7ZZ7SCSVQ5VOJORNRCTRK/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:RWQLO7ZZ7SCSVQ5VOJORNRCTRK","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":"b5f517e2dc55e8fb0ad769ea4e0a67fbc2f94b42c47ab3b06a85443b6c1d0e4e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2014-04-21T19:16:51Z","title_canon_sha256":"db8399e714adda114fbd138f53e6ea58a5b2bb5de4a3a0c8178fcb3871af6ded"},"schema_version":"1.0","source":{"id":"1404.5566","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1404.5566","created_at":"2026-05-18T02:53:28Z"},{"alias_kind":"arxiv_version","alias_value":"1404.5566v2","created_at":"2026-05-18T02:53:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1404.5566","created_at":"2026-05-18T02:53:28Z"},{"alias_kind":"pith_short_12","alias_value":"RWQLO7ZZ7SCS","created_at":"2026-05-18T12:28:46Z"},{"alias_kind":"pith_short_16","alias_value":"RWQLO7ZZ7SCSVQ5V","created_at":"2026-05-18T12:28:46Z"},{"alias_kind":"pith_short_8","alias_value":"RWQLO7ZZ","created_at":"2026-05-18T12:28:46Z"}],"graph_snapshots":[{"event_id":"sha256:d1521bc5d7cd6137a845d941c0ef57c8d778f330ef1426275d28648e44d5c836","target":"graph","created_at":"2026-05-18T02:53:28Z","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 problem of finding an optimal vertex cover in a graph is a classic NP-complete problem, and is a special case of the hitting set question. On the other hand, the hitting set problem, when asked in the context of induced geometric objects, often turns out to be exactly the vertex cover problem on restricted classes of graphs. In this work we explore a particular instance of such a phenomenon. We consider the problem of hitting all axis-parallel slabs induced by a point set P, and show that it is equivalent to the problem of finding a vertex cover on a graph whose edge set is the union of tw","authors_text":"Akanksha Agrawal, Neeldhara Misra, Sathish Govindarajan","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2014-04-21T19:16:51Z","title":"Vertex Cover Gets Faster and Harder on Low Degree Graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.5566","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:f997518766bdf099b4449e0226a2a2f6301bc1db235ecc6e4cda8281ce68ed32","target":"record","created_at":"2026-05-18T02:53:28Z","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":"b5f517e2dc55e8fb0ad769ea4e0a67fbc2f94b42c47ab3b06a85443b6c1d0e4e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2014-04-21T19:16:51Z","title_canon_sha256":"db8399e714adda114fbd138f53e6ea58a5b2bb5de4a3a0c8178fcb3871af6ded"},"schema_version":"1.0","source":{"id":"1404.5566","kind":"arxiv","version":2}},"canonical_sha256":"8da0b77f39fc852ac3b5725d16c4538a99f8e3d2ef8d206ef4c53ba6b864a2a8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8da0b77f39fc852ac3b5725d16c4538a99f8e3d2ef8d206ef4c53ba6b864a2a8","first_computed_at":"2026-05-18T02:53:28.357992Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:53:28.357992Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"0Ym9c5Ll9UIYAoMVsdwoBOkV5e1m73bw1tCF+36hC/LNgAy5r6h99kjOy0O2px0XsYjQIJqgQGkNSlnwH6etAg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:53:28.358791Z","signed_message":"canonical_sha256_bytes"},"source_id":"1404.5566","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f997518766bdf099b4449e0226a2a2f6301bc1db235ecc6e4cda8281ce68ed32","sha256:d1521bc5d7cd6137a845d941c0ef57c8d778f330ef1426275d28648e44d5c836"],"state_sha256":"63db6d67d43bdd376d265d612005d2a21c2cb738f515987734ec4050c247defe"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WG7sPBF1BWVWOIaJqcMjBQSzjgoog/442DGgYTzEks4ENslTWtVAOH7RDfPFlMDogNFkRlP3QS5LYwFp6UydAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T20:07:32.534416Z","bundle_sha256":"82fb96140dd70b585cbad88c27b713191a9e2830e34f784fb812df53a1514561"}}