{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:IHLOR77PMQ734XWZH3WKQCBTVI","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":"a6bb90633d4eeaf96858b6795880b56467ce95df317927292a4ccf465c460aeb","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.CG","submitted_at":"2018-09-26T15:50:00Z","title_canon_sha256":"d9c0772a4ba6dd5802f49130899468ba71b9f97d3cc64ef5baddc172a8fe1188"},"schema_version":"1.0","source":{"id":"1809.10078","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1809.10078","created_at":"2026-05-18T00:04:42Z"},{"alias_kind":"arxiv_version","alias_value":"1809.10078v1","created_at":"2026-05-18T00:04:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1809.10078","created_at":"2026-05-18T00:04:42Z"},{"alias_kind":"pith_short_12","alias_value":"IHLOR77PMQ73","created_at":"2026-05-18T12:32:28Z"},{"alias_kind":"pith_short_16","alias_value":"IHLOR77PMQ734XWZ","created_at":"2026-05-18T12:32:28Z"},{"alias_kind":"pith_short_8","alias_value":"IHLOR77P","created_at":"2026-05-18T12:32:28Z"}],"graph_snapshots":[{"event_id":"sha256:6f1685d7681a04be02d61a0e3b141a8d0229b161cb613dea6071e76544ad04ce","target":"graph","created_at":"2026-05-18T00:04:42Z","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 consider the problem of testing, for a given set of planar regions $\\cal R$ and an integer $k$, whether there exists a convex shape whose boundary intersects at least $k$ regions of $\\cal R$. We provide a polynomial time algorithm for the case where the regions are disjoint line segments with a constant number of orientations. On the other hand, we show that the problem is NP-hard when the regions are intersecting axis-aligned rectangles or 3-oriented line segments. For several natural intermediate classes of shapes (arbitrary disjoint segments, intersecting 2-oriented segments) the problem","authors_text":"Frank Staals, Irina Kostitsyna, J\\'er\\^ome Urhausen, Jordi L. Vermeulen, Lionov Wiratma, Maarten L\\\"offler, Marc van Kreveld, Mees van de Kerkhof, Vahideh Keikha","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.CG","submitted_at":"2018-09-26T15:50:00Z","title":"Convex partial transversals of planar regions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.10078","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:c5e31d356a41b4a21569567a2e1c8f899ae330566277f155c3d660310c664af8","target":"record","created_at":"2026-05-18T00:04:42Z","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":"a6bb90633d4eeaf96858b6795880b56467ce95df317927292a4ccf465c460aeb","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.CG","submitted_at":"2018-09-26T15:50:00Z","title_canon_sha256":"d9c0772a4ba6dd5802f49130899468ba71b9f97d3cc64ef5baddc172a8fe1188"},"schema_version":"1.0","source":{"id":"1809.10078","kind":"arxiv","version":1}},"canonical_sha256":"41d6e8ffef643fbe5ed93eeca80833aa1b4c5fa3b92439719b058aa559582469","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"41d6e8ffef643fbe5ed93eeca80833aa1b4c5fa3b92439719b058aa559582469","first_computed_at":"2026-05-18T00:04:42.648821Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:04:42.648821Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"95Aqf/u+tXeaFJKYXneg2RgT3PhveRCswu7KIEEDtwqch/sS0dAfKpqMLuUqk9qLsQ6U5OCxjhKQ14K2w4swDw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:04:42.649384Z","signed_message":"canonical_sha256_bytes"},"source_id":"1809.10078","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c5e31d356a41b4a21569567a2e1c8f899ae330566277f155c3d660310c664af8","sha256:6f1685d7681a04be02d61a0e3b141a8d0229b161cb613dea6071e76544ad04ce"],"state_sha256":"6fed5a88e0042f840338e5634a5fe4411bcc9caf421c70186bafea3bb585b2a0"}