{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:GC2HGJQYU73I3VGKVBN7UONDEP","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":"85fce723b95c7afe680269932b000624be7b0613f5cb298e82ce5d602c3c1afa","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2016-03-23T17:35:54Z","title_canon_sha256":"06a10785595cf4e0d7c2f5333e50bff2782f753e534b4ee5563812d75452fcfe"},"schema_version":"1.0","source":{"id":"1603.07282","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1603.07282","created_at":"2026-05-18T01:18:23Z"},{"alias_kind":"arxiv_version","alias_value":"1603.07282v1","created_at":"2026-05-18T01:18:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1603.07282","created_at":"2026-05-18T01:18:23Z"},{"alias_kind":"pith_short_12","alias_value":"GC2HGJQYU73I","created_at":"2026-05-18T12:30:15Z"},{"alias_kind":"pith_short_16","alias_value":"GC2HGJQYU73I3VGK","created_at":"2026-05-18T12:30:15Z"},{"alias_kind":"pith_short_8","alias_value":"GC2HGJQY","created_at":"2026-05-18T12:30:15Z"}],"graph_snapshots":[{"event_id":"sha256:67e04b208d81d9ca11f0bef48216cd2fdf83b2c22f10eef216f98e15e092da52","target":"graph","created_at":"2026-05-18T01:18:23Z","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":"In the Line Cover problem a set of n points is given and the task is to cover the points using either the minimum number of lines or at most k lines. In Curve Cover, a generalization of Line Cover, the task is to cover the points using curves with d degrees of freedom. Another generalization is the Hyperplane Cover problem where points in d-dimensional space are to be covered by hyperplanes. All these problems have kernels of polynomial size, where the parameter is the minimum number of lines, curves, or hyperplanes needed. First we give a non-parameterized algorithm for both problems in O*(2^","authors_text":"Edvin Berglin, Ingo van Duijn, Jesper Sindahl Nielsen, Peyman Afshani","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2016-03-23T17:35:54Z","title":"Applications of incidence bounds in point covering problems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.07282","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":"sha256:6c2c8f511b5759e315f6d3f28d9896bc693ae3f09a65bb62bbcf4f783fcc1356","target":"record","created_at":"2026-05-18T01:18:23Z","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":"85fce723b95c7afe680269932b000624be7b0613f5cb298e82ce5d602c3c1afa","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2016-03-23T17:35:54Z","title_canon_sha256":"06a10785595cf4e0d7c2f5333e50bff2782f753e534b4ee5563812d75452fcfe"},"schema_version":"1.0","source":{"id":"1603.07282","kind":"arxiv","version":1}},"canonical_sha256":"30b4732618a7f68dd4caa85bfa39a323fe9288bd9cacf1447200395ca5b3bbf0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"30b4732618a7f68dd4caa85bfa39a323fe9288bd9cacf1447200395ca5b3bbf0","first_computed_at":"2026-05-18T01:18:23.904049Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:18:23.904049Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"MeR9H95+jOAY3wHrazF3QCckqkiUU9zI7nwFzEveixvX+DUPpYON5g5Y8KGSKASvfuhUWznnrAiqfHYhjsKrAw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:18:23.904645Z","signed_message":"canonical_sha256_bytes"},"source_id":"1603.07282","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6c2c8f511b5759e315f6d3f28d9896bc693ae3f09a65bb62bbcf4f783fcc1356","sha256:67e04b208d81d9ca11f0bef48216cd2fdf83b2c22f10eef216f98e15e092da52"],"state_sha256":"8a567153c1e9fdbf6e369bdc30a1d0ffe6dc1a5dd272a174b2ff53f217e9743d"}