{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:V7LFRPGHBQQYH5EWLV6BDMDWGK","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":"31080cb29a9a1cf7a1c32f413eefacef32a871313feece23b3245229f982c3d9","cross_cats_sorted":["cs.CC","cs.DM","cs.DS","math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2010-04-06T01:06:27Z","title_canon_sha256":"b02ea44093fd8cd86a9c55d990a25fe6460dc7714057e5a6c764355fb3f938e7"},"schema_version":"1.0","source":{"id":"1004.0744","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1004.0744","created_at":"2026-05-18T02:24:17Z"},{"alias_kind":"arxiv_version","alias_value":"1004.0744v1","created_at":"2026-05-18T02:24:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1004.0744","created_at":"2026-05-18T02:24:17Z"},{"alias_kind":"pith_short_12","alias_value":"V7LFRPGHBQQY","created_at":"2026-05-18T12:26:15Z"},{"alias_kind":"pith_short_16","alias_value":"V7LFRPGHBQQYH5EW","created_at":"2026-05-18T12:26:15Z"},{"alias_kind":"pith_short_8","alias_value":"V7LFRPGH","created_at":"2026-05-18T12:26:15Z"}],"graph_snapshots":[{"event_id":"sha256:a97f88254a336f471e3f185d21327db67fcebc61f5b2946599e8c2d13eed93d4","target":"graph","created_at":"2026-05-18T02:24:17Z","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 following problem: Given a finite set of straight line segments in the plane, determine the positions of a minimal number of points on the segments, from which guards can see all segments. This problem can be interpreted as looking for a minimal number of locations of policemen, guards, cameras or other sensors, that can observe a network of streets, corridors, tunnels, tubes, etc. We show that the problem is strongly NP-complete even for a set of segments with a cubic graph structure, but in P for tree structures.","authors_text":"Valentin E. Brimkov","cross_cats":["cs.CC","cs.DM","cs.DS","math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2010-04-06T01:06:27Z","title":"Patrolling a Street Network is Strongly NP-Complete but in P for Tree Structures"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1004.0744","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":"sha256:121461fb62f6ee1a00b4398f8b520e971260953d922926aa1b9ea0a8cedd7d3a","target":"record","created_at":"2026-05-18T02:24:17Z","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":"31080cb29a9a1cf7a1c32f413eefacef32a871313feece23b3245229f982c3d9","cross_cats_sorted":["cs.CC","cs.DM","cs.DS","math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2010-04-06T01:06:27Z","title_canon_sha256":"b02ea44093fd8cd86a9c55d990a25fe6460dc7714057e5a6c764355fb3f938e7"},"schema_version":"1.0","source":{"id":"1004.0744","kind":"arxiv","version":1}},"canonical_sha256":"afd658bcc70c2183f4965d7c11b07632a3020f5324cc53211b288e4e661acdad","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"afd658bcc70c2183f4965d7c11b07632a3020f5324cc53211b288e4e661acdad","first_computed_at":"2026-05-18T02:24:17.500779Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:24:17.500779Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"QV3KBdFLJtDVwPty/txf9dB+4JZb+uijqgo7Sdmf1HExQocCkYJFw9/1J8i1bAcuHroQhDvE7IWXRLh9qqQdDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:24:17.501457Z","signed_message":"canonical_sha256_bytes"},"source_id":"1004.0744","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:121461fb62f6ee1a00b4398f8b520e971260953d922926aa1b9ea0a8cedd7d3a","sha256:a97f88254a336f471e3f185d21327db67fcebc61f5b2946599e8c2d13eed93d4"],"state_sha256":"4e1db7a342fae808ddfe967f89800d49d3a758440ccb0af84f577edad0c81bdb"}