{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:2Q2OMSRIOMTQQVBWJHIQ7K2O6G","short_pith_number":"pith:2Q2OMSRI","schema_version":"1.0","canonical_sha256":"d434e64a28732708543649d10fab4ef1affc32f1e8658fc19d716a18a6fb6632","source":{"kind":"arxiv","id":"1810.10961","version":2},"attestation_state":"computed","paper":{"title":"Art gallery problem with rook and queen vision","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"cs.CC","authors_text":"\\'Erika Rold\\'an, Hannah Alpert","submitted_at":"2018-10-25T16:31:09Z","abstract_excerpt":"How many chess rooks or queens does it take to guard all the squares of a given polyomino, the union of square tiles from a square grid? This question is a version of the art gallery problem in which the guards can \"see\" whichever squares the rook or queen attacks. We show that floor(n/2) rooks or floor(n/3) queens are sufficient and sometimes necessary to guard a polyomino with n tiles. We also prove that finding the minimum number of rooks or the minimum number of queens needed to guard a polyomino is NP-hard. These results also apply to d-dimensional rooks and queens on d-dimensional polycu"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1810.10961","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2018-10-25T16:31:09Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"cddf36bc914be4cc49b8219fe5c9dead2c519a2e84289a095d374f8cc802ae3e","abstract_canon_sha256":"aabf4fabf17e802a6a0114c50f1f88336a4c6862ca019b171e580fc40215b571"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:00:17.732067Z","signature_b64":"crC5lHWA4gZHkLBOCMAzeqkblA6ZsuP216fi535fTf1IEczDHRk13O4v/vvzxJU1wYBsn5rI/VGhvXsmKyXyCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d434e64a28732708543649d10fab4ef1affc32f1e8658fc19d716a18a6fb6632","last_reissued_at":"2026-05-18T00:00:17.731531Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:00:17.731531Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Art gallery problem with rook and queen vision","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"cs.CC","authors_text":"\\'Erika Rold\\'an, Hannah Alpert","submitted_at":"2018-10-25T16:31:09Z","abstract_excerpt":"How many chess rooks or queens does it take to guard all the squares of a given polyomino, the union of square tiles from a square grid? This question is a version of the art gallery problem in which the guards can \"see\" whichever squares the rook or queen attacks. We show that floor(n/2) rooks or floor(n/3) queens are sufficient and sometimes necessary to guard a polyomino with n tiles. We also prove that finding the minimum number of rooks or the minimum number of queens needed to guard a polyomino is NP-hard. These results also apply to d-dimensional rooks and queens on d-dimensional polycu"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.10961","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1810.10961","created_at":"2026-05-18T00:00:17.731614+00:00"},{"alias_kind":"arxiv_version","alias_value":"1810.10961v2","created_at":"2026-05-18T00:00:17.731614+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1810.10961","created_at":"2026-05-18T00:00:17.731614+00:00"},{"alias_kind":"pith_short_12","alias_value":"2Q2OMSRIOMTQ","created_at":"2026-05-18T12:32:02.567920+00:00"},{"alias_kind":"pith_short_16","alias_value":"2Q2OMSRIOMTQQVBW","created_at":"2026-05-18T12:32:02.567920+00:00"},{"alias_kind":"pith_short_8","alias_value":"2Q2OMSRI","created_at":"2026-05-18T12:32:02.567920+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/2Q2OMSRIOMTQQVBWJHIQ7K2O6G","json":"https://pith.science/pith/2Q2OMSRIOMTQQVBWJHIQ7K2O6G.json","graph_json":"https://pith.science/api/pith-number/2Q2OMSRIOMTQQVBWJHIQ7K2O6G/graph.json","events_json":"https://pith.science/api/pith-number/2Q2OMSRIOMTQQVBWJHIQ7K2O6G/events.json","paper":"https://pith.science/paper/2Q2OMSRI"},"agent_actions":{"view_html":"https://pith.science/pith/2Q2OMSRIOMTQQVBWJHIQ7K2O6G","download_json":"https://pith.science/pith/2Q2OMSRIOMTQQVBWJHIQ7K2O6G.json","view_paper":"https://pith.science/paper/2Q2OMSRI","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1810.10961&json=true","fetch_graph":"https://pith.science/api/pith-number/2Q2OMSRIOMTQQVBWJHIQ7K2O6G/graph.json","fetch_events":"https://pith.science/api/pith-number/2Q2OMSRIOMTQQVBWJHIQ7K2O6G/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/2Q2OMSRIOMTQQVBWJHIQ7K2O6G/action/timestamp_anchor","attest_storage":"https://pith.science/pith/2Q2OMSRIOMTQQVBWJHIQ7K2O6G/action/storage_attestation","attest_author":"https://pith.science/pith/2Q2OMSRIOMTQQVBWJHIQ7K2O6G/action/author_attestation","sign_citation":"https://pith.science/pith/2Q2OMSRIOMTQQVBWJHIQ7K2O6G/action/citation_signature","submit_replication":"https://pith.science/pith/2Q2OMSRIOMTQQVBWJHIQ7K2O6G/action/replication_record"}},"created_at":"2026-05-18T00:00:17.731614+00:00","updated_at":"2026-05-18T00:00:17.731614+00:00"}