{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:MCVP7MZ4CCI2A7TUCLQOF3GKOY","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":"89ad990fba8d4c4a6c25ce0e0671067f55cb60a239a099ed331cf80862124d67","cross_cats_sorted":["math.MG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2021-11-18T14:06:43Z","title_canon_sha256":"4ec30e73455d23907a8e1a7a06e6a82dd36aa5c4ac293a6f4bee52bccf8604fb"},"schema_version":"1.0","source":{"id":"2111.09702","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2111.09702","created_at":"2026-07-05T06:35:22Z"},{"alias_kind":"arxiv_version","alias_value":"2111.09702v3","created_at":"2026-07-05T06:35:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2111.09702","created_at":"2026-07-05T06:35:22Z"},{"alias_kind":"pith_short_12","alias_value":"MCVP7MZ4CCI2","created_at":"2026-07-05T06:35:22Z"},{"alias_kind":"pith_short_16","alias_value":"MCVP7MZ4CCI2A7TU","created_at":"2026-07-05T06:35:22Z"},{"alias_kind":"pith_short_8","alias_value":"MCVP7MZ4","created_at":"2026-07-05T06:35:22Z"}],"graph_snapshots":[{"event_id":"sha256:82a9f9cc458cc7328cb56b6394c5f21cb3bdb24661a6b941baf71a8ac91e51da","target":"graph","created_at":"2026-07-05T06:35:22Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2111.09702/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We consider the minimum number of lines $h_n$ and $p_n$ needed to intersect or pierce, respectively, all the cells of the $n \\times n$ chessboard. Determining these values can also be interpreted as a strengthening of the classical plank problem for integer points. Using the symmetric plank theorem of K. Ball, we prove that $h_n = \\lceil \\frac n 2 \\rceil$ for each $n \\geq 1$. Studying the piercing problem, we show that $0.7n \\leq p_n \\leq n-1$ for $n\\geq 3$, where the upper bound is conjectured to be sharp. The lower bound is proven by using the linear programming method, whose limitations are","authors_text":"D\\'aniel Varga, Gergely Ambrus, Imre B\\'ar\\'any, P\\'eter Frankl","cross_cats":["math.MG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2021-11-18T14:06:43Z","title":"Piercing the chessboard"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2111.09702","kind":"arxiv","version":3},"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":"sha256:1ddb2beabe6574e9671dea7c12f7a0c0e1ceaed9ceab7fb04308de11b7812282","target":"record","created_at":"2026-07-05T06:35:22Z","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":"89ad990fba8d4c4a6c25ce0e0671067f55cb60a239a099ed331cf80862124d67","cross_cats_sorted":["math.MG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2021-11-18T14:06:43Z","title_canon_sha256":"4ec30e73455d23907a8e1a7a06e6a82dd36aa5c4ac293a6f4bee52bccf8604fb"},"schema_version":"1.0","source":{"id":"2111.09702","kind":"arxiv","version":3}},"canonical_sha256":"60aaffb33c1091a07e7412e0e2ecca7634e116ec9909adc586e22b00a95cc8c7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"60aaffb33c1091a07e7412e0e2ecca7634e116ec9909adc586e22b00a95cc8c7","first_computed_at":"2026-07-05T06:35:22.900122Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T06:35:22.900122Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"LdajvfcdtSEr9s/XjH/Jf4gifRQRJXwB9eXm7lQ6TTfiiPAk2J+Ouf8LtSafDV+CkUgmz1xn20ImkSiOKMEKDQ==","signature_status":"signed_v1","signed_at":"2026-07-05T06:35:22.900509Z","signed_message":"canonical_sha256_bytes"},"source_id":"2111.09702","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1ddb2beabe6574e9671dea7c12f7a0c0e1ceaed9ceab7fb04308de11b7812282","sha256:82a9f9cc458cc7328cb56b6394c5f21cb3bdb24661a6b941baf71a8ac91e51da"],"state_sha256":"d3bddca5062794d659050d1560eb910623d040632fcaf0ba5d83a1786c227a78"}