{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:WGA46QXTJQLTUHXVRV3UTANWV3","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":"b9a7a98a526f75abc2d9e7c3c84f8af55bf16e3bc5b45c076c7cfa828e485513","cross_cats_sorted":["math.AT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-07-26T16:33:50Z","title_canon_sha256":"1056b2b61a23ee23b211347569ac8e3b0fa59a775417953342c148ae957c9257"},"schema_version":"1.0","source":{"id":"1807.10231","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1807.10231","created_at":"2026-05-18T00:09:42Z"},{"alias_kind":"arxiv_version","alias_value":"1807.10231v1","created_at":"2026-05-18T00:09:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1807.10231","created_at":"2026-05-18T00:09:42Z"},{"alias_kind":"pith_short_12","alias_value":"WGA46QXTJQLT","created_at":"2026-05-18T12:32:59Z"},{"alias_kind":"pith_short_16","alias_value":"WGA46QXTJQLTUHXV","created_at":"2026-05-18T12:32:59Z"},{"alias_kind":"pith_short_8","alias_value":"WGA46QXT","created_at":"2026-05-18T12:32:59Z"}],"graph_snapshots":[{"event_id":"sha256:aa5b4abb12eda32ecf6df70350b2e3e0f58268cfe9c2ca81e5568af691bd290b","target":"graph","created_at":"2026-05-18T00:09:42Z","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":"What is the maximum number of holes that a polyomino with $n$ tiles can enclose? Call this number $f(n)$. We show that if $n_k = \\left( 2^{2k+1} + 3 \\cdot 2^{k+1}+4 \\right) / 3$ and $h_k = \\left( 2^{2k}-1 \\right) /3$, then $f(n_k) = h_k$ for $k \\ge 1$. We also give nearly matching upper and lower bounds for large $n$, showing as a corollary that $f(n) \\approx n/2$.","authors_text":"\\'Erika Rold\\'an, Matthew Kahle","cross_cats":["math.AT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-07-26T16:33:50Z","title":"Polyominoes with maximally many holes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.10231","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":"sha256:4e2d489094e69e0c38eb81b3db797999fa7726b17c6c05f804aeb90f659b7ec7","target":"record","created_at":"2026-05-18T00:09:42Z","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":"b9a7a98a526f75abc2d9e7c3c84f8af55bf16e3bc5b45c076c7cfa828e485513","cross_cats_sorted":["math.AT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-07-26T16:33:50Z","title_canon_sha256":"1056b2b61a23ee23b211347569ac8e3b0fa59a775417953342c148ae957c9257"},"schema_version":"1.0","source":{"id":"1807.10231","kind":"arxiv","version":1}},"canonical_sha256":"b181cf42f34c173a1ef58d774981b6aeda4c35245ad407f07367bbee240072cf","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b181cf42f34c173a1ef58d774981b6aeda4c35245ad407f07367bbee240072cf","first_computed_at":"2026-05-18T00:09:42.787246Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:09:42.787246Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"+VmANQADU8pxB6ZTZPakDZ47YvwGBY5jHrXpwhRSBx7Cqdf3O8wdM7I2Yq7gaHbbc7gwcOPO0192BjB4Q1XnBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:09:42.787797Z","signed_message":"canonical_sha256_bytes"},"source_id":"1807.10231","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4e2d489094e69e0c38eb81b3db797999fa7726b17c6c05f804aeb90f659b7ec7","sha256:aa5b4abb12eda32ecf6df70350b2e3e0f58268cfe9c2ca81e5568af691bd290b"],"state_sha256":"e5d6eca5aceed240a7ab7436a9af80a3b8266029e7eb83061d7b140389f7be3f"}