{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:SU3WA4KPJDJR5OTOV63ONZWZS6","short_pith_number":"pith:SU3WA4KP","canonical_record":{"source":{"id":"1903.01095","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2019-03-04T07:07:25Z","cross_cats_sorted":[],"title_canon_sha256":"9b639062133fbf3809ced60324b7e973c1bb9bb1218f19e0d599201e750b4f36","abstract_canon_sha256":"aaac91af29d4c71deeb839efd20dbabc8c7cad656129ec52d5e71192c3d02143"},"schema_version":"1.0"},"canonical_sha256":"953760714f48d31eba6eafb6e6e6d997ba3ee508ea8ee559366ed94ac34c5299","source":{"kind":"arxiv","id":"1903.01095","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1903.01095","created_at":"2026-05-17T23:52:12Z"},{"alias_kind":"arxiv_version","alias_value":"1903.01095v1","created_at":"2026-05-17T23:52:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1903.01095","created_at":"2026-05-17T23:52:12Z"},{"alias_kind":"pith_short_12","alias_value":"SU3WA4KPJDJR","created_at":"2026-05-18T12:33:27Z"},{"alias_kind":"pith_short_16","alias_value":"SU3WA4KPJDJR5OTO","created_at":"2026-05-18T12:33:27Z"},{"alias_kind":"pith_short_8","alias_value":"SU3WA4KP","created_at":"2026-05-18T12:33:27Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:SU3WA4KPJDJR5OTOV63ONZWZS6","target":"record","payload":{"canonical_record":{"source":{"id":"1903.01095","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2019-03-04T07:07:25Z","cross_cats_sorted":[],"title_canon_sha256":"9b639062133fbf3809ced60324b7e973c1bb9bb1218f19e0d599201e750b4f36","abstract_canon_sha256":"aaac91af29d4c71deeb839efd20dbabc8c7cad656129ec52d5e71192c3d02143"},"schema_version":"1.0"},"canonical_sha256":"953760714f48d31eba6eafb6e6e6d997ba3ee508ea8ee559366ed94ac34c5299","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:52:12.332263Z","signature_b64":"BwWHb0wRTj+z+FekUIWYYETIqiyclaeaY7vIy8QHPXT3sYgGj13DwNxLQ4ULM4Qt+V+cTnoV1jLcaC//CQtJCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"953760714f48d31eba6eafb6e6e6d997ba3ee508ea8ee559366ed94ac34c5299","last_reissued_at":"2026-05-17T23:52:12.331545Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:52:12.331545Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1903.01095","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:52:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"T5/WyLErAZ1BKvJYxumiRWs+RXUC9bK1rQX8txPXNAddPmLfwli/N7balbJBAGlBwdz3FlAmgiQAa+cPI2cNBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T17:01:35.051798Z"},"content_sha256":"d76a63a0526ae3f9ab16a9ce1e3d31d50887795108b04603bbc6ebacd033526f","schema_version":"1.0","event_id":"sha256:d76a63a0526ae3f9ab16a9ce1e3d31d50887795108b04603bbc6ebacd033526f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:SU3WA4KPJDJR5OTOV63ONZWZS6","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The Number of Convex Polyominoes with Given Height and Width","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Andr\\'e Schulz, G\\\"unter Rote, Kevin Buchin, Man-Kwun Chiu, Stefan Felsner","submitted_at":"2019-03-04T07:07:25Z","abstract_excerpt":"We give a new combinatorial proof for the number of convex polyominoes whose minimum enclosing rectangle has given dimensions. We also count the subclass of these polyominoes that contain the lower left corner of the enclosing rectangle (directed polyominoes). We indicate how to sample random polyominoes in these classes. As a side result, we calculate the first and second moments of the number of common points of two monotone lattice paths between two given points."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1903.01095","kind":"arxiv","version":1},"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:52:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/m3B7rjwAlrtY/juqmW1R1RsCjDmgH/Jd7EHcH3J8izcvkf0EYkBHRiEEGVmdv/KjRgknnL41MiRFmEea+wXDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T17:01:35.052514Z"},"content_sha256":"215c8f911fc0d73e9bbd2cf2289bbe2595e027b7a63a2aa0877ac2c7653ec281","schema_version":"1.0","event_id":"sha256:215c8f911fc0d73e9bbd2cf2289bbe2595e027b7a63a2aa0877ac2c7653ec281"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/SU3WA4KPJDJR5OTOV63ONZWZS6/bundle.json","state_url":"https://pith.science/pith/SU3WA4KPJDJR5OTOV63ONZWZS6/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/SU3WA4KPJDJR5OTOV63ONZWZS6/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-05-28T17:01:35Z","links":{"resolver":"https://pith.science/pith/SU3WA4KPJDJR5OTOV63ONZWZS6","bundle":"https://pith.science/pith/SU3WA4KPJDJR5OTOV63ONZWZS6/bundle.json","state":"https://pith.science/pith/SU3WA4KPJDJR5OTOV63ONZWZS6/state.json","well_known_bundle":"https://pith.science/.well-known/pith/SU3WA4KPJDJR5OTOV63ONZWZS6/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:SU3WA4KPJDJR5OTOV63ONZWZS6","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":"aaac91af29d4c71deeb839efd20dbabc8c7cad656129ec52d5e71192c3d02143","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2019-03-04T07:07:25Z","title_canon_sha256":"9b639062133fbf3809ced60324b7e973c1bb9bb1218f19e0d599201e750b4f36"},"schema_version":"1.0","source":{"id":"1903.01095","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1903.01095","created_at":"2026-05-17T23:52:12Z"},{"alias_kind":"arxiv_version","alias_value":"1903.01095v1","created_at":"2026-05-17T23:52:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1903.01095","created_at":"2026-05-17T23:52:12Z"},{"alias_kind":"pith_short_12","alias_value":"SU3WA4KPJDJR","created_at":"2026-05-18T12:33:27Z"},{"alias_kind":"pith_short_16","alias_value":"SU3WA4KPJDJR5OTO","created_at":"2026-05-18T12:33:27Z"},{"alias_kind":"pith_short_8","alias_value":"SU3WA4KP","created_at":"2026-05-18T12:33:27Z"}],"graph_snapshots":[{"event_id":"sha256:215c8f911fc0d73e9bbd2cf2289bbe2595e027b7a63a2aa0877ac2c7653ec281","target":"graph","created_at":"2026-05-17T23:52:12Z","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 give a new combinatorial proof for the number of convex polyominoes whose minimum enclosing rectangle has given dimensions. We also count the subclass of these polyominoes that contain the lower left corner of the enclosing rectangle (directed polyominoes). We indicate how to sample random polyominoes in these classes. As a side result, we calculate the first and second moments of the number of common points of two monotone lattice paths between two given points.","authors_text":"Andr\\'e Schulz, G\\\"unter Rote, Kevin Buchin, Man-Kwun Chiu, Stefan Felsner","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2019-03-04T07:07:25Z","title":"The Number of Convex Polyominoes with Given Height and Width"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1903.01095","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:d76a63a0526ae3f9ab16a9ce1e3d31d50887795108b04603bbc6ebacd033526f","target":"record","created_at":"2026-05-17T23:52:12Z","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":"aaac91af29d4c71deeb839efd20dbabc8c7cad656129ec52d5e71192c3d02143","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2019-03-04T07:07:25Z","title_canon_sha256":"9b639062133fbf3809ced60324b7e973c1bb9bb1218f19e0d599201e750b4f36"},"schema_version":"1.0","source":{"id":"1903.01095","kind":"arxiv","version":1}},"canonical_sha256":"953760714f48d31eba6eafb6e6e6d997ba3ee508ea8ee559366ed94ac34c5299","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"953760714f48d31eba6eafb6e6e6d997ba3ee508ea8ee559366ed94ac34c5299","first_computed_at":"2026-05-17T23:52:12.331545Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:52:12.331545Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"BwWHb0wRTj+z+FekUIWYYETIqiyclaeaY7vIy8QHPXT3sYgGj13DwNxLQ4ULM4Qt+V+cTnoV1jLcaC//CQtJCQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:52:12.332263Z","signed_message":"canonical_sha256_bytes"},"source_id":"1903.01095","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d76a63a0526ae3f9ab16a9ce1e3d31d50887795108b04603bbc6ebacd033526f","sha256:215c8f911fc0d73e9bbd2cf2289bbe2595e027b7a63a2aa0877ac2c7653ec281"],"state_sha256":"b2b09ab8de3e6ede120c87478a20e37ca5c4fc90918dfab23591566d157cd482"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TNMcsRabV1VBlsl73h4CJPSaNQrGmMfM5AG0ls+lnvQFdYJj/gt+GWgr6VQhR0N2FpfxDx82mh52cE3VwTT0Bg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T17:01:35.056449Z","bundle_sha256":"8bb10b8c96d0178d911749823aaf41ff289bf591801585f03ec4e77a748f9a72"}}