{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:XXGDKHIBG2565WWMYQSE2ZFGQX","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":"dba823e1c1f6da407eb8a76c581d665aa166c186abb4f8992726367b31a5b382","cross_cats_sorted":["math.CO"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AC","submitted_at":"2022-10-23T08:48:16Z","title_canon_sha256":"98dc76ecb779694a2bbecf7de58d56640d503ab9bcc6d6870c82f3319837a13f"},"schema_version":"1.0","source":{"id":"2210.12665","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2210.12665","created_at":"2026-07-05T10:25:02Z"},{"alias_kind":"arxiv_version","alias_value":"2210.12665v4","created_at":"2026-07-05T10:25:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2210.12665","created_at":"2026-07-05T10:25:02Z"},{"alias_kind":"pith_short_12","alias_value":"XXGDKHIBG256","created_at":"2026-07-05T10:25:02Z"},{"alias_kind":"pith_short_16","alias_value":"XXGDKHIBG2565WWM","created_at":"2026-07-05T10:25:02Z"},{"alias_kind":"pith_short_8","alias_value":"XXGDKHIB","created_at":"2026-07-05T10:25:02Z"}],"graph_snapshots":[{"event_id":"sha256:2fcc00105d82b6951be2dbcda7a9dcd6c292daeb99d5773287e010a62906db41","target":"graph","created_at":"2026-07-05T10:25:02Z","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/2210.12665/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study the K\\H{o}nig type property for non-simple polyominoes. We prove that, for closed path polyominoes, the polyomino ideals are of K\\H{o}nig type, extending the results of Herzog and Hibi for simple thin polyominoes. As an application of this result, we give a combinatorial interpretation for the canonical module of the coordinate ring of a sub-class of closed path polyominoes, namely circle closed path polyominoes. In this case, we compute also the Cohen-Macaulay type and we show that $K[\\mathcal{P}]$ is a level ring.","authors_text":"Francesco Navarra, Rodica Dinu","cross_cats":["math.CO"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AC","submitted_at":"2022-10-23T08:48:16Z","title":"Non-simple polyominoes of K\\H{o}nig type and their canonical module"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2210.12665","kind":"arxiv","version":4},"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:d624bf201d6350ef713409158763759d918a6456c16f11cd1fff14ee87f7b795","target":"record","created_at":"2026-07-05T10:25:02Z","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":"dba823e1c1f6da407eb8a76c581d665aa166c186abb4f8992726367b31a5b382","cross_cats_sorted":["math.CO"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AC","submitted_at":"2022-10-23T08:48:16Z","title_canon_sha256":"98dc76ecb779694a2bbecf7de58d56640d503ab9bcc6d6870c82f3319837a13f"},"schema_version":"1.0","source":{"id":"2210.12665","kind":"arxiv","version":4}},"canonical_sha256":"bdcc351d0136bbeedaccc4244d64a685ca5e398337cd8aa7180a2ea286546708","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"bdcc351d0136bbeedaccc4244d64a685ca5e398337cd8aa7180a2ea286546708","first_computed_at":"2026-07-05T10:25:02.044818Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T10:25:02.044818Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"xEbnk584DaCkaYYkMTfcjli1b66uZb6lBL/2nJRcdTwKIldQCzYbJqkm3R2RbH8aATpWnOpttkAmPeu8TiycDA==","signature_status":"signed_v1","signed_at":"2026-07-05T10:25:02.045497Z","signed_message":"canonical_sha256_bytes"},"source_id":"2210.12665","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d624bf201d6350ef713409158763759d918a6456c16f11cd1fff14ee87f7b795","sha256:2fcc00105d82b6951be2dbcda7a9dcd6c292daeb99d5773287e010a62906db41"],"state_sha256":"a7145315dc42ce7e8def36eae6aafb646e301faea9e4677a2c1e12a986ec66a2"}