{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:TDCSW2N2KALB6GIKSZTRWX46UH","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":"a4e101c53f32afd77e59b58373ec8acdc73316619b6f7c7ccf9c9e55eb0ce2f6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2015-11-13T08:57:14Z","title_canon_sha256":"394ab08872be6163a49c4e7faf4477001620cfeca1957813da021ec718c9ecc5"},"schema_version":"1.0","source":{"id":"1511.04204","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1511.04204","created_at":"2026-05-18T01:24:02Z"},{"alias_kind":"arxiv_version","alias_value":"1511.04204v3","created_at":"2026-05-18T01:24:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1511.04204","created_at":"2026-05-18T01:24:02Z"},{"alias_kind":"pith_short_12","alias_value":"TDCSW2N2KALB","created_at":"2026-05-18T12:29:42Z"},{"alias_kind":"pith_short_16","alias_value":"TDCSW2N2KALB6GIK","created_at":"2026-05-18T12:29:42Z"},{"alias_kind":"pith_short_8","alias_value":"TDCSW2N2","created_at":"2026-05-18T12:29:42Z"}],"graph_snapshots":[{"event_id":"sha256:eee108b6931d59d4a510dd2f0d284246f6544b69a3855971f0857cc29e4b09f4","target":"graph","created_at":"2026-05-18T01:24:02Z","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"},"paper":{"abstract_excerpt":"In this paper we give a toric representation of the associated ring of a polyomino which is obtained by removing a convex polyomino from its ambient rectangle.","authors_text":"Akihiro Shikama","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2015-11-13T08:57:14Z","title":"Toric representations of algebras defined by certain nonsimple polyominoes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.04204","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":"sha256:5e2a88635d5ea89a2778435ebcc42cc38adfb56fb2d9c16de0742b4a9e8d0e8d","target":"record","created_at":"2026-05-18T01:24:02Z","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":"a4e101c53f32afd77e59b58373ec8acdc73316619b6f7c7ccf9c9e55eb0ce2f6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2015-11-13T08:57:14Z","title_canon_sha256":"394ab08872be6163a49c4e7faf4477001620cfeca1957813da021ec718c9ecc5"},"schema_version":"1.0","source":{"id":"1511.04204","kind":"arxiv","version":3}},"canonical_sha256":"98c52b69ba50161f190a96671b5f9ea1d2841948a857633be9d3b7a573b2d180","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"98c52b69ba50161f190a96671b5f9ea1d2841948a857633be9d3b7a573b2d180","first_computed_at":"2026-05-18T01:24:02.986218Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:24:02.986218Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"iKOSX+c2XWYAy2sR1EE6LCsTH/6H5vUenncQEKcLe0xeXMXDgic2sqoCx3VXGDNmDGXIL8/KG0Xw2TwG0ZSsDA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:24:02.986835Z","signed_message":"canonical_sha256_bytes"},"source_id":"1511.04204","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5e2a88635d5ea89a2778435ebcc42cc38adfb56fb2d9c16de0742b4a9e8d0e8d","sha256:eee108b6931d59d4a510dd2f0d284246f6544b69a3855971f0857cc29e4b09f4"],"state_sha256":"69c7608e329c9e8d36d1e867c88921086cb3ada0571f17a86f3da753dbbcd1ba"}