{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:DABLYHEKJRYKC7KCSPRA3UX2CD","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":"b07ff9320c9ebc41a3c8c93b48e10579e1192da32fe8de4aa437640f2e6fc105","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2014-07-21T17:00:05Z","title_canon_sha256":"2920f03b47c01623ee1ee807108c5b69a080a6398860dd93a04e0081872060c9"},"schema_version":"1.0","source":{"id":"1407.5571","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1407.5571","created_at":"2026-05-18T02:47:13Z"},{"alias_kind":"arxiv_version","alias_value":"1407.5571v1","created_at":"2026-05-18T02:47:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1407.5571","created_at":"2026-05-18T02:47:13Z"},{"alias_kind":"pith_short_12","alias_value":"DABLYHEKJRYK","created_at":"2026-05-18T12:28:25Z"},{"alias_kind":"pith_short_16","alias_value":"DABLYHEKJRYKC7KC","created_at":"2026-05-18T12:28:25Z"},{"alias_kind":"pith_short_8","alias_value":"DABLYHEK","created_at":"2026-05-18T12:28:25Z"}],"graph_snapshots":[{"event_id":"sha256:b96c214ca109b9671db145868e08ae8bbf86c406a25be477a46d66fc7b6bbf32","target":"graph","created_at":"2026-05-18T02:47:13Z","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":"Let $R$ be a polynomial ring over a field $K$. To a given squarefree monomial ideal $I \\subset R$, one can associate a hypergraph $H(I)$. In this article, we prove that the arithmetical rank of $I$ is equal to the projective dimension of $R/I$ when $H(I)$ is a string or a cycle hypergraph.","authors_text":"Kyouko Kimura, Paolo Mantero","cross_cats":["math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2014-07-21T17:00:05Z","title":"Arithmetical rank of strings and cycles"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.5571","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:d5df0ae003416171ef9167101d3a1b217b71a65347fa68bbc905ae2d1d3e203a","target":"record","created_at":"2026-05-18T02:47:13Z","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":"b07ff9320c9ebc41a3c8c93b48e10579e1192da32fe8de4aa437640f2e6fc105","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2014-07-21T17:00:05Z","title_canon_sha256":"2920f03b47c01623ee1ee807108c5b69a080a6398860dd93a04e0081872060c9"},"schema_version":"1.0","source":{"id":"1407.5571","kind":"arxiv","version":1}},"canonical_sha256":"1802bc1c8a4c70a17d4293e20dd2fa10f7afd171da7caebed5c8853d211a58a9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1802bc1c8a4c70a17d4293e20dd2fa10f7afd171da7caebed5c8853d211a58a9","first_computed_at":"2026-05-18T02:47:13.706625Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:47:13.706625Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"bnpGqDR/+pTeKoczLa5H4SqKumSGIe9Opvcra4WEys4eStjXVMhXrl3zl9yjmyaRa/UBuAmuoxuk0sUy0yzgAw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:47:13.707311Z","signed_message":"canonical_sha256_bytes"},"source_id":"1407.5571","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d5df0ae003416171ef9167101d3a1b217b71a65347fa68bbc905ae2d1d3e203a","sha256:b96c214ca109b9671db145868e08ae8bbf86c406a25be477a46d66fc7b6bbf32"],"state_sha256":"8ab1ac55d0f1359d9ef83e6f113634f902e39c6085099a696bae658a96f05cd6"}