{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:DABLYHEKJRYKC7KCSPRA3UX2CD","short_pith_number":"pith:DABLYHEK","schema_version":"1.0","canonical_sha256":"1802bc1c8a4c70a17d4293e20dd2fa10f7afd171da7caebed5c8853d211a58a9","source":{"kind":"arxiv","id":"1407.5571","version":1},"attestation_state":"computed","paper":{"title":"Arithmetical rank of strings and cycles","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.AC","authors_text":"Kyouko Kimura, Paolo Mantero","submitted_at":"2014-07-21T17:00:05Z","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."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1407.5571","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2014-07-21T17:00:05Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"2920f03b47c01623ee1ee807108c5b69a080a6398860dd93a04e0081872060c9","abstract_canon_sha256":"b07ff9320c9ebc41a3c8c93b48e10579e1192da32fe8de4aa437640f2e6fc105"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:47:13.707311Z","signature_b64":"bnpGqDR/+pTeKoczLa5H4SqKumSGIe9Opvcra4WEys4eStjXVMhXrl3zl9yjmyaRa/UBuAmuoxuk0sUy0yzgAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1802bc1c8a4c70a17d4293e20dd2fa10f7afd171da7caebed5c8853d211a58a9","last_reissued_at":"2026-05-18T02:47:13.706625Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:47:13.706625Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Arithmetical rank of strings and cycles","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.AC","authors_text":"Kyouko Kimura, Paolo Mantero","submitted_at":"2014-07-21T17:00:05Z","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."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.5571","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1407.5571","created_at":"2026-05-18T02:47:13.706709+00:00"},{"alias_kind":"arxiv_version","alias_value":"1407.5571v1","created_at":"2026-05-18T02:47:13.706709+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1407.5571","created_at":"2026-05-18T02:47:13.706709+00:00"},{"alias_kind":"pith_short_12","alias_value":"DABLYHEKJRYK","created_at":"2026-05-18T12:28:25.294606+00:00"},{"alias_kind":"pith_short_16","alias_value":"DABLYHEKJRYKC7KC","created_at":"2026-05-18T12:28:25.294606+00:00"},{"alias_kind":"pith_short_8","alias_value":"DABLYHEK","created_at":"2026-05-18T12:28:25.294606+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/DABLYHEKJRYKC7KCSPRA3UX2CD","json":"https://pith.science/pith/DABLYHEKJRYKC7KCSPRA3UX2CD.json","graph_json":"https://pith.science/api/pith-number/DABLYHEKJRYKC7KCSPRA3UX2CD/graph.json","events_json":"https://pith.science/api/pith-number/DABLYHEKJRYKC7KCSPRA3UX2CD/events.json","paper":"https://pith.science/paper/DABLYHEK"},"agent_actions":{"view_html":"https://pith.science/pith/DABLYHEKJRYKC7KCSPRA3UX2CD","download_json":"https://pith.science/pith/DABLYHEKJRYKC7KCSPRA3UX2CD.json","view_paper":"https://pith.science/paper/DABLYHEK","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1407.5571&json=true","fetch_graph":"https://pith.science/api/pith-number/DABLYHEKJRYKC7KCSPRA3UX2CD/graph.json","fetch_events":"https://pith.science/api/pith-number/DABLYHEKJRYKC7KCSPRA3UX2CD/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/DABLYHEKJRYKC7KCSPRA3UX2CD/action/timestamp_anchor","attest_storage":"https://pith.science/pith/DABLYHEKJRYKC7KCSPRA3UX2CD/action/storage_attestation","attest_author":"https://pith.science/pith/DABLYHEKJRYKC7KCSPRA3UX2CD/action/author_attestation","sign_citation":"https://pith.science/pith/DABLYHEKJRYKC7KCSPRA3UX2CD/action/citation_signature","submit_replication":"https://pith.science/pith/DABLYHEKJRYKC7KCSPRA3UX2CD/action/replication_record"}},"created_at":"2026-05-18T02:47:13.706709+00:00","updated_at":"2026-05-18T02:47:13.706709+00:00"}