{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:ET7MZS7BOYYNV6FHHHH5FSUC23","short_pith_number":"pith:ET7MZS7B","schema_version":"1.0","canonical_sha256":"24fecccbe17630daf8a739cfd2ca82d6d4efb0d6c6221a1e88874655c975958b","source":{"kind":"arxiv","id":"1707.07417","version":1},"attestation_state":"computed","paper":{"title":"Multiprojective spaces and the arithmetically Cohen-Macaulay property","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AC"],"primary_cat":"math.AG","authors_text":"Giuseppe Favacchio, Juan Migliore","submitted_at":"2017-07-24T06:32:32Z","abstract_excerpt":"In this paper we study the arithmetically Cohen-Macaulay (ACM) property for sets of points in multiprojective spaces. Most of what is known is for $\\mathbb P^1\\times \\mathbb P^1$ and, more recently, in $(\\mathbb P^1)^r.$ In $\\mathbb P^1\\times \\mathbb P^1$ the so called inclusion property characterizes the ACM property. We extend the definition in any multiprojective space and we prove that the inclusion property implies the ACM property in $\\mathbb P^m\\times \\mathbb P^n$. In such an ambient space it is equivalent to the so-called $(\\star)$-property. Moreover, we start an investigation of the A"},"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":"1707.07417","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2017-07-24T06:32:32Z","cross_cats_sorted":["math.AC"],"title_canon_sha256":"3e6877600024b29c30e671a1831078e9322e1f2d769e80b852aaad55eb753925","abstract_canon_sha256":"7c21743ec50f987c857a6b94bc064104d84a1ed633cdbd31e5b56fda8471a535"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:39:42.294539Z","signature_b64":"bi8H8ywf4+7VcJO1kLxi9gX39BSpebnLrZH7VQl+QOpVog17f3F6UH82FMhZi5HkObrnj9s/w3W/DaAV0rraAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"24fecccbe17630daf8a739cfd2ca82d6d4efb0d6c6221a1e88874655c975958b","last_reissued_at":"2026-05-18T00:39:42.293866Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:39:42.293866Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Multiprojective spaces and the arithmetically Cohen-Macaulay property","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AC"],"primary_cat":"math.AG","authors_text":"Giuseppe Favacchio, Juan Migliore","submitted_at":"2017-07-24T06:32:32Z","abstract_excerpt":"In this paper we study the arithmetically Cohen-Macaulay (ACM) property for sets of points in multiprojective spaces. Most of what is known is for $\\mathbb P^1\\times \\mathbb P^1$ and, more recently, in $(\\mathbb P^1)^r.$ In $\\mathbb P^1\\times \\mathbb P^1$ the so called inclusion property characterizes the ACM property. We extend the definition in any multiprojective space and we prove that the inclusion property implies the ACM property in $\\mathbb P^m\\times \\mathbb P^n$. In such an ambient space it is equivalent to the so-called $(\\star)$-property. Moreover, we start an investigation of the A"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.07417","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":"1707.07417","created_at":"2026-05-18T00:39:42.293968+00:00"},{"alias_kind":"arxiv_version","alias_value":"1707.07417v1","created_at":"2026-05-18T00:39:42.293968+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1707.07417","created_at":"2026-05-18T00:39:42.293968+00:00"},{"alias_kind":"pith_short_12","alias_value":"ET7MZS7BOYYN","created_at":"2026-05-18T12:31:12.930513+00:00"},{"alias_kind":"pith_short_16","alias_value":"ET7MZS7BOYYNV6FH","created_at":"2026-05-18T12:31:12.930513+00:00"},{"alias_kind":"pith_short_8","alias_value":"ET7MZS7B","created_at":"2026-05-18T12:31:12.930513+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/ET7MZS7BOYYNV6FHHHH5FSUC23","json":"https://pith.science/pith/ET7MZS7BOYYNV6FHHHH5FSUC23.json","graph_json":"https://pith.science/api/pith-number/ET7MZS7BOYYNV6FHHHH5FSUC23/graph.json","events_json":"https://pith.science/api/pith-number/ET7MZS7BOYYNV6FHHHH5FSUC23/events.json","paper":"https://pith.science/paper/ET7MZS7B"},"agent_actions":{"view_html":"https://pith.science/pith/ET7MZS7BOYYNV6FHHHH5FSUC23","download_json":"https://pith.science/pith/ET7MZS7BOYYNV6FHHHH5FSUC23.json","view_paper":"https://pith.science/paper/ET7MZS7B","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1707.07417&json=true","fetch_graph":"https://pith.science/api/pith-number/ET7MZS7BOYYNV6FHHHH5FSUC23/graph.json","fetch_events":"https://pith.science/api/pith-number/ET7MZS7BOYYNV6FHHHH5FSUC23/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ET7MZS7BOYYNV6FHHHH5FSUC23/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ET7MZS7BOYYNV6FHHHH5FSUC23/action/storage_attestation","attest_author":"https://pith.science/pith/ET7MZS7BOYYNV6FHHHH5FSUC23/action/author_attestation","sign_citation":"https://pith.science/pith/ET7MZS7BOYYNV6FHHHH5FSUC23/action/citation_signature","submit_replication":"https://pith.science/pith/ET7MZS7BOYYNV6FHHHH5FSUC23/action/replication_record"}},"created_at":"2026-05-18T00:39:42.293968+00:00","updated_at":"2026-05-18T00:39:42.293968+00:00"}