{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:ET7MZS7BOYYNV6FHHHH5FSUC23","short_pith_number":"pith:ET7MZS7B","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"},"canonical_sha256":"24fecccbe17630daf8a739cfd2ca82d6d4efb0d6c6221a1e88874655c975958b","source":{"kind":"arxiv","id":"1707.07417","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1707.07417","created_at":"2026-05-18T00:39:42Z"},{"alias_kind":"arxiv_version","alias_value":"1707.07417v1","created_at":"2026-05-18T00:39:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1707.07417","created_at":"2026-05-18T00:39:42Z"},{"alias_kind":"pith_short_12","alias_value":"ET7MZS7BOYYN","created_at":"2026-05-18T12:31:12Z"},{"alias_kind":"pith_short_16","alias_value":"ET7MZS7BOYYNV6FH","created_at":"2026-05-18T12:31:12Z"},{"alias_kind":"pith_short_8","alias_value":"ET7MZS7B","created_at":"2026-05-18T12:31:12Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:ET7MZS7BOYYNV6FHHHH5FSUC23","target":"record","payload":{"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"},"canonical_sha256":"24fecccbe17630daf8a739cfd2ca82d6d4efb0d6c6221a1e88874655c975958b","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"},"source_kind":"arxiv","source_id":"1707.07417","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:39:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"laAqJmNrAUNc2oDaBCYV50e9FsowWoVg+Lw/Juo1mGg1x1u0h780W6Cue0HlgPKPNIwSJhvmFbt77lPGFkBPAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T16:20:16.846590Z"},"content_sha256":"ca551d5b911a65dca31ee2f4f3fc86a32dbabc74e188b9b73648db8a888af27a","schema_version":"1.0","event_id":"sha256:ca551d5b911a65dca31ee2f4f3fc86a32dbabc74e188b9b73648db8a888af27a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:ET7MZS7BOYYNV6FHHHH5FSUC23","target":"graph","payload":{"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:39:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6mqdLqMUZJEXxHTM7bMvpxT++OVSFbccYNUwwF+qhjgrzxJqj/JDvZLWZMPhed/JimsUTuoLwAfbih+sKxkfBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T16:20:16.846962Z"},"content_sha256":"b70173eecfcd0837b0aef32496784bd1f1367bde7efaccc8c4b2b163a8955e46","schema_version":"1.0","event_id":"sha256:b70173eecfcd0837b0aef32496784bd1f1367bde7efaccc8c4b2b163a8955e46"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ET7MZS7BOYYNV6FHHHH5FSUC23/bundle.json","state_url":"https://pith.science/pith/ET7MZS7BOYYNV6FHHHH5FSUC23/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ET7MZS7BOYYNV6FHHHH5FSUC23/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-06T16:20:16Z","links":{"resolver":"https://pith.science/pith/ET7MZS7BOYYNV6FHHHH5FSUC23","bundle":"https://pith.science/pith/ET7MZS7BOYYNV6FHHHH5FSUC23/bundle.json","state":"https://pith.science/pith/ET7MZS7BOYYNV6FHHHH5FSUC23/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ET7MZS7BOYYNV6FHHHH5FSUC23/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:ET7MZS7BOYYNV6FHHHH5FSUC23","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":"7c21743ec50f987c857a6b94bc064104d84a1ed633cdbd31e5b56fda8471a535","cross_cats_sorted":["math.AC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2017-07-24T06:32:32Z","title_canon_sha256":"3e6877600024b29c30e671a1831078e9322e1f2d769e80b852aaad55eb753925"},"schema_version":"1.0","source":{"id":"1707.07417","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1707.07417","created_at":"2026-05-18T00:39:42Z"},{"alias_kind":"arxiv_version","alias_value":"1707.07417v1","created_at":"2026-05-18T00:39:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1707.07417","created_at":"2026-05-18T00:39:42Z"},{"alias_kind":"pith_short_12","alias_value":"ET7MZS7BOYYN","created_at":"2026-05-18T12:31:12Z"},{"alias_kind":"pith_short_16","alias_value":"ET7MZS7BOYYNV6FH","created_at":"2026-05-18T12:31:12Z"},{"alias_kind":"pith_short_8","alias_value":"ET7MZS7B","created_at":"2026-05-18T12:31:12Z"}],"graph_snapshots":[{"event_id":"sha256:b70173eecfcd0837b0aef32496784bd1f1367bde7efaccc8c4b2b163a8955e46","target":"graph","created_at":"2026-05-18T00:39:42Z","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 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","authors_text":"Giuseppe Favacchio, Juan Migliore","cross_cats":["math.AC"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2017-07-24T06:32:32Z","title":"Multiprojective spaces and the arithmetically Cohen-Macaulay property"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.07417","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:ca551d5b911a65dca31ee2f4f3fc86a32dbabc74e188b9b73648db8a888af27a","target":"record","created_at":"2026-05-18T00:39:42Z","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":"7c21743ec50f987c857a6b94bc064104d84a1ed633cdbd31e5b56fda8471a535","cross_cats_sorted":["math.AC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2017-07-24T06:32:32Z","title_canon_sha256":"3e6877600024b29c30e671a1831078e9322e1f2d769e80b852aaad55eb753925"},"schema_version":"1.0","source":{"id":"1707.07417","kind":"arxiv","version":1}},"canonical_sha256":"24fecccbe17630daf8a739cfd2ca82d6d4efb0d6c6221a1e88874655c975958b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"24fecccbe17630daf8a739cfd2ca82d6d4efb0d6c6221a1e88874655c975958b","first_computed_at":"2026-05-18T00:39:42.293866Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:39:42.293866Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"bi8H8ywf4+7VcJO1kLxi9gX39BSpebnLrZH7VQl+QOpVog17f3F6UH82FMhZi5HkObrnj9s/w3W/DaAV0rraAg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:39:42.294539Z","signed_message":"canonical_sha256_bytes"},"source_id":"1707.07417","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ca551d5b911a65dca31ee2f4f3fc86a32dbabc74e188b9b73648db8a888af27a","sha256:b70173eecfcd0837b0aef32496784bd1f1367bde7efaccc8c4b2b163a8955e46"],"state_sha256":"dd94ec2f455c34dfe446912a78be8ffdebb5e16f37813ccf458bf32304f693cc"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"k/w9gjOoV0WhnfhRxJpbeB5Mc6mN7Xc26h//OAqfDioaW0SJH5BsscN1J28to+Wp1nUXuIopHmJodM4kGvlxAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-06T16:20:16.849557Z","bundle_sha256":"88c4684f2715963fb67997e849a2c4cb5872b5c307a48a1f89f2f74cffec9fbc"}}