{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:ZRMJOHX4J52PVVTLZVDTIRRJFY","short_pith_number":"pith:ZRMJOHX4","schema_version":"1.0","canonical_sha256":"cc58971efc4f74fad66bcd473446292e1ab4bb36eaf45fe3e5afad3b7787e93d","source":{"kind":"arxiv","id":"1605.04769","version":3},"attestation_state":"computed","paper":{"title":"The minimal free resolution of fat almost complete intersections in $\\mathbb{P}^1\\times\\mathbb{P}^1$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AC"],"primary_cat":"math.AG","authors_text":"Elena Guardo, Giuseppe Favacchio","submitted_at":"2016-05-16T13:39:06Z","abstract_excerpt":"A current research theme is to compare symbolic powers of an ideal $I$ with the regular powers of $I$. In this paper, we focus on the case that $I=I_X$ is an ideal defining an almost complete intersection (ACI) sets of points $X$ in $\\mathbb{P}^1\\times\\mathbb{P}^1$. In particular, we describe a minimal free bigraded resolution of a non arithmetically Cohen-Macaulay (also non homogeneus) set of fat points $\\mathcal Z$ whose support is an ACI. We call $\\mathcal Z$ a fat ACI. We also show that its symbolic and ordinary powers are equal, i.e, $I_{\\mathcal Z}^{(m)}=I_{\\mathcal Z}^{m}$ for any $m\\ge"},"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":"1605.04769","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2016-05-16T13:39:06Z","cross_cats_sorted":["math.AC"],"title_canon_sha256":"5886cb9108968a950661edea188ad54b78274a20eaa2efc19e4fec41d605f534","abstract_canon_sha256":"ccdf1bcb24ef9b990804d8221a6bd60fd297eb9ca86627fd36e04bb70f9f2f82"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:00:35.115775Z","signature_b64":"w1H2XRo7Ppwx37U0dVuI1IQZ/nPxAESIXrtPIlYcSm2wfIKjz/AlBW9EsO+ileuX4a28evNfW9Xo3s6ICq7zDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cc58971efc4f74fad66bcd473446292e1ab4bb36eaf45fe3e5afad3b7787e93d","last_reissued_at":"2026-05-18T01:00:35.115092Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:00:35.115092Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The minimal free resolution of fat almost complete intersections in $\\mathbb{P}^1\\times\\mathbb{P}^1$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AC"],"primary_cat":"math.AG","authors_text":"Elena Guardo, Giuseppe Favacchio","submitted_at":"2016-05-16T13:39:06Z","abstract_excerpt":"A current research theme is to compare symbolic powers of an ideal $I$ with the regular powers of $I$. In this paper, we focus on the case that $I=I_X$ is an ideal defining an almost complete intersection (ACI) sets of points $X$ in $\\mathbb{P}^1\\times\\mathbb{P}^1$. In particular, we describe a minimal free bigraded resolution of a non arithmetically Cohen-Macaulay (also non homogeneus) set of fat points $\\mathcal Z$ whose support is an ACI. We call $\\mathcal Z$ a fat ACI. We also show that its symbolic and ordinary powers are equal, i.e, $I_{\\mathcal Z}^{(m)}=I_{\\mathcal Z}^{m}$ for any $m\\ge"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.04769","kind":"arxiv","version":3},"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":"1605.04769","created_at":"2026-05-18T01:00:35.115194+00:00"},{"alias_kind":"arxiv_version","alias_value":"1605.04769v3","created_at":"2026-05-18T01:00:35.115194+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1605.04769","created_at":"2026-05-18T01:00:35.115194+00:00"},{"alias_kind":"pith_short_12","alias_value":"ZRMJOHX4J52P","created_at":"2026-05-18T12:30:55.937587+00:00"},{"alias_kind":"pith_short_16","alias_value":"ZRMJOHX4J52PVVTL","created_at":"2026-05-18T12:30:55.937587+00:00"},{"alias_kind":"pith_short_8","alias_value":"ZRMJOHX4","created_at":"2026-05-18T12:30:55.937587+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/ZRMJOHX4J52PVVTLZVDTIRRJFY","json":"https://pith.science/pith/ZRMJOHX4J52PVVTLZVDTIRRJFY.json","graph_json":"https://pith.science/api/pith-number/ZRMJOHX4J52PVVTLZVDTIRRJFY/graph.json","events_json":"https://pith.science/api/pith-number/ZRMJOHX4J52PVVTLZVDTIRRJFY/events.json","paper":"https://pith.science/paper/ZRMJOHX4"},"agent_actions":{"view_html":"https://pith.science/pith/ZRMJOHX4J52PVVTLZVDTIRRJFY","download_json":"https://pith.science/pith/ZRMJOHX4J52PVVTLZVDTIRRJFY.json","view_paper":"https://pith.science/paper/ZRMJOHX4","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1605.04769&json=true","fetch_graph":"https://pith.science/api/pith-number/ZRMJOHX4J52PVVTLZVDTIRRJFY/graph.json","fetch_events":"https://pith.science/api/pith-number/ZRMJOHX4J52PVVTLZVDTIRRJFY/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ZRMJOHX4J52PVVTLZVDTIRRJFY/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ZRMJOHX4J52PVVTLZVDTIRRJFY/action/storage_attestation","attest_author":"https://pith.science/pith/ZRMJOHX4J52PVVTLZVDTIRRJFY/action/author_attestation","sign_citation":"https://pith.science/pith/ZRMJOHX4J52PVVTLZVDTIRRJFY/action/citation_signature","submit_replication":"https://pith.science/pith/ZRMJOHX4J52PVVTLZVDTIRRJFY/action/replication_record"}},"created_at":"2026-05-18T01:00:35.115194+00:00","updated_at":"2026-05-18T01:00:35.115194+00:00"}