{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:DGW5T4UO5ZGOPVYXDAKFSVTYHM","short_pith_number":"pith:DGW5T4UO","schema_version":"1.0","canonical_sha256":"19add9f28eee4ce7d71718145956783b0ee2578f20f10a4fd418df19762c9d04","source":{"kind":"arxiv","id":"1601.07136","version":1},"attestation_state":"computed","paper":{"title":"Controlling the Dimensions of Formal Fibers of a Unique Factorization Domain at the Height One Prime Ideals","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"David Schwein, Lena Ji, Nina Pande, Peter M. McDonald, Sarah M. Fleming, S. Loepp","submitted_at":"2016-01-26T19:15:50Z","abstract_excerpt":"Let T be a complete local (Noetherian) equidimensional ring with maximal ideal m such that the Krull dimension of T is at least two and the depth of T is at least two. Suppose that no integer of T is a zerodivisor and that |T|=|T/m|. Let d and t be integers such that 1 $\\leq$ d $\\leq$ dimT-1, 0 $\\leq$ t $\\leq$ dimT - 1, and d - 1 $\\leq$ t. Assume that, for every p in AssT, ht(p) $\\leq$ d-1 and that if z is a regular element of T and Q is in Ass(T/zT), then ht(Q) $\\leq$ d. We construct a local unique factorization domain A such that the completion of A is T and such that the dimension of the fo"},"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":"1601.07136","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2016-01-26T19:15:50Z","cross_cats_sorted":[],"title_canon_sha256":"05948c95841437f046fa93214309114b1af581d29dcb540f39aae8ec1ea28a8c","abstract_canon_sha256":"9c662814f2b1d4585ff16110e64919fecf26afff919de339db5e7b0385eeee52"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:21:57.335536Z","signature_b64":"GYoXx2vLbCQ6yEuMuOPQl19xioRJEswQPOg0XHd4EocYxxcjHEPbmQ2pqz23yC8McFqg8JtUXY2RcPnhJHC5DA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"19add9f28eee4ce7d71718145956783b0ee2578f20f10a4fd418df19762c9d04","last_reissued_at":"2026-05-18T01:21:57.334658Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:21:57.334658Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Controlling the Dimensions of Formal Fibers of a Unique Factorization Domain at the Height One Prime Ideals","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"David Schwein, Lena Ji, Nina Pande, Peter M. McDonald, Sarah M. Fleming, S. Loepp","submitted_at":"2016-01-26T19:15:50Z","abstract_excerpt":"Let T be a complete local (Noetherian) equidimensional ring with maximal ideal m such that the Krull dimension of T is at least two and the depth of T is at least two. Suppose that no integer of T is a zerodivisor and that |T|=|T/m|. Let d and t be integers such that 1 $\\leq$ d $\\leq$ dimT-1, 0 $\\leq$ t $\\leq$ dimT - 1, and d - 1 $\\leq$ t. Assume that, for every p in AssT, ht(p) $\\leq$ d-1 and that if z is a regular element of T and Q is in Ass(T/zT), then ht(Q) $\\leq$ d. We construct a local unique factorization domain A such that the completion of A is T and such that the dimension of the fo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.07136","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":"1601.07136","created_at":"2026-05-18T01:21:57.334886+00:00"},{"alias_kind":"arxiv_version","alias_value":"1601.07136v1","created_at":"2026-05-18T01:21:57.334886+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1601.07136","created_at":"2026-05-18T01:21:57.334886+00:00"},{"alias_kind":"pith_short_12","alias_value":"DGW5T4UO5ZGO","created_at":"2026-05-18T12:30:12.583610+00:00"},{"alias_kind":"pith_short_16","alias_value":"DGW5T4UO5ZGOPVYX","created_at":"2026-05-18T12:30:12.583610+00:00"},{"alias_kind":"pith_short_8","alias_value":"DGW5T4UO","created_at":"2026-05-18T12:30:12.583610+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/DGW5T4UO5ZGOPVYXDAKFSVTYHM","json":"https://pith.science/pith/DGW5T4UO5ZGOPVYXDAKFSVTYHM.json","graph_json":"https://pith.science/api/pith-number/DGW5T4UO5ZGOPVYXDAKFSVTYHM/graph.json","events_json":"https://pith.science/api/pith-number/DGW5T4UO5ZGOPVYXDAKFSVTYHM/events.json","paper":"https://pith.science/paper/DGW5T4UO"},"agent_actions":{"view_html":"https://pith.science/pith/DGW5T4UO5ZGOPVYXDAKFSVTYHM","download_json":"https://pith.science/pith/DGW5T4UO5ZGOPVYXDAKFSVTYHM.json","view_paper":"https://pith.science/paper/DGW5T4UO","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1601.07136&json=true","fetch_graph":"https://pith.science/api/pith-number/DGW5T4UO5ZGOPVYXDAKFSVTYHM/graph.json","fetch_events":"https://pith.science/api/pith-number/DGW5T4UO5ZGOPVYXDAKFSVTYHM/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/DGW5T4UO5ZGOPVYXDAKFSVTYHM/action/timestamp_anchor","attest_storage":"https://pith.science/pith/DGW5T4UO5ZGOPVYXDAKFSVTYHM/action/storage_attestation","attest_author":"https://pith.science/pith/DGW5T4UO5ZGOPVYXDAKFSVTYHM/action/author_attestation","sign_citation":"https://pith.science/pith/DGW5T4UO5ZGOPVYXDAKFSVTYHM/action/citation_signature","submit_replication":"https://pith.science/pith/DGW5T4UO5ZGOPVYXDAKFSVTYHM/action/replication_record"}},"created_at":"2026-05-18T01:21:57.334886+00:00","updated_at":"2026-05-18T01:21:57.334886+00:00"}