{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:7DME52Z6CG52WR4PZVU2NQFSFH","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":"f609b3eb536ae79bf372795311e10b0038af119b17e87ee2e49c8c953e68c26f","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2012-09-04T15:29:22Z","title_canon_sha256":"1f619c814966b0c5a8ad7b4688b4cefa5395eca1700337017d85f6164fd6eb66"},"schema_version":"1.0","source":{"id":"1209.0672","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1209.0672","created_at":"2026-05-18T02:29:25Z"},{"alias_kind":"arxiv_version","alias_value":"1209.0672v1","created_at":"2026-05-18T02:29:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1209.0672","created_at":"2026-05-18T02:29:25Z"},{"alias_kind":"pith_short_12","alias_value":"7DME52Z6CG52","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_16","alias_value":"7DME52Z6CG52WR4P","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_8","alias_value":"7DME52Z6","created_at":"2026-05-18T12:26:56Z"}],"graph_snapshots":[{"event_id":"sha256:99d8da29dea77431dd388484b55eaff2d8438878ae275a5665de9407c9f3b77f","target":"graph","created_at":"2026-05-18T02:29:25Z","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 2007, Y. Shimoda, in connection with a long-standing question of J. Sally, asked whether a Noetherian local ring, such that all its prime ideals different from the maximal ideal are complete intersections, has Krull dimension at most two. In this paper, having reduced the conjecture to the case of dimension three, if the ring is regular and local of dimension three, we explicitly describe a family of prime ideals of height two minimally generated by three elements. Weakening the hypothesis of regularity, we find that, to achieve the same end, we need to add extra hypotheses, such as complet","authors_text":"Francesc Planas-Vilanova, Liam O'Carroll, Shiro Goto","cross_cats":["math.AG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2012-09-04T15:29:22Z","title":"J. Sally's question and a conjecture of Y. Shimoda"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1209.0672","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":"sha256:801a24cb05ab3e9c902ba9cbc547a801e02f50b9626d4e51aa584384d97f2e27","target":"record","created_at":"2026-05-18T02:29:25Z","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":"f609b3eb536ae79bf372795311e10b0038af119b17e87ee2e49c8c953e68c26f","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2012-09-04T15:29:22Z","title_canon_sha256":"1f619c814966b0c5a8ad7b4688b4cefa5395eca1700337017d85f6164fd6eb66"},"schema_version":"1.0","source":{"id":"1209.0672","kind":"arxiv","version":1}},"canonical_sha256":"f8d84eeb3e11bbab478fcd69a6c0b229c86f6b6888f30730183638c0386a6804","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f8d84eeb3e11bbab478fcd69a6c0b229c86f6b6888f30730183638c0386a6804","first_computed_at":"2026-05-18T02:29:25.385481Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:29:25.385481Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"AeEzOcVwOC105l5UUmSfWiS1BlVFf+417lGjvGgCPul1nzXkjmrefQd0ipzMvbpUX6rMPWw6pXIlwuIgy6oCAw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:29:25.385964Z","signed_message":"canonical_sha256_bytes"},"source_id":"1209.0672","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:801a24cb05ab3e9c902ba9cbc547a801e02f50b9626d4e51aa584384d97f2e27","sha256:99d8da29dea77431dd388484b55eaff2d8438878ae275a5665de9407c9f3b77f"],"state_sha256":"81bd2ee47f0d887c828b9b8560ba86cf1665d4899adc6aa28d330b9ab12dd30c"}