{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:MRDKRWMYX2BJOJV6R5DFXPUYHD","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":"85e7de2bc04b4044b6ef587177cb8eb674c4c48e8a48a0d5b51550d0d9814254","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-08-30T19:37:22Z","title_canon_sha256":"dc751ac63a5ddaa8683f48a407155134719da55ea4ce10f5e867466acfc88dde"},"schema_version":"1.0","source":{"id":"1508.07624","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1508.07624","created_at":"2026-05-18T01:34:31Z"},{"alias_kind":"arxiv_version","alias_value":"1508.07624v1","created_at":"2026-05-18T01:34:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1508.07624","created_at":"2026-05-18T01:34:31Z"},{"alias_kind":"pith_short_12","alias_value":"MRDKRWMYX2BJ","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_16","alias_value":"MRDKRWMYX2BJOJV6","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_8","alias_value":"MRDKRWMY","created_at":"2026-05-18T12:29:32Z"}],"graph_snapshots":[{"event_id":"sha256:da6e3df2557e8c176e1dc5f098d8ca1297a804e0d3ee6a426caea0ca12d9a499","target":"graph","created_at":"2026-05-18T01:34:31Z","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":"This work is motivated by the papers [EG85] and [Ngu15] in which the following two problems are solved. Let $\\mathcal{O}$ is a finitely generated $\\mathbb{Z}$-algebra that is an integrally closed domain of characteristic zero, consider the following problems:\n  (A) Fix $s$ that is integral over $\\mathcal{O}$, describe all $t$ such that $\\mathcal{O}[s]=\\mathcal{O}[t]$.\n  (B) Fix $s$ and $t$ that are integral over $\\mathcal{O}$, describe all pairs $(m,n)\\in\\mathbb{N}^2$ such that $\\mathcal{O}[s^m]=\\mathcal{O}[t^n]$.\n  In this paper, we solve these problems and provide a uniform bound for a certa","authors_text":"Jason P. Bell, Khoa D. Nguyen","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-08-30T19:37:22Z","title":"Some finiteness results on monogenic orders in positive characteristic"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.07624","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":"sha256:97646e907b5ebb610de585ff0fbd366d264310c55a3c0ebe1ed300420ae5c6fb","target":"record","created_at":"2026-05-18T01:34:31Z","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":"85e7de2bc04b4044b6ef587177cb8eb674c4c48e8a48a0d5b51550d0d9814254","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-08-30T19:37:22Z","title_canon_sha256":"dc751ac63a5ddaa8683f48a407155134719da55ea4ce10f5e867466acfc88dde"},"schema_version":"1.0","source":{"id":"1508.07624","kind":"arxiv","version":1}},"canonical_sha256":"6446a8d998be829726be8f465bbe9838cf73553813f731d99d19f5db1a8efae3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6446a8d998be829726be8f465bbe9838cf73553813f731d99d19f5db1a8efae3","first_computed_at":"2026-05-18T01:34:31.825083Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:34:31.825083Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"88aw4wjPgDU7fdYWwUA7mSSEHBkD+8DaWp1AAERaIMW8K/yU3cdJeOij2lg8V9uwJcpXNNfyt4Ly0kmzAw54BA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:34:31.825767Z","signed_message":"canonical_sha256_bytes"},"source_id":"1508.07624","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:97646e907b5ebb610de585ff0fbd366d264310c55a3c0ebe1ed300420ae5c6fb","sha256:da6e3df2557e8c176e1dc5f098d8ca1297a804e0d3ee6a426caea0ca12d9a499"],"state_sha256":"5237a457855cf9b5b75f6b871a51e94c253fe067ab0df85ac1f121d535acf8d5"}