{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:MRDKRWMYX2BJOJV6R5DFXPUYHD","short_pith_number":"pith:MRDKRWMY","canonical_record":{"source":{"id":"1508.07624","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-08-30T19:37:22Z","cross_cats_sorted":[],"title_canon_sha256":"dc751ac63a5ddaa8683f48a407155134719da55ea4ce10f5e867466acfc88dde","abstract_canon_sha256":"85e7de2bc04b4044b6ef587177cb8eb674c4c48e8a48a0d5b51550d0d9814254"},"schema_version":"1.0"},"canonical_sha256":"6446a8d998be829726be8f465bbe9838cf73553813f731d99d19f5db1a8efae3","source":{"kind":"arxiv","id":"1508.07624","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"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:MRDKRWMYX2BJOJV6R5DFXPUYHD","target":"record","payload":{"canonical_record":{"source":{"id":"1508.07624","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-08-30T19:37:22Z","cross_cats_sorted":[],"title_canon_sha256":"dc751ac63a5ddaa8683f48a407155134719da55ea4ce10f5e867466acfc88dde","abstract_canon_sha256":"85e7de2bc04b4044b6ef587177cb8eb674c4c48e8a48a0d5b51550d0d9814254"},"schema_version":"1.0"},"canonical_sha256":"6446a8d998be829726be8f465bbe9838cf73553813f731d99d19f5db1a8efae3","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:34:31.825767Z","signature_b64":"88aw4wjPgDU7fdYWwUA7mSSEHBkD+8DaWp1AAERaIMW8K/yU3cdJeOij2lg8V9uwJcpXNNfyt4Ly0kmzAw54BA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6446a8d998be829726be8f465bbe9838cf73553813f731d99d19f5db1a8efae3","last_reissued_at":"2026-05-18T01:34:31.825083Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:34:31.825083Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1508.07624","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":"2026-05-18T01:34:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Ij1lC+rlHWo1IOMJLCvG1VyT0x7X4LvHnmTgXM6VHakAPeath6FJb28DwU/JuCWLKLj+1DHEuBUq0/1a8fBcDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T11:56:30.151114Z"},"content_sha256":"97646e907b5ebb610de585ff0fbd366d264310c55a3c0ebe1ed300420ae5c6fb","schema_version":"1.0","event_id":"sha256:97646e907b5ebb610de585ff0fbd366d264310c55a3c0ebe1ed300420ae5c6fb"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:MRDKRWMYX2BJOJV6R5DFXPUYHD","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Some finiteness results on monogenic orders in positive characteristic","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Jason P. Bell, Khoa D. Nguyen","submitted_at":"2015-08-30T19:37:22Z","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"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.07624","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":"2026-05-18T01:34:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"basDsjPmMKP9sRNk20h3YyJ2LwslGzEIAN0ECBYdwpuhw63ZKlG8KMiLsrPf1blqCQxn/PRlQlsjUntI8dkVDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T11:56:30.151737Z"},"content_sha256":"da6e3df2557e8c176e1dc5f098d8ca1297a804e0d3ee6a426caea0ca12d9a499","schema_version":"1.0","event_id":"sha256:da6e3df2557e8c176e1dc5f098d8ca1297a804e0d3ee6a426caea0ca12d9a499"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/MRDKRWMYX2BJOJV6R5DFXPUYHD/bundle.json","state_url":"https://pith.science/pith/MRDKRWMYX2BJOJV6R5DFXPUYHD/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/MRDKRWMYX2BJOJV6R5DFXPUYHD/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":"2026-05-27T11:56:30Z","links":{"resolver":"https://pith.science/pith/MRDKRWMYX2BJOJV6R5DFXPUYHD","bundle":"https://pith.science/pith/MRDKRWMYX2BJOJV6R5DFXPUYHD/bundle.json","state":"https://pith.science/pith/MRDKRWMYX2BJOJV6R5DFXPUYHD/state.json","well_known_bundle":"https://pith.science/.well-known/pith/MRDKRWMYX2BJOJV6R5DFXPUYHD/bundle.json"},"state":{"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"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Zv8HAPhnkktOYQZ5aWZqASYv12EFqPHHC/4Fb9PQNBRtoIKjg9egyBZ1w8xG+aGNwba+0H5C+6E1TRl1ATowBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T11:56:30.154933Z","bundle_sha256":"4a0c0a0fe61e28d29655e373d12870fe0ae1a2dc8e50fc9eede46391c3e3b41c"}}