{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2023:7TE3IUMO5UJSUAZEFS7IFQNBLW","short_pith_number":"pith:7TE3IUMO","schema_version":"1.0","canonical_sha256":"fcc9b4518eed132a03242cbe82c1a15d931fe9373a2b31ebb099caa4324924b0","source":{"kind":"arxiv","id":"2311.15797","version":1},"attestation_state":"computed","paper":{"title":"Controlling Formal Fibers of Countably Many Principal Prime Ideals","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Ammar Eltigani, AnaMaria Perez, David Baron, M. Teplitskiy, S. Loepp","submitted_at":"2023-11-27T13:20:24Z","abstract_excerpt":"Let $T$ be a complete local (Noetherian) ring. For each $i \\in \\mathbb{N}$, let $C_i$ be a nonempty countable set of nonmaximal pairwise incomparable prime ideals of $T$, and suppose that if $i \\neq j$, then either $C_i = C_j$ or no element of $C_i$ is contained in an element of $C_j$. We provide necessary and sufficient conditions for $T$ to be the completion of a local integral domain $A$ satisfying the condition that, for all $i \\in \\mathbb{N}$, there is a nonzero prime element $p_i$ of $A$, such that $C_i$ is exactly the set of maximal elements of the formal fiber of $A$ at $p_iA$. We then"},"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":"2311.15797","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2023-11-27T13:20:24Z","cross_cats_sorted":[],"title_canon_sha256":"62dd6192ad9d6ea4167b248e7d6f1470ad65bad49b658204550eb3789fe5515e","abstract_canon_sha256":"6720b94269fc952ea2fda60073890b023466bcf0e25ce1eee9dc9dd30e62c2a4"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T07:17:09.667923Z","signature_b64":"3NktBMqlsQJGAUMJYDDq2DeQwqCPmY3hqa3yNQgcIqQrRSZE+d9cFzVs57wyBzAo8+IgHpG3t0KbN4w3sTC9BQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fcc9b4518eed132a03242cbe82c1a15d931fe9373a2b31ebb099caa4324924b0","last_reissued_at":"2026-07-05T07:17:09.667413Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T07:17:09.667413Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Controlling Formal Fibers of Countably Many Principal Prime Ideals","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Ammar Eltigani, AnaMaria Perez, David Baron, M. Teplitskiy, S. Loepp","submitted_at":"2023-11-27T13:20:24Z","abstract_excerpt":"Let $T$ be a complete local (Noetherian) ring. For each $i \\in \\mathbb{N}$, let $C_i$ be a nonempty countable set of nonmaximal pairwise incomparable prime ideals of $T$, and suppose that if $i \\neq j$, then either $C_i = C_j$ or no element of $C_i$ is contained in an element of $C_j$. We provide necessary and sufficient conditions for $T$ to be the completion of a local integral domain $A$ satisfying the condition that, for all $i \\in \\mathbb{N}$, there is a nonzero prime element $p_i$ of $A$, such that $C_i$ is exactly the set of maximal elements of the formal fiber of $A$ at $p_iA$. We then"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2311.15797","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2311.15797/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2311.15797","created_at":"2026-07-05T07:17:09.667473+00:00"},{"alias_kind":"arxiv_version","alias_value":"2311.15797v1","created_at":"2026-07-05T07:17:09.667473+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2311.15797","created_at":"2026-07-05T07:17:09.667473+00:00"},{"alias_kind":"pith_short_12","alias_value":"7TE3IUMO5UJS","created_at":"2026-07-05T07:17:09.667473+00:00"},{"alias_kind":"pith_short_16","alias_value":"7TE3IUMO5UJSUAZE","created_at":"2026-07-05T07:17:09.667473+00:00"},{"alias_kind":"pith_short_8","alias_value":"7TE3IUMO","created_at":"2026-07-05T07:17:09.667473+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/7TE3IUMO5UJSUAZEFS7IFQNBLW","json":"https://pith.science/pith/7TE3IUMO5UJSUAZEFS7IFQNBLW.json","graph_json":"https://pith.science/api/pith-number/7TE3IUMO5UJSUAZEFS7IFQNBLW/graph.json","events_json":"https://pith.science/api/pith-number/7TE3IUMO5UJSUAZEFS7IFQNBLW/events.json","paper":"https://pith.science/paper/7TE3IUMO"},"agent_actions":{"view_html":"https://pith.science/pith/7TE3IUMO5UJSUAZEFS7IFQNBLW","download_json":"https://pith.science/pith/7TE3IUMO5UJSUAZEFS7IFQNBLW.json","view_paper":"https://pith.science/paper/7TE3IUMO","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2311.15797&json=true","fetch_graph":"https://pith.science/api/pith-number/7TE3IUMO5UJSUAZEFS7IFQNBLW/graph.json","fetch_events":"https://pith.science/api/pith-number/7TE3IUMO5UJSUAZEFS7IFQNBLW/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/7TE3IUMO5UJSUAZEFS7IFQNBLW/action/timestamp_anchor","attest_storage":"https://pith.science/pith/7TE3IUMO5UJSUAZEFS7IFQNBLW/action/storage_attestation","attest_author":"https://pith.science/pith/7TE3IUMO5UJSUAZEFS7IFQNBLW/action/author_attestation","sign_citation":"https://pith.science/pith/7TE3IUMO5UJSUAZEFS7IFQNBLW/action/citation_signature","submit_replication":"https://pith.science/pith/7TE3IUMO5UJSUAZEFS7IFQNBLW/action/replication_record"}},"created_at":"2026-07-05T07:17:09.667473+00:00","updated_at":"2026-07-05T07:17:09.667473+00:00"}