{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:4R6RIWU5PFWOGDHUCPVBP4INNB","short_pith_number":"pith:4R6RIWU5","schema_version":"1.0","canonical_sha256":"e47d145a9d796ce30cf413ea17f10d68530ceae8d0ac4b6e1144f5469533cf3b","source":{"kind":"arxiv","id":"1801.07191","version":2},"attestation_state":"computed","paper":{"title":"Vector lattice covers of ideals and bands in pre-Riesz spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Anke Kalauch, Helena Malinowski","submitted_at":"2018-01-22T16:53:33Z","abstract_excerpt":"Pre-Riesz spaces are ordered vector spaces which can be order densely embedded into vector lattices, their so-called vector lattice covers. Given a vector lattice cover $Y$ for a pre-Riesz space $X$, we address the question how to find vector lattice covers for subspaces of $X$, such as ideals and bands. We provide conditions such that for a directed ideal $I$ in $X$ its smallest extension ideal in $Y$ is a vector lattice cover. We show a criterion for bands in $X$ and their extension bands in $Y$ as well. Moreover, we state properties of ideals and bands in $X$ which are generated by sets, an"},"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":"1801.07191","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2018-01-22T16:53:33Z","cross_cats_sorted":[],"title_canon_sha256":"2867c78e451232e8864223ee9a4498c5d7510e91005187e029e1050d2e4b0683","abstract_canon_sha256":"fea5e69e92f4a0aae4c9ea9956ccc60b4a66ae98b0f8a4c2d58c85a135086be3"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:01:15.165349Z","signature_b64":"b3L8DaXyGF7dMgxe5PgmkvdKkSnoFY4eWGDiI2kgQ6tjUEWefIAuiVDkXJRqLT8pPwPuiIyTgP4t1/uD/KNYBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e47d145a9d796ce30cf413ea17f10d68530ceae8d0ac4b6e1144f5469533cf3b","last_reissued_at":"2026-05-18T00:01:15.164737Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:01:15.164737Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Vector lattice covers of ideals and bands in pre-Riesz spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Anke Kalauch, Helena Malinowski","submitted_at":"2018-01-22T16:53:33Z","abstract_excerpt":"Pre-Riesz spaces are ordered vector spaces which can be order densely embedded into vector lattices, their so-called vector lattice covers. Given a vector lattice cover $Y$ for a pre-Riesz space $X$, we address the question how to find vector lattice covers for subspaces of $X$, such as ideals and bands. We provide conditions such that for a directed ideal $I$ in $X$ its smallest extension ideal in $Y$ is a vector lattice cover. We show a criterion for bands in $X$ and their extension bands in $Y$ as well. Moreover, we state properties of ideals and bands in $X$ which are generated by sets, an"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.07191","kind":"arxiv","version":2},"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":"1801.07191","created_at":"2026-05-18T00:01:15.164833+00:00"},{"alias_kind":"arxiv_version","alias_value":"1801.07191v2","created_at":"2026-05-18T00:01:15.164833+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1801.07191","created_at":"2026-05-18T00:01:15.164833+00:00"},{"alias_kind":"pith_short_12","alias_value":"4R6RIWU5PFWO","created_at":"2026-05-18T12:32:05.422762+00:00"},{"alias_kind":"pith_short_16","alias_value":"4R6RIWU5PFWOGDHU","created_at":"2026-05-18T12:32:05.422762+00:00"},{"alias_kind":"pith_short_8","alias_value":"4R6RIWU5","created_at":"2026-05-18T12:32:05.422762+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/4R6RIWU5PFWOGDHUCPVBP4INNB","json":"https://pith.science/pith/4R6RIWU5PFWOGDHUCPVBP4INNB.json","graph_json":"https://pith.science/api/pith-number/4R6RIWU5PFWOGDHUCPVBP4INNB/graph.json","events_json":"https://pith.science/api/pith-number/4R6RIWU5PFWOGDHUCPVBP4INNB/events.json","paper":"https://pith.science/paper/4R6RIWU5"},"agent_actions":{"view_html":"https://pith.science/pith/4R6RIWU5PFWOGDHUCPVBP4INNB","download_json":"https://pith.science/pith/4R6RIWU5PFWOGDHUCPVBP4INNB.json","view_paper":"https://pith.science/paper/4R6RIWU5","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1801.07191&json=true","fetch_graph":"https://pith.science/api/pith-number/4R6RIWU5PFWOGDHUCPVBP4INNB/graph.json","fetch_events":"https://pith.science/api/pith-number/4R6RIWU5PFWOGDHUCPVBP4INNB/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/4R6RIWU5PFWOGDHUCPVBP4INNB/action/timestamp_anchor","attest_storage":"https://pith.science/pith/4R6RIWU5PFWOGDHUCPVBP4INNB/action/storage_attestation","attest_author":"https://pith.science/pith/4R6RIWU5PFWOGDHUCPVBP4INNB/action/author_attestation","sign_citation":"https://pith.science/pith/4R6RIWU5PFWOGDHUCPVBP4INNB/action/citation_signature","submit_replication":"https://pith.science/pith/4R6RIWU5PFWOGDHUCPVBP4INNB/action/replication_record"}},"created_at":"2026-05-18T00:01:15.164833+00:00","updated_at":"2026-05-18T00:01:15.164833+00:00"}