{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:CKO2APHT5FGGTGWZYPS2WPUQNH","short_pith_number":"pith:CKO2APHT","schema_version":"1.0","canonical_sha256":"129da03cf3e94c699ad9c3e5ab3e9069d334f01465fa3d7ca12bfd126baee0e8","source":{"kind":"arxiv","id":"1807.01003","version":1},"attestation_state":"computed","paper":{"title":"A short note on band projections in partially ordered vector spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Jochen Gl\\\"uck","submitted_at":"2018-07-03T07:44:09Z","abstract_excerpt":"Consider an Archimedean partially ordered vector space $X$ with generating cone (or, more generally, a pre-Riesz space $X$). Let $P$ be a linear projection on $X$ such that both $P$ and its complementary projection $I - P$ are positive; we prove that the range of $P$ is a band. This shows that the well-known concept of band projections on vector lattices can, to a certain extent, be transferred to the framework of ordered vector spaces."},"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":"1807.01003","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2018-07-03T07:44:09Z","cross_cats_sorted":[],"title_canon_sha256":"b272ce8e540c4dcef92bc27e7ed91321e434dc398c4e4f3af5552d075f160a31","abstract_canon_sha256":"6005d22da482c65c810cb14bab04d856c347d062afb71ee617461320e5f864e3"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:11:45.715882Z","signature_b64":"TFVcXwCFTwQfs5arHlTQNz3PW3rZDgaK4Ioqn83a6kwO7bxNyLNRKbtI5FNR+iT+OIFhCn4+gIq0SNoOqYcWDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"129da03cf3e94c699ad9c3e5ab3e9069d334f01465fa3d7ca12bfd126baee0e8","last_reissued_at":"2026-05-18T00:11:45.715203Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:11:45.715203Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A short note on band projections in partially ordered vector spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Jochen Gl\\\"uck","submitted_at":"2018-07-03T07:44:09Z","abstract_excerpt":"Consider an Archimedean partially ordered vector space $X$ with generating cone (or, more generally, a pre-Riesz space $X$). Let $P$ be a linear projection on $X$ such that both $P$ and its complementary projection $I - P$ are positive; we prove that the range of $P$ is a band. This shows that the well-known concept of band projections on vector lattices can, to a certain extent, be transferred to the framework of ordered vector spaces."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.01003","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1807.01003","created_at":"2026-05-18T00:11:45.715301+00:00"},{"alias_kind":"arxiv_version","alias_value":"1807.01003v1","created_at":"2026-05-18T00:11:45.715301+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1807.01003","created_at":"2026-05-18T00:11:45.715301+00:00"},{"alias_kind":"pith_short_12","alias_value":"CKO2APHT5FGG","created_at":"2026-05-18T12:32:16.446611+00:00"},{"alias_kind":"pith_short_16","alias_value":"CKO2APHT5FGGTGWZ","created_at":"2026-05-18T12:32:16.446611+00:00"},{"alias_kind":"pith_short_8","alias_value":"CKO2APHT","created_at":"2026-05-18T12:32:16.446611+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/CKO2APHT5FGGTGWZYPS2WPUQNH","json":"https://pith.science/pith/CKO2APHT5FGGTGWZYPS2WPUQNH.json","graph_json":"https://pith.science/api/pith-number/CKO2APHT5FGGTGWZYPS2WPUQNH/graph.json","events_json":"https://pith.science/api/pith-number/CKO2APHT5FGGTGWZYPS2WPUQNH/events.json","paper":"https://pith.science/paper/CKO2APHT"},"agent_actions":{"view_html":"https://pith.science/pith/CKO2APHT5FGGTGWZYPS2WPUQNH","download_json":"https://pith.science/pith/CKO2APHT5FGGTGWZYPS2WPUQNH.json","view_paper":"https://pith.science/paper/CKO2APHT","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1807.01003&json=true","fetch_graph":"https://pith.science/api/pith-number/CKO2APHT5FGGTGWZYPS2WPUQNH/graph.json","fetch_events":"https://pith.science/api/pith-number/CKO2APHT5FGGTGWZYPS2WPUQNH/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/CKO2APHT5FGGTGWZYPS2WPUQNH/action/timestamp_anchor","attest_storage":"https://pith.science/pith/CKO2APHT5FGGTGWZYPS2WPUQNH/action/storage_attestation","attest_author":"https://pith.science/pith/CKO2APHT5FGGTGWZYPS2WPUQNH/action/author_attestation","sign_citation":"https://pith.science/pith/CKO2APHT5FGGTGWZYPS2WPUQNH/action/citation_signature","submit_replication":"https://pith.science/pith/CKO2APHT5FGGTGWZYPS2WPUQNH/action/replication_record"}},"created_at":"2026-05-18T00:11:45.715301+00:00","updated_at":"2026-05-18T00:11:45.715301+00:00"}