{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:CKO2APHT5FGGTGWZYPS2WPUQNH","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":"6005d22da482c65c810cb14bab04d856c347d062afb71ee617461320e5f864e3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2018-07-03T07:44:09Z","title_canon_sha256":"b272ce8e540c4dcef92bc27e7ed91321e434dc398c4e4f3af5552d075f160a31"},"schema_version":"1.0","source":{"id":"1807.01003","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1807.01003","created_at":"2026-05-18T00:11:45Z"},{"alias_kind":"arxiv_version","alias_value":"1807.01003v1","created_at":"2026-05-18T00:11:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1807.01003","created_at":"2026-05-18T00:11:45Z"},{"alias_kind":"pith_short_12","alias_value":"CKO2APHT5FGG","created_at":"2026-05-18T12:32:16Z"},{"alias_kind":"pith_short_16","alias_value":"CKO2APHT5FGGTGWZ","created_at":"2026-05-18T12:32:16Z"},{"alias_kind":"pith_short_8","alias_value":"CKO2APHT","created_at":"2026-05-18T12:32:16Z"}],"graph_snapshots":[{"event_id":"sha256:24550f9d2450a00468c91843761c7ec6e18601e2f6ca2b590b603f35fd8e01bf","target":"graph","created_at":"2026-05-18T00:11:45Z","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":"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.","authors_text":"Jochen Gl\\\"uck","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2018-07-03T07:44:09Z","title":"A short note on band projections in partially ordered vector spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.01003","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":"sha256:59e55cc98da5f0f1f009a4cf629c09b91904a6d7e2b31634e7573c3a319bdf47","target":"record","created_at":"2026-05-18T00:11:45Z","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":"6005d22da482c65c810cb14bab04d856c347d062afb71ee617461320e5f864e3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2018-07-03T07:44:09Z","title_canon_sha256":"b272ce8e540c4dcef92bc27e7ed91321e434dc398c4e4f3af5552d075f160a31"},"schema_version":"1.0","source":{"id":"1807.01003","kind":"arxiv","version":1}},"canonical_sha256":"129da03cf3e94c699ad9c3e5ab3e9069d334f01465fa3d7ca12bfd126baee0e8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"129da03cf3e94c699ad9c3e5ab3e9069d334f01465fa3d7ca12bfd126baee0e8","first_computed_at":"2026-05-18T00:11:45.715203Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:11:45.715203Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"TFVcXwCFTwQfs5arHlTQNz3PW3rZDgaK4Ioqn83a6kwO7bxNyLNRKbtI5FNR+iT+OIFhCn4+gIq0SNoOqYcWDA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:11:45.715882Z","signed_message":"canonical_sha256_bytes"},"source_id":"1807.01003","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:59e55cc98da5f0f1f009a4cf629c09b91904a6d7e2b31634e7573c3a319bdf47","sha256:24550f9d2450a00468c91843761c7ec6e18601e2f6ca2b590b603f35fd8e01bf"],"state_sha256":"e44c91aeb93d4a07f2f5b66125f8fcf1d8515b2f2aeff1f812f681369d656edf"}