{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:RCELX6AKEBA64VCTH5MAUAZMMD","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":"bcd027b2fa413c10fbc945e06c0ea6e43672423a83183332f4deb38a0f2090c3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2009-04-24T02:51:39Z","title_canon_sha256":"97c628fc9ef19608fb8b44fe936b62b20e89dd2c18382a3181adee1b636f8540"},"schema_version":"1.0","source":{"id":"0904.3783","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0904.3783","created_at":"2026-05-18T02:58:03Z"},{"alias_kind":"arxiv_version","alias_value":"0904.3783v2","created_at":"2026-05-18T02:58:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0904.3783","created_at":"2026-05-18T02:58:03Z"},{"alias_kind":"pith_short_12","alias_value":"RCELX6AKEBA6","created_at":"2026-05-18T12:26:01Z"},{"alias_kind":"pith_short_16","alias_value":"RCELX6AKEBA64VCT","created_at":"2026-05-18T12:26:01Z"},{"alias_kind":"pith_short_8","alias_value":"RCELX6AK","created_at":"2026-05-18T12:26:01Z"}],"graph_snapshots":[{"event_id":"sha256:29b20f8aa688fe96e852fa46fc71274a5ed6fc4556751654b3177e85810b6e16","target":"graph","created_at":"2026-05-18T02:58:03Z","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":"Given an Archimedean order unit space (V,V^+,e), we construct a minimal operator system OMIN(V) and a maximal operator system OMAX(V), which are the analogues of the minimal and maximal operator spaces of a normed space. We develop some of the key properties of these operator systems and make some progress on characterizing when an operator system S is completely boundedly isomorphic to either OMIN(S) or to OMAX(S). We then apply these concepts to the study of entanglement breaking maps. We prove that for matrix algebras a linear map is completely positive from OMIN(M_n) to OMAX(M_m) if and on","authors_text":"Ivan Todorov, Mark Tomforde, Vern Paulsen","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2009-04-24T02:51:39Z","title":"Operator system structures on ordered spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0904.3783","kind":"arxiv","version":2},"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":"sha256:2ab4dbd77d96f82afb0cc5c211f5a600f9844d0353f629f02ea0b5c7a52d2a89","target":"record","created_at":"2026-05-18T02:58:03Z","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":"bcd027b2fa413c10fbc945e06c0ea6e43672423a83183332f4deb38a0f2090c3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2009-04-24T02:51:39Z","title_canon_sha256":"97c628fc9ef19608fb8b44fe936b62b20e89dd2c18382a3181adee1b636f8540"},"schema_version":"1.0","source":{"id":"0904.3783","kind":"arxiv","version":2}},"canonical_sha256":"8888bbf80a2041ee54533f580a032c60e70b71819649ba2f570002d724e6b391","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8888bbf80a2041ee54533f580a032c60e70b71819649ba2f570002d724e6b391","first_computed_at":"2026-05-18T02:58:03.332131Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:58:03.332131Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"uytZxSXN25nGzbi1bW0LVUfcwYw9XPc6+P/d44Gc8heXneuve0cAcZDje4xzCOdFyPvxoU3rAzbaAAw0h8QFBA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:58:03.333009Z","signed_message":"canonical_sha256_bytes"},"source_id":"0904.3783","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2ab4dbd77d96f82afb0cc5c211f5a600f9844d0353f629f02ea0b5c7a52d2a89","sha256:29b20f8aa688fe96e852fa46fc71274a5ed6fc4556751654b3177e85810b6e16"],"state_sha256":"c3aa23b0cd5f708a7dd539766bc76b28168bae0deb4b5d9dc8b8c5f0d0dc560d"}