{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2010:F3JU2J6UV5BU7YQESDBOEBTUEI","short_pith_number":"pith:F3JU2J6U","schema_version":"1.0","canonical_sha256":"2ed34d27d4af434fe20490c2e20674223b7a6e9888f2940008d5cc370f9ba8f7","source":{"kind":"arxiv","id":"1010.1432","version":1},"attestation_state":"computed","paper":{"title":"Minimal and Maximal Operator Spaces and Operator Systems in Entanglement Theory","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA","quant-ph"],"primary_cat":"math.OA","authors_text":"David W. Kribs, Nathaniel Johnston, Rajesh Pereira, Vern I. Paulsen","submitted_at":"2010-10-07T13:48:28Z","abstract_excerpt":"We examine k-minimal and k-maximal operator spaces and operator systems, and investigate their relationships with the separability problem in quantum information theory. We show that the matrix norms that define the k-minimal operator spaces are equal to a family of norms that have been studied independently as a tool for detecting k-positive linear maps and bound entanglement. Similarly, we investigate the k-super minimal and k-super maximal operator systems that were recently introduced and show that their cones of positive elements are exactly the cones of k-block positive operators and (un"},"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":"1010.1432","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2010-10-07T13:48:28Z","cross_cats_sorted":["math.FA","quant-ph"],"title_canon_sha256":"4577c5e88553240002922dbb036a68143a19bcd25a3d6e555682e90a3e847250","abstract_canon_sha256":"c8a339742d52421406527283d4cce03b8846d0c383363ba89183c6730838a99f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:29:55.472202Z","signature_b64":"EROl4mMy/hfVRfs7I6ZuTg34K24zEgtbTCIpy5xUMt0Eo1/jgFYGkFfshZDmQnfFAmm//zo90Vr9NHKtCLrQAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2ed34d27d4af434fe20490c2e20674223b7a6e9888f2940008d5cc370f9ba8f7","last_reissued_at":"2026-05-18T04:29:55.471646Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:29:55.471646Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Minimal and Maximal Operator Spaces and Operator Systems in Entanglement Theory","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA","quant-ph"],"primary_cat":"math.OA","authors_text":"David W. Kribs, Nathaniel Johnston, Rajesh Pereira, Vern I. Paulsen","submitted_at":"2010-10-07T13:48:28Z","abstract_excerpt":"We examine k-minimal and k-maximal operator spaces and operator systems, and investigate their relationships with the separability problem in quantum information theory. We show that the matrix norms that define the k-minimal operator spaces are equal to a family of norms that have been studied independently as a tool for detecting k-positive linear maps and bound entanglement. Similarly, we investigate the k-super minimal and k-super maximal operator systems that were recently introduced and show that their cones of positive elements are exactly the cones of k-block positive operators and (un"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1010.1432","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":"1010.1432","created_at":"2026-05-18T04:29:55.471739+00:00"},{"alias_kind":"arxiv_version","alias_value":"1010.1432v1","created_at":"2026-05-18T04:29:55.471739+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1010.1432","created_at":"2026-05-18T04:29:55.471739+00:00"},{"alias_kind":"pith_short_12","alias_value":"F3JU2J6UV5BU","created_at":"2026-05-18T12:26:06.534383+00:00"},{"alias_kind":"pith_short_16","alias_value":"F3JU2J6UV5BU7YQE","created_at":"2026-05-18T12:26:06.534383+00:00"},{"alias_kind":"pith_short_8","alias_value":"F3JU2J6U","created_at":"2026-05-18T12:26:06.534383+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/F3JU2J6UV5BU7YQESDBOEBTUEI","json":"https://pith.science/pith/F3JU2J6UV5BU7YQESDBOEBTUEI.json","graph_json":"https://pith.science/api/pith-number/F3JU2J6UV5BU7YQESDBOEBTUEI/graph.json","events_json":"https://pith.science/api/pith-number/F3JU2J6UV5BU7YQESDBOEBTUEI/events.json","paper":"https://pith.science/paper/F3JU2J6U"},"agent_actions":{"view_html":"https://pith.science/pith/F3JU2J6UV5BU7YQESDBOEBTUEI","download_json":"https://pith.science/pith/F3JU2J6UV5BU7YQESDBOEBTUEI.json","view_paper":"https://pith.science/paper/F3JU2J6U","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1010.1432&json=true","fetch_graph":"https://pith.science/api/pith-number/F3JU2J6UV5BU7YQESDBOEBTUEI/graph.json","fetch_events":"https://pith.science/api/pith-number/F3JU2J6UV5BU7YQESDBOEBTUEI/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/F3JU2J6UV5BU7YQESDBOEBTUEI/action/timestamp_anchor","attest_storage":"https://pith.science/pith/F3JU2J6UV5BU7YQESDBOEBTUEI/action/storage_attestation","attest_author":"https://pith.science/pith/F3JU2J6UV5BU7YQESDBOEBTUEI/action/author_attestation","sign_citation":"https://pith.science/pith/F3JU2J6UV5BU7YQESDBOEBTUEI/action/citation_signature","submit_replication":"https://pith.science/pith/F3JU2J6UV5BU7YQESDBOEBTUEI/action/replication_record"}},"created_at":"2026-05-18T04:29:55.471739+00:00","updated_at":"2026-05-18T04:29:55.471739+00:00"}