{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:RJ4EH33SF72SZHU5HUBGG7I4J2","short_pith_number":"pith:RJ4EH33S","schema_version":"1.0","canonical_sha256":"8a7843ef722ff52c9e9d3d02637d1c4e82e5e7e0adb4a5d4595da1346649d342","source":{"kind":"arxiv","id":"1305.2435","version":1},"attestation_state":"computed","paper":{"title":"A few algebraic problems in the theory of quantum entanglement","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP","quant-ph"],"primary_cat":"math-ph","authors_text":"{\\L}ukasz Skowronek","submitted_at":"2013-05-10T20:45:48Z","abstract_excerpt":"We present solutions to a set of problems that arise in quantum entanglement theory, whose common trait is the use of algebraic methods. The backbone of the thesis consists of two general theorems, pertaining to specific convex sets of quantum maps. They are complemented by solutions of many more specific problems of rather technical character. These problems concerned questions such as the higher rank numerical ranges, the lengths of separable states, the solutions of compression equations, the completely entangled subspaces, and maximally entangled states. The solutions were obtained partly "},"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":"1305.2435","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2013-05-10T20:45:48Z","cross_cats_sorted":["math.MP","quant-ph"],"title_canon_sha256":"d92767f3d9636815264467f7ec0bcf5952aa5bf19bd2a32f7f01a67756b90c47","abstract_canon_sha256":"2a955c61a60695d1ec46a472b95d74336744d210f358eaa66c1fc0c614496b0e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:25:57.875698Z","signature_b64":"wxVPZKme6FaUtuU+5ww+DtHuyNB1c6+yKP7tqP/DMEK+zi1hUsAZLK6ZnWEEpvxC9SHRFYQpplD42xJ3gx5lAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8a7843ef722ff52c9e9d3d02637d1c4e82e5e7e0adb4a5d4595da1346649d342","last_reissued_at":"2026-05-18T03:25:57.875134Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:25:57.875134Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A few algebraic problems in the theory of quantum entanglement","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP","quant-ph"],"primary_cat":"math-ph","authors_text":"{\\L}ukasz Skowronek","submitted_at":"2013-05-10T20:45:48Z","abstract_excerpt":"We present solutions to a set of problems that arise in quantum entanglement theory, whose common trait is the use of algebraic methods. The backbone of the thesis consists of two general theorems, pertaining to specific convex sets of quantum maps. They are complemented by solutions of many more specific problems of rather technical character. These problems concerned questions such as the higher rank numerical ranges, the lengths of separable states, the solutions of compression equations, the completely entangled subspaces, and maximally entangled states. The solutions were obtained partly "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.2435","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":"1305.2435","created_at":"2026-05-18T03:25:57.875215+00:00"},{"alias_kind":"arxiv_version","alias_value":"1305.2435v1","created_at":"2026-05-18T03:25:57.875215+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1305.2435","created_at":"2026-05-18T03:25:57.875215+00:00"},{"alias_kind":"pith_short_12","alias_value":"RJ4EH33SF72S","created_at":"2026-05-18T12:27:57.521954+00:00"},{"alias_kind":"pith_short_16","alias_value":"RJ4EH33SF72SZHU5","created_at":"2026-05-18T12:27:57.521954+00:00"},{"alias_kind":"pith_short_8","alias_value":"RJ4EH33S","created_at":"2026-05-18T12:27:57.521954+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/RJ4EH33SF72SZHU5HUBGG7I4J2","json":"https://pith.science/pith/RJ4EH33SF72SZHU5HUBGG7I4J2.json","graph_json":"https://pith.science/api/pith-number/RJ4EH33SF72SZHU5HUBGG7I4J2/graph.json","events_json":"https://pith.science/api/pith-number/RJ4EH33SF72SZHU5HUBGG7I4J2/events.json","paper":"https://pith.science/paper/RJ4EH33S"},"agent_actions":{"view_html":"https://pith.science/pith/RJ4EH33SF72SZHU5HUBGG7I4J2","download_json":"https://pith.science/pith/RJ4EH33SF72SZHU5HUBGG7I4J2.json","view_paper":"https://pith.science/paper/RJ4EH33S","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1305.2435&json=true","fetch_graph":"https://pith.science/api/pith-number/RJ4EH33SF72SZHU5HUBGG7I4J2/graph.json","fetch_events":"https://pith.science/api/pith-number/RJ4EH33SF72SZHU5HUBGG7I4J2/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/RJ4EH33SF72SZHU5HUBGG7I4J2/action/timestamp_anchor","attest_storage":"https://pith.science/pith/RJ4EH33SF72SZHU5HUBGG7I4J2/action/storage_attestation","attest_author":"https://pith.science/pith/RJ4EH33SF72SZHU5HUBGG7I4J2/action/author_attestation","sign_citation":"https://pith.science/pith/RJ4EH33SF72SZHU5HUBGG7I4J2/action/citation_signature","submit_replication":"https://pith.science/pith/RJ4EH33SF72SZHU5HUBGG7I4J2/action/replication_record"}},"created_at":"2026-05-18T03:25:57.875215+00:00","updated_at":"2026-05-18T03:25:57.875215+00:00"}