{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:MYWMEYZLLHOXNVES7EPJUZ7Z5O","short_pith_number":"pith:MYWMEYZL","schema_version":"1.0","canonical_sha256":"662cc2632b59dd76d492f91e9a67f9eb8790ab37ed6860512f6d7f45c2eb5d66","source":{"kind":"arxiv","id":"1302.4459","version":1},"attestation_state":"computed","paper":{"title":"A link between Quantum Entanglement, Secant varieties and Sphericity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.AG","math.MP","math.RT"],"primary_cat":"quant-ph","authors_text":"Adam Sawicki, Valdemar V. Tsanov","submitted_at":"2013-02-18T21:17:23Z","abstract_excerpt":"In this paper, we shed light on relations between three concepts studied in representations theory, algebraic geometry and quantum information theory. First - spherical actions of reductive groups on projective spaces. Second - secant varieties of homogeneous projective varieties, and the related notions of rank and border rank. Third - quantum entanglement. Our main result concerns the relation between the problem of the state reconstruction from its reduced one-particle density matrices and the minimal number of separable summands in its decomposition. More precisely, we show that sphericity"},"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":"1302.4459","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2013-02-18T21:17:23Z","cross_cats_sorted":["math-ph","math.AG","math.MP","math.RT"],"title_canon_sha256":"33d6439ea016084cc0fcef25496b58b8743e114586286eab94e33c77796f6ceb","abstract_canon_sha256":"9a48655d8e3ac9c83d3f2d5a60de260f73d77320d2ffcfac3fd6e0244b218253"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:22:49.148531Z","signature_b64":"gUmYoJQNSkjIiaEWS4mKobNMe5O+dltBBRvs74oZ/B27xDKgmyh3V+C1gDI7YP0gMQ40CV8rbWeTm/2G1qcRBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"662cc2632b59dd76d492f91e9a67f9eb8790ab37ed6860512f6d7f45c2eb5d66","last_reissued_at":"2026-05-18T01:22:49.147999Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:22:49.147999Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A link between Quantum Entanglement, Secant varieties and Sphericity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.AG","math.MP","math.RT"],"primary_cat":"quant-ph","authors_text":"Adam Sawicki, Valdemar V. Tsanov","submitted_at":"2013-02-18T21:17:23Z","abstract_excerpt":"In this paper, we shed light on relations between three concepts studied in representations theory, algebraic geometry and quantum information theory. First - spherical actions of reductive groups on projective spaces. Second - secant varieties of homogeneous projective varieties, and the related notions of rank and border rank. Third - quantum entanglement. Our main result concerns the relation between the problem of the state reconstruction from its reduced one-particle density matrices and the minimal number of separable summands in its decomposition. More precisely, we show that sphericity"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.4459","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":"1302.4459","created_at":"2026-05-18T01:22:49.148079+00:00"},{"alias_kind":"arxiv_version","alias_value":"1302.4459v1","created_at":"2026-05-18T01:22:49.148079+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1302.4459","created_at":"2026-05-18T01:22:49.148079+00:00"},{"alias_kind":"pith_short_12","alias_value":"MYWMEYZLLHOX","created_at":"2026-05-18T12:27:52.871228+00:00"},{"alias_kind":"pith_short_16","alias_value":"MYWMEYZLLHOXNVES","created_at":"2026-05-18T12:27:52.871228+00:00"},{"alias_kind":"pith_short_8","alias_value":"MYWMEYZL","created_at":"2026-05-18T12:27:52.871228+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/MYWMEYZLLHOXNVES7EPJUZ7Z5O","json":"https://pith.science/pith/MYWMEYZLLHOXNVES7EPJUZ7Z5O.json","graph_json":"https://pith.science/api/pith-number/MYWMEYZLLHOXNVES7EPJUZ7Z5O/graph.json","events_json":"https://pith.science/api/pith-number/MYWMEYZLLHOXNVES7EPJUZ7Z5O/events.json","paper":"https://pith.science/paper/MYWMEYZL"},"agent_actions":{"view_html":"https://pith.science/pith/MYWMEYZLLHOXNVES7EPJUZ7Z5O","download_json":"https://pith.science/pith/MYWMEYZLLHOXNVES7EPJUZ7Z5O.json","view_paper":"https://pith.science/paper/MYWMEYZL","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1302.4459&json=true","fetch_graph":"https://pith.science/api/pith-number/MYWMEYZLLHOXNVES7EPJUZ7Z5O/graph.json","fetch_events":"https://pith.science/api/pith-number/MYWMEYZLLHOXNVES7EPJUZ7Z5O/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/MYWMEYZLLHOXNVES7EPJUZ7Z5O/action/timestamp_anchor","attest_storage":"https://pith.science/pith/MYWMEYZLLHOXNVES7EPJUZ7Z5O/action/storage_attestation","attest_author":"https://pith.science/pith/MYWMEYZLLHOXNVES7EPJUZ7Z5O/action/author_attestation","sign_citation":"https://pith.science/pith/MYWMEYZLLHOXNVES7EPJUZ7Z5O/action/citation_signature","submit_replication":"https://pith.science/pith/MYWMEYZLLHOXNVES7EPJUZ7Z5O/action/replication_record"}},"created_at":"2026-05-18T01:22:49.148079+00:00","updated_at":"2026-05-18T01:22:49.148079+00:00"}