{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:VTWH7R7LUWWCBC4ZY3UQ4V3CCJ","short_pith_number":"pith:VTWH7R7L","schema_version":"1.0","canonical_sha256":"acec7fc7eba5ac208b99c6e90e5762126d938a70793023970354dfe14645d7a9","source":{"kind":"arxiv","id":"1307.1362","version":1},"attestation_state":"computed","paper":{"title":"Geometry for separable states and construction of entangled states with positive partial transposes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OA"],"primary_cat":"quant-ph","authors_text":"Kil-Chan Ha, Seung-Hyeok Kye","submitted_at":"2013-07-04T14:54:39Z","abstract_excerpt":"We construct faces of the convex set of all $2\\otimes 4$ bipartite separable states, which are affinely isomorphic to the simplex $\\Delta_{9}$ with ten extreme points. Every interior point of these faces is a separable state which has a unique decomposition into 10 product states, even though ranks of the state and its partial transpose are 5 and 7, respectively. We also note that the number 10 is greater than $2\\times 4$, to disprove a conjecture on the lengths of qubit-qudit separable states. This face is inscribed in the corresponding face of the convex set of all PPT states so that sub-sim"},"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":"1307.1362","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2013-07-04T14:54:39Z","cross_cats_sorted":["math.OA"],"title_canon_sha256":"d339b9c793097a1ff9769e54b7ec4190d9bbca4a04ee277c758545868b17b5d2","abstract_canon_sha256":"b802be59ac7ace4c1c4ba52dc19030f0af482f876e6bf489a49380fea160e18a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:14:08.230831Z","signature_b64":"sYQKlXVCY4AmyOpJz1j9G4X95tCrK9zZGb4FqByYm+ERbo9EvXGQdHOSoodAlNjlqME49UjUU5NFPHEThzIYBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"acec7fc7eba5ac208b99c6e90e5762126d938a70793023970354dfe14645d7a9","last_reissued_at":"2026-05-18T03:14:08.230429Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:14:08.230429Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Geometry for separable states and construction of entangled states with positive partial transposes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OA"],"primary_cat":"quant-ph","authors_text":"Kil-Chan Ha, Seung-Hyeok Kye","submitted_at":"2013-07-04T14:54:39Z","abstract_excerpt":"We construct faces of the convex set of all $2\\otimes 4$ bipartite separable states, which are affinely isomorphic to the simplex $\\Delta_{9}$ with ten extreme points. Every interior point of these faces is a separable state which has a unique decomposition into 10 product states, even though ranks of the state and its partial transpose are 5 and 7, respectively. We also note that the number 10 is greater than $2\\times 4$, to disprove a conjecture on the lengths of qubit-qudit separable states. This face is inscribed in the corresponding face of the convex set of all PPT states so that sub-sim"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.1362","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":"1307.1362","created_at":"2026-05-18T03:14:08.230491+00:00"},{"alias_kind":"arxiv_version","alias_value":"1307.1362v1","created_at":"2026-05-18T03:14:08.230491+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1307.1362","created_at":"2026-05-18T03:14:08.230491+00:00"},{"alias_kind":"pith_short_12","alias_value":"VTWH7R7LUWWC","created_at":"2026-05-18T12:28:04.890932+00:00"},{"alias_kind":"pith_short_16","alias_value":"VTWH7R7LUWWCBC4Z","created_at":"2026-05-18T12:28:04.890932+00:00"},{"alias_kind":"pith_short_8","alias_value":"VTWH7R7L","created_at":"2026-05-18T12:28:04.890932+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/VTWH7R7LUWWCBC4ZY3UQ4V3CCJ","json":"https://pith.science/pith/VTWH7R7LUWWCBC4ZY3UQ4V3CCJ.json","graph_json":"https://pith.science/api/pith-number/VTWH7R7LUWWCBC4ZY3UQ4V3CCJ/graph.json","events_json":"https://pith.science/api/pith-number/VTWH7R7LUWWCBC4ZY3UQ4V3CCJ/events.json","paper":"https://pith.science/paper/VTWH7R7L"},"agent_actions":{"view_html":"https://pith.science/pith/VTWH7R7LUWWCBC4ZY3UQ4V3CCJ","download_json":"https://pith.science/pith/VTWH7R7LUWWCBC4ZY3UQ4V3CCJ.json","view_paper":"https://pith.science/paper/VTWH7R7L","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1307.1362&json=true","fetch_graph":"https://pith.science/api/pith-number/VTWH7R7LUWWCBC4ZY3UQ4V3CCJ/graph.json","fetch_events":"https://pith.science/api/pith-number/VTWH7R7LUWWCBC4ZY3UQ4V3CCJ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/VTWH7R7LUWWCBC4ZY3UQ4V3CCJ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/VTWH7R7LUWWCBC4ZY3UQ4V3CCJ/action/storage_attestation","attest_author":"https://pith.science/pith/VTWH7R7LUWWCBC4ZY3UQ4V3CCJ/action/author_attestation","sign_citation":"https://pith.science/pith/VTWH7R7LUWWCBC4ZY3UQ4V3CCJ/action/citation_signature","submit_replication":"https://pith.science/pith/VTWH7R7LUWWCBC4ZY3UQ4V3CCJ/action/replication_record"}},"created_at":"2026-05-18T03:14:08.230491+00:00","updated_at":"2026-05-18T03:14:08.230491+00:00"}