{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:MN5JNGTV7RJ3P2VR3VVMVGTCSU","short_pith_number":"pith:MN5JNGTV","schema_version":"1.0","canonical_sha256":"637a969a75fc53b7eab1dd6aca9a62950304710d9de7de166254e9dff41d56b7","source":{"kind":"arxiv","id":"1501.00745","version":2},"attestation_state":"computed","paper":{"title":"Dimension formula for induced maximal faces of separable states and genuine entanglement","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Dragomir Z. Djokovic, Lin Chen","submitted_at":"2015-01-05T02:00:24Z","abstract_excerpt":"The normalized separable states of a finite-dimensional multipartite quantum system, represented by its Hilbert space ${\\cal H}$, form a closed convex set ${\\cal S}_1$. The set ${\\cal S}_1$ has two kinds of faces, induced and non-induced. An induced face, $F$, has the form $F=\\Gamma(F_V)$, where $V$ is a subspace of ${\\cal H}$, $F_V$ is the set of $\\rho\\in{\\cal S}_1$ whose range is contained in $V$, and $\\Gamma$ is a partial transposition operator. Such $F$ is a maximal face if and only if $V$ is a hyperplane. We give a simple formula for the dimension of any induced maximal face. We also prov"},"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":"1501.00745","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2015-01-05T02:00:24Z","cross_cats_sorted":[],"title_canon_sha256":"0012bad82d4a4008314e7a8250a36000c370ae3c620909cb782b2b76db64a364","abstract_canon_sha256":"622753bbbf73b660580e600fc2fa842da95e4f764def9cf7bcfec9b3e401de69"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:29:54.640551Z","signature_b64":"Hh8VXwPjiF2z7J0ia+g7mc71ImrF7AzWmyapwWDl5PQ1mQbhvD40Yt+i5d+IYWL3QIAu1hli+pMvepbJPm34DA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"637a969a75fc53b7eab1dd6aca9a62950304710d9de7de166254e9dff41d56b7","last_reissued_at":"2026-05-18T01:29:54.640088Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:29:54.640088Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Dimension formula for induced maximal faces of separable states and genuine entanglement","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Dragomir Z. Djokovic, Lin Chen","submitted_at":"2015-01-05T02:00:24Z","abstract_excerpt":"The normalized separable states of a finite-dimensional multipartite quantum system, represented by its Hilbert space ${\\cal H}$, form a closed convex set ${\\cal S}_1$. The set ${\\cal S}_1$ has two kinds of faces, induced and non-induced. An induced face, $F$, has the form $F=\\Gamma(F_V)$, where $V$ is a subspace of ${\\cal H}$, $F_V$ is the set of $\\rho\\in{\\cal S}_1$ whose range is contained in $V$, and $\\Gamma$ is a partial transposition operator. Such $F$ is a maximal face if and only if $V$ is a hyperplane. We give a simple formula for the dimension of any induced maximal face. We also prov"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.00745","kind":"arxiv","version":2},"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":"1501.00745","created_at":"2026-05-18T01:29:54.640156+00:00"},{"alias_kind":"arxiv_version","alias_value":"1501.00745v2","created_at":"2026-05-18T01:29:54.640156+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1501.00745","created_at":"2026-05-18T01:29:54.640156+00:00"},{"alias_kind":"pith_short_12","alias_value":"MN5JNGTV7RJ3","created_at":"2026-05-18T12:29:32.376354+00:00"},{"alias_kind":"pith_short_16","alias_value":"MN5JNGTV7RJ3P2VR","created_at":"2026-05-18T12:29:32.376354+00:00"},{"alias_kind":"pith_short_8","alias_value":"MN5JNGTV","created_at":"2026-05-18T12:29:32.376354+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/MN5JNGTV7RJ3P2VR3VVMVGTCSU","json":"https://pith.science/pith/MN5JNGTV7RJ3P2VR3VVMVGTCSU.json","graph_json":"https://pith.science/api/pith-number/MN5JNGTV7RJ3P2VR3VVMVGTCSU/graph.json","events_json":"https://pith.science/api/pith-number/MN5JNGTV7RJ3P2VR3VVMVGTCSU/events.json","paper":"https://pith.science/paper/MN5JNGTV"},"agent_actions":{"view_html":"https://pith.science/pith/MN5JNGTV7RJ3P2VR3VVMVGTCSU","download_json":"https://pith.science/pith/MN5JNGTV7RJ3P2VR3VVMVGTCSU.json","view_paper":"https://pith.science/paper/MN5JNGTV","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1501.00745&json=true","fetch_graph":"https://pith.science/api/pith-number/MN5JNGTV7RJ3P2VR3VVMVGTCSU/graph.json","fetch_events":"https://pith.science/api/pith-number/MN5JNGTV7RJ3P2VR3VVMVGTCSU/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/MN5JNGTV7RJ3P2VR3VVMVGTCSU/action/timestamp_anchor","attest_storage":"https://pith.science/pith/MN5JNGTV7RJ3P2VR3VVMVGTCSU/action/storage_attestation","attest_author":"https://pith.science/pith/MN5JNGTV7RJ3P2VR3VVMVGTCSU/action/author_attestation","sign_citation":"https://pith.science/pith/MN5JNGTV7RJ3P2VR3VVMVGTCSU/action/citation_signature","submit_replication":"https://pith.science/pith/MN5JNGTV7RJ3P2VR3VVMVGTCSU/action/replication_record"}},"created_at":"2026-05-18T01:29:54.640156+00:00","updated_at":"2026-05-18T01:29:54.640156+00:00"}