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Proceeding in related analytical frameworks, using a further determinantal $4F3$-hypergeometric moment formula (Appendix A), we reach, {\\it via} density-approximation procedures, the conclusion that one-half ($\\frac{4}{33}$) of this probability arises when the determinantal inequality $|\\rho^{PT}|>|\\rho|$, where $PT$ denotes the partial transpose, is satisfied, and"},"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":"1404.1860","kind":"arxiv","version":6},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2014-04-07T17:50:59Z","cross_cats_sorted":["math-ph","math.MP","math.PR"],"title_canon_sha256":"891bbae7de650ecacf7455c3a192a1bdff785c94435b32753b0150854e291074","abstract_canon_sha256":"233d8ae40cd963a28739019666e50fb89834847d2096d109be64b5c7f98d9d12"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:25:40.396183Z","signature_b64":"wo+y56WWoJ09yqCFe+y8F2henF0GyKTL42bGxasrrIq/m78abm54RsA7lbLHKdE6Qmo75hXCbRJ93EZyUpm7Cg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cf13d2bc23ac0c712a96549ea58793f3b623ebe8e8a21ede1ab1600f2ff5f153","last_reissued_at":"2026-05-18T02:25:40.395788Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:25:40.395788Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Generalized Two-Qubit Whole and Half Hilbert-Schmidt Separability Probabilities","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP","math.PR"],"primary_cat":"quant-ph","authors_text":"Charles F. Dunkl, Paul B. Slater","submitted_at":"2014-04-07T17:50:59Z","abstract_excerpt":"Compelling evidence-though yet no formal proof-has been adduced that the probability that a generic (standard) two-qubit state ($\\rho$) is separable/disentangled is $\\frac{8}{33}$ (arXiv:1301.6617, arXiv:1109.2560, arXiv:0704.3723). Proceeding in related analytical frameworks, using a further determinantal $4F3$-hypergeometric moment formula (Appendix A), we reach, {\\it via} density-approximation procedures, the conclusion that one-half ($\\frac{4}{33}$) of this probability arises when the determinantal inequality $|\\rho^{PT}|>|\\rho|$, where $PT$ denotes the partial transpose, is satisfied, and"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.1860","kind":"arxiv","version":6},"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":"1404.1860","created_at":"2026-05-18T02:25:40.395843+00:00"},{"alias_kind":"arxiv_version","alias_value":"1404.1860v6","created_at":"2026-05-18T02:25:40.395843+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1404.1860","created_at":"2026-05-18T02:25:40.395843+00:00"},{"alias_kind":"pith_short_12","alias_value":"Z4J5FPBDVQGH","created_at":"2026-05-18T12:28:59.999130+00:00"},{"alias_kind":"pith_short_16","alias_value":"Z4J5FPBDVQGHCKUW","created_at":"2026-05-18T12:28:59.999130+00:00"},{"alias_kind":"pith_short_8","alias_value":"Z4J5FPBD","created_at":"2026-05-18T12:28:59.999130+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/Z4J5FPBDVQGHCKUWKSPKLB4T6O","json":"https://pith.science/pith/Z4J5FPBDVQGHCKUWKSPKLB4T6O.json","graph_json":"https://pith.science/api/pith-number/Z4J5FPBDVQGHCKUWKSPKLB4T6O/graph.json","events_json":"https://pith.science/api/pith-number/Z4J5FPBDVQGHCKUWKSPKLB4T6O/events.json","paper":"https://pith.science/paper/Z4J5FPBD"},"agent_actions":{"view_html":"https://pith.science/pith/Z4J5FPBDVQGHCKUWKSPKLB4T6O","download_json":"https://pith.science/pith/Z4J5FPBDVQGHCKUWKSPKLB4T6O.json","view_paper":"https://pith.science/paper/Z4J5FPBD","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1404.1860&json=true","fetch_graph":"https://pith.science/api/pith-number/Z4J5FPBDVQGHCKUWKSPKLB4T6O/graph.json","fetch_events":"https://pith.science/api/pith-number/Z4J5FPBDVQGHCKUWKSPKLB4T6O/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/Z4J5FPBDVQGHCKUWKSPKLB4T6O/action/timestamp_anchor","attest_storage":"https://pith.science/pith/Z4J5FPBDVQGHCKUWKSPKLB4T6O/action/storage_attestation","attest_author":"https://pith.science/pith/Z4J5FPBDVQGHCKUWKSPKLB4T6O/action/author_attestation","sign_citation":"https://pith.science/pith/Z4J5FPBDVQGHCKUWKSPKLB4T6O/action/citation_signature","submit_replication":"https://pith.science/pith/Z4J5FPBDVQGHCKUWKSPKLB4T6O/action/replication_record"}},"created_at":"2026-05-18T02:25:40.395843+00:00","updated_at":"2026-05-18T02:25:40.395843+00:00"}