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Proceeding in related analytical frameworks, using a further determinantal moment formula of C. Dunkl (Appendix), we reach the conclusion that one-half of this probability arises when the determinantal inequality $|\\rho^{PT}|>|\\rho|$, where $PT$ denotes the partial transpose, is satisfied, and, the other half, when $|\\rho|>|\\rho^{PT}|$. These probabilities are taken with respect to the f"},"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":"1403.1825","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2014-03-07T17:46:01Z","cross_cats_sorted":["math-ph","math.MP","math.PR"],"title_canon_sha256":"44d3b24878d31cb2d3d37a9d9bb2e37939341e4ab367d91b4ea432809463febc","abstract_canon_sha256":"a4dadde21e61113b2d61f7a00ee637625ef78e18415fc17b2097e80967cf2fcc"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:56:52.484605Z","signature_b64":"tgypJ6sjMzKSdzD+EUdFO5tXI4bMU+CY8eZjDylgBTkNfNpREV1IuPr0TtXXnzjAIXXDNFFwWs4azgtkxn0yCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"22fb0e94932b97559663d0dcaabd8f7cb16968114c5f28896b6ca7dc4ca1de01","last_reissued_at":"2026-05-18T02:56:52.484166Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:56:52.484166Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Symmetric Halves of the 8/33-Probability that the Joint State of Two Quantum Bits is Disentangled","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP","math.PR"],"primary_cat":"quant-ph","authors_text":"Paul B. 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