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Slater","submitted_at":"2018-03-28T15:26:12Z","abstract_excerpt":"We begin by seeking the qubit-qutrit and rebit-retrit counterparts to the now well-established Hilbert-Schmidt separability probabilities for (the 15-dimensional convex set of) two-qubits of $\\frac{8}{33} = \\frac{2^3}{3 \\cdot 11} \\approx 0.242424$ and (the 9-dimensional) two-rebits of $\\frac{29}{64} =\\frac{29}{2^6} \\approx 0.453125$. Based in part on extensive numerical computations, we advance the possibilities of a qubit-qutrit value of $\\frac{27}{1000} = (\\frac{3}{10})^3 =\\frac{3^3}{2^3 \\cdot 5^3} = 0.027$ and a rebit-retrit one of $\\frac{860}{6561} =\\frac{2^2 \\cdot 5 \\cdot 43}{3^8} \\approx"},"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":"1803.10680","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2018-03-28T15:26:12Z","cross_cats_sorted":["math-ph","math.MP","math.PR"],"title_canon_sha256":"e00c743ffced64e02f9a222c85cc2e983a45893cb07a933b67b30fc328afe0a7","abstract_canon_sha256":"8dee736afaed927822831833d1f4b71e505ac414d180a86c462c3212ec613a50"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:17:38.046625Z","signature_b64":"vCrnsz6ZxLDrH0nl/7BmRdof8WZogHfufHG4GioOdxVXw1vozOUAQGZHXMjNeignq54QJFHYjsuu4u2mbGOtDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c666ff3132423ff1e6d76d409ef7feea380f796a1635664cbcc803c432c8d643","last_reissued_at":"2026-05-18T00:17:38.045898Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:17:38.045898Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Qubit-Qudit Separability/PPT-Probability Analyses and Lovas-Andai Formula Extensions to Induced Measures","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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Based in part on extensive numerical computations, we advance the possibilities of a qubit-qutrit value of $\\frac{27}{1000} = (\\frac{3}{10})^3 =\\frac{3^3}{2^3 \\cdot 5^3} = 0.027$ and a rebit-retrit one of $\\frac{860}{6561} =\\frac{2^2 \\cdot 5 \\cdot 43}{3^8} \\approx"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.10680","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":"1803.10680","created_at":"2026-05-18T00:17:38.046024+00:00"},{"alias_kind":"arxiv_version","alias_value":"1803.10680v2","created_at":"2026-05-18T00:17:38.046024+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1803.10680","created_at":"2026-05-18T00:17:38.046024+00:00"},{"alias_kind":"pith_short_12","alias_value":"YZTP6MJSII77","created_at":"2026-05-18T12:33:04.347982+00:00"},{"alias_kind":"pith_short_16","alias_value":"YZTP6MJSII77DZWX","created_at":"2026-05-18T12:33:04.347982+00:00"},{"alias_kind":"pith_short_8","alias_value":"YZTP6MJS","created_at":"2026-05-18T12:33:04.347982+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/YZTP6MJSII77DZWXNVAJ55765I","json":"https://pith.science/pith/YZTP6MJSII77DZWXNVAJ55765I.json","graph_json":"https://pith.science/api/pith-number/YZTP6MJSII77DZWXNVAJ55765I/graph.json","events_json":"https://pith.science/api/pith-number/YZTP6MJSII77DZWXNVAJ55765I/events.json","paper":"https://pith.science/paper/YZTP6MJS"},"agent_actions":{"view_html":"https://pith.science/pith/YZTP6MJSII77DZWXNVAJ55765I","download_json":"https://pith.science/pith/YZTP6MJSII77DZWXNVAJ55765I.json","view_paper":"https://pith.science/paper/YZTP6MJS","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1803.10680&json=true","fetch_graph":"https://pith.science/api/pith-number/YZTP6MJSII77DZWXNVAJ55765I/graph.json","fetch_events":"https://pith.science/api/pith-number/YZTP6MJSII77DZWXNVAJ55765I/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/YZTP6MJSII77DZWXNVAJ55765I/action/timestamp_anchor","attest_storage":"https://pith.science/pith/YZTP6MJSII77DZWXNVAJ55765I/action/storage_attestation","attest_author":"https://pith.science/pith/YZTP6MJSII77DZWXNVAJ55765I/action/author_attestation","sign_citation":"https://pith.science/pith/YZTP6MJSII77DZWXNVAJ55765I/action/citation_signature","submit_replication":"https://pith.science/pith/YZTP6MJSII77DZWXNVAJ55765I/action/replication_record"}},"created_at":"2026-05-18T00:17:38.046024+00:00","updated_at":"2026-05-18T00:17:38.046024+00:00"}