{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:P42CZQZ2UY7V6OVCEIQRJAVZ2Z","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"cd33b8af8a81aaf8b241ee91905c1011f3fe2e96238a0d5514a3637a8901d2cf","cross_cats_sorted":["math-ph","math.MP","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2014-11-10T20:08:20Z","title_canon_sha256":"baa49b9ef707eb8252031e94366a6d114262e87fdcf84d26e51c7b352043a6f2"},"schema_version":"1.0","source":{"id":"1411.2561","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1411.2561","created_at":"2026-05-18T02:00:58Z"},{"alias_kind":"arxiv_version","alias_value":"1411.2561v3","created_at":"2026-05-18T02:00:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1411.2561","created_at":"2026-05-18T02:00:58Z"},{"alias_kind":"pith_short_12","alias_value":"P42CZQZ2UY7V","created_at":"2026-05-18T12:28:43Z"},{"alias_kind":"pith_short_16","alias_value":"P42CZQZ2UY7V6OVC","created_at":"2026-05-18T12:28:43Z"},{"alias_kind":"pith_short_8","alias_value":"P42CZQZ2","created_at":"2026-05-18T12:28:43Z"}],"graph_snapshots":[{"event_id":"sha256:e74b372c1aa18ed956034b8629857410c0c08de5cf808361a83be315fb7a5057","target":"graph","created_at":"2026-05-18T02:00:58Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"Previously, a formula, incorporating a $5F4$ hypergeometric function, for the Hilbert-Schmidt-averaged determinantal moments $\\left\\langle \\left\\vert \\rho^{PT}\\right\\vert ^{n}\\left\\vert \\rho\\right\\vert ^{k}\\right\\rangle /\\left\\langle \\left\\vert \\rho\\right\\vert ^{k}\\right\\rangle$ of $4 \\times 4$ density-matrices ($\\rho$), and their partial transposes ($\\rho^{PT}|$) was applied with $k=0$ to the generalized two-qubit separability-probability question. The formula can, further, be viewed we note here, as an averaging over \"induced measures in the space of mixed quantum states\". The associated ind","authors_text":"Charles F. Dunkl, Paul B. Slater","cross_cats":["math-ph","math.MP","math.PR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2014-11-10T20:08:20Z","title":"Formulas for Rational-Valued Separability Probabilities of Random Induced Generalized Two-Qubit States"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.2561","kind":"arxiv","version":3},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:ea8e31e226faf55c1910066611f9add3840f8c8c8d0071b5e549f2b1e3dc59af","target":"record","created_at":"2026-05-18T02:00:58Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"cd33b8af8a81aaf8b241ee91905c1011f3fe2e96238a0d5514a3637a8901d2cf","cross_cats_sorted":["math-ph","math.MP","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2014-11-10T20:08:20Z","title_canon_sha256":"baa49b9ef707eb8252031e94366a6d114262e87fdcf84d26e51c7b352043a6f2"},"schema_version":"1.0","source":{"id":"1411.2561","kind":"arxiv","version":3}},"canonical_sha256":"7f342cc33aa63f5f3aa222211482b9d661a9817cc2c3183cca3e77ef629a61b8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7f342cc33aa63f5f3aa222211482b9d661a9817cc2c3183cca3e77ef629a61b8","first_computed_at":"2026-05-18T02:00:58.746686Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:00:58.746686Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"c0LFxB0LnvcrAwqItxsldtkDvnLjDm4OUVOyUhOkCE7hhPUr+X3gw3PgPS0/mHjW37Js/nspdAl4CPez5IYpCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:00:58.747225Z","signed_message":"canonical_sha256_bytes"},"source_id":"1411.2561","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ea8e31e226faf55c1910066611f9add3840f8c8c8d0071b5e549f2b1e3dc59af","sha256:e74b372c1aa18ed956034b8629857410c0c08de5cf808361a83be315fb7a5057"],"state_sha256":"0be5a7593cc61392ae10d7caafe9a1dcec98544cfcd3d0f27a15556f3f4a907a"}