{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:IGQ37HRKMFKLI6V3RCLJWTVVEM","short_pith_number":"pith:IGQ37HRK","canonical_record":{"source":{"id":"1010.5180","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2010-10-25T16:23:15Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"b85251b0b24b09c1dcbe662d63f0827d196f4be957f1ed0b18242940823b0761","abstract_canon_sha256":"7de3c582af253bd5007aea75135eeac077457197577fb524d7db9b5857b547e3"},"schema_version":"1.0"},"canonical_sha256":"41a1bf9e2a6154b47abb88969b4eb5232e731a30b3e9be11c0a1e8e357fa94cb","source":{"kind":"arxiv","id":"1010.5180","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1010.5180","created_at":"2026-05-18T04:12:44Z"},{"alias_kind":"arxiv_version","alias_value":"1010.5180v4","created_at":"2026-05-18T04:12:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1010.5180","created_at":"2026-05-18T04:12:44Z"},{"alias_kind":"pith_short_12","alias_value":"IGQ37HRKMFKL","created_at":"2026-05-18T12:26:09Z"},{"alias_kind":"pith_short_16","alias_value":"IGQ37HRKMFKLI6V3","created_at":"2026-05-18T12:26:09Z"},{"alias_kind":"pith_short_8","alias_value":"IGQ37HRK","created_at":"2026-05-18T12:26:09Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:IGQ37HRKMFKLI6V3RCLJWTVVEM","target":"record","payload":{"canonical_record":{"source":{"id":"1010.5180","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2010-10-25T16:23:15Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"b85251b0b24b09c1dcbe662d63f0827d196f4be957f1ed0b18242940823b0761","abstract_canon_sha256":"7de3c582af253bd5007aea75135eeac077457197577fb524d7db9b5857b547e3"},"schema_version":"1.0"},"canonical_sha256":"41a1bf9e2a6154b47abb88969b4eb5232e731a30b3e9be11c0a1e8e357fa94cb","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:12:44.752395Z","signature_b64":"odGGtesWEUWeeU1Pt5XE+xQMsWk08D/Vo0YI+REO0lb3B6cCgPUz7lUxyCJcayCWnUO06WbOLxjAhBLDyh1KBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"41a1bf9e2a6154b47abb88969b4eb5232e731a30b3e9be11c0a1e8e357fa94cb","last_reissued_at":"2026-05-18T04:12:44.751698Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:12:44.751698Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1010.5180","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:12:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Ru3ktWThRIlcs7YObsIk1HmZZpitsuf/WaypxAhxaQ2vJ4YHPDI4FgmQr0gQ1oFCRxY+y+xNpuTsLWFLFbQPBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T07:08:04.686053Z"},"content_sha256":"cf36490b7805af03bff230b3eab6bc71490c9db6136005f9761acb4c1a054ca2","schema_version":"1.0","event_id":"sha256:cf36490b7805af03bff230b3eab6bc71490c9db6136005f9761acb4c1a054ca2"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:IGQ37HRKMFKLI6V3RCLJWTVVEM","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Radial and Azimuthal Profiles of Two-Qubit/Rebit Hilbert-Schmidt Separability Probabilities and Related 3-D Visualization Analyses","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"quant-ph","authors_text":"Paul B. Slater","submitted_at":"2010-10-25T16:23:15Z","abstract_excerpt":"Firstly, we reduce the long-standing problem of ascertaining the Hilbert-Schmidt probability that a generic pair of qubits is separable to that of determining the specific nature of a one-dimensional (separability) function of the radial coordinate (r) of the unit ball in 15-dimensional Euclidean space, and similarly for a generic pair of rebits, using the 9-dimensional unit ball. Separability probabilities, could, then, be directly obtained by integrating the products of these functions (which we numerically estimate and plot) with jacobian factors of r^m over r in [0,1], with m=17 for the tw"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1010.5180","kind":"arxiv","version":4},"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:12:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"CQOvO3dkVtlhs3gn95eJUeNRgVZdjM2UrCfbm0dktczz/WzvgkEg36s6Mfl7HkYDwgez8rTTki6xOMqnI2PNDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T07:08:04.686449Z"},"content_sha256":"e269cb8a101a00ea7c203004f8b157daa6d5bd9f88b3f0b9e0f0890f044aab8d","schema_version":"1.0","event_id":"sha256:e269cb8a101a00ea7c203004f8b157daa6d5bd9f88b3f0b9e0f0890f044aab8d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/IGQ37HRKMFKLI6V3RCLJWTVVEM/bundle.json","state_url":"https://pith.science/pith/IGQ37HRKMFKLI6V3RCLJWTVVEM/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/IGQ37HRKMFKLI6V3RCLJWTVVEM/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-05-26T07:08:04Z","links":{"resolver":"https://pith.science/pith/IGQ37HRKMFKLI6V3RCLJWTVVEM","bundle":"https://pith.science/pith/IGQ37HRKMFKLI6V3RCLJWTVVEM/bundle.json","state":"https://pith.science/pith/IGQ37HRKMFKLI6V3RCLJWTVVEM/state.json","well_known_bundle":"https://pith.science/.well-known/pith/IGQ37HRKMFKLI6V3RCLJWTVVEM/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:IGQ37HRKMFKLI6V3RCLJWTVVEM","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":"7de3c582af253bd5007aea75135eeac077457197577fb524d7db9b5857b547e3","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2010-10-25T16:23:15Z","title_canon_sha256":"b85251b0b24b09c1dcbe662d63f0827d196f4be957f1ed0b18242940823b0761"},"schema_version":"1.0","source":{"id":"1010.5180","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1010.5180","created_at":"2026-05-18T04:12:44Z"},{"alias_kind":"arxiv_version","alias_value":"1010.5180v4","created_at":"2026-05-18T04:12:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1010.5180","created_at":"2026-05-18T04:12:44Z"},{"alias_kind":"pith_short_12","alias_value":"IGQ37HRKMFKL","created_at":"2026-05-18T12:26:09Z"},{"alias_kind":"pith_short_16","alias_value":"IGQ37HRKMFKLI6V3","created_at":"2026-05-18T12:26:09Z"},{"alias_kind":"pith_short_8","alias_value":"IGQ37HRK","created_at":"2026-05-18T12:26:09Z"}],"graph_snapshots":[{"event_id":"sha256:e269cb8a101a00ea7c203004f8b157daa6d5bd9f88b3f0b9e0f0890f044aab8d","target":"graph","created_at":"2026-05-18T04:12:44Z","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":"Firstly, we reduce the long-standing problem of ascertaining the Hilbert-Schmidt probability that a generic pair of qubits is separable to that of determining the specific nature of a one-dimensional (separability) function of the radial coordinate (r) of the unit ball in 15-dimensional Euclidean space, and similarly for a generic pair of rebits, using the 9-dimensional unit ball. Separability probabilities, could, then, be directly obtained by integrating the products of these functions (which we numerically estimate and plot) with jacobian factors of r^m over r in [0,1], with m=17 for the tw","authors_text":"Paul B. Slater","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2010-10-25T16:23:15Z","title":"Radial and Azimuthal Profiles of Two-Qubit/Rebit Hilbert-Schmidt Separability Probabilities and Related 3-D Visualization Analyses"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1010.5180","kind":"arxiv","version":4},"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:cf36490b7805af03bff230b3eab6bc71490c9db6136005f9761acb4c1a054ca2","target":"record","created_at":"2026-05-18T04:12:44Z","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":"7de3c582af253bd5007aea75135eeac077457197577fb524d7db9b5857b547e3","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2010-10-25T16:23:15Z","title_canon_sha256":"b85251b0b24b09c1dcbe662d63f0827d196f4be957f1ed0b18242940823b0761"},"schema_version":"1.0","source":{"id":"1010.5180","kind":"arxiv","version":4}},"canonical_sha256":"41a1bf9e2a6154b47abb88969b4eb5232e731a30b3e9be11c0a1e8e357fa94cb","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"41a1bf9e2a6154b47abb88969b4eb5232e731a30b3e9be11c0a1e8e357fa94cb","first_computed_at":"2026-05-18T04:12:44.751698Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:12:44.751698Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"odGGtesWEUWeeU1Pt5XE+xQMsWk08D/Vo0YI+REO0lb3B6cCgPUz7lUxyCJcayCWnUO06WbOLxjAhBLDyh1KBA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:12:44.752395Z","signed_message":"canonical_sha256_bytes"},"source_id":"1010.5180","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cf36490b7805af03bff230b3eab6bc71490c9db6136005f9761acb4c1a054ca2","sha256:e269cb8a101a00ea7c203004f8b157daa6d5bd9f88b3f0b9e0f0890f044aab8d"],"state_sha256":"5bc5cb6f266b25684f53de990eb7b16959dcc80880299d669cafc21d498b33c4"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DoaOwr+yJO5vSM5oRhhjekHhx9ypJe6CxXCNmJsKkOGbbypx60jpnFnymb1tOjDFm5+j81khElt6E938+DCJAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T07:08:04.689580Z","bundle_sha256":"f87dc5f4880425f316de426aae87b2edc9f172d1874940fce0d37b94734df52a"}}