{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:FJ67XDMWTKJQXFU2XHZS3TXBW6","short_pith_number":"pith:FJ67XDMW","canonical_record":{"source":{"id":"1807.08505","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"eess.SP","submitted_at":"2018-07-23T09:42:30Z","cross_cats_sorted":[],"title_canon_sha256":"b00f6151256dec5ef2ff3b82e5c9fa043bcc7a9e5a696ef9f51ff925fb0c13f2","abstract_canon_sha256":"4fad56b7cb44b6b3397a1b223d7c2951175ea1f47ccaa09e8ca56f6c42df93c7"},"schema_version":"1.0"},"canonical_sha256":"2a7dfb8d969a930b969ab9f32dcee1b78f4acac7ccb0a92605bda58ecae5bff5","source":{"kind":"arxiv","id":"1807.08505","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1807.08505","created_at":"2026-05-17T23:52:52Z"},{"alias_kind":"arxiv_version","alias_value":"1807.08505v2","created_at":"2026-05-17T23:52:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1807.08505","created_at":"2026-05-17T23:52:52Z"},{"alias_kind":"pith_short_12","alias_value":"FJ67XDMWTKJQ","created_at":"2026-05-18T12:32:22Z"},{"alias_kind":"pith_short_16","alias_value":"FJ67XDMWTKJQXFU2","created_at":"2026-05-18T12:32:22Z"},{"alias_kind":"pith_short_8","alias_value":"FJ67XDMW","created_at":"2026-05-18T12:32:22Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:FJ67XDMWTKJQXFU2XHZS3TXBW6","target":"record","payload":{"canonical_record":{"source":{"id":"1807.08505","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"eess.SP","submitted_at":"2018-07-23T09:42:30Z","cross_cats_sorted":[],"title_canon_sha256":"b00f6151256dec5ef2ff3b82e5c9fa043bcc7a9e5a696ef9f51ff925fb0c13f2","abstract_canon_sha256":"4fad56b7cb44b6b3397a1b223d7c2951175ea1f47ccaa09e8ca56f6c42df93c7"},"schema_version":"1.0"},"canonical_sha256":"2a7dfb8d969a930b969ab9f32dcee1b78f4acac7ccb0a92605bda58ecae5bff5","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:52:52.640376Z","signature_b64":"iE/EAQlj4I3inrcZsjQ5bhEDQLrQuHzQjI+L4DRt+/OBv9q4fI6uoo21CqoZrK70lpPoeZAC/I6AW/KyCow7DA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2a7dfb8d969a930b969ab9f32dcee1b78f4acac7ccb0a92605bda58ecae5bff5","last_reissued_at":"2026-05-17T23:52:52.639598Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:52:52.639598Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1807.08505","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:52:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nw3tTLVtK0bSyrTH86l475LeP/Zc5SxORZvE1iMVrYY0/WvWBv/yOqjBG/3hQpBGLKs28D3BrKh0hCkMLtqGAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T12:40:09.061632Z"},"content_sha256":"0840aa41a9ce95e825e30881c6285d103141db3485f591ddd4acafac6c699eab","schema_version":"1.0","event_id":"sha256:0840aa41a9ce95e825e30881c6285d103141db3485f591ddd4acafac6c699eab"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:FJ67XDMWTKJQXFU2XHZS3TXBW6","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The Semiparametric Cram\\'er-Rao Bound for Complex Elliptically Symmetric Distributions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"eess.SP","authors_text":"Abdelhak M. Zoubir, Fulvio Gini, Maria S. Greco, Stefano Fortunati","submitted_at":"2018-07-23T09:42:30Z","abstract_excerpt":"This letter aims at extending the Constrained Semiparametric Cramer-Rao Bound (CSCRB) for the joint estimation of mean vector and scatter matrix of Real Elliptically Symmetric (RES) distributions to Complex Elliptically Symmetric (CES) distributions. A closed form expression for the complex CSCRB (CCSCRB) is derived by exploiting the so-called \\textit{Wirtinger} or $\\mathbb{C}\\mathbb{R}$-\\textit{calculus}. Finally, the CCSCRB for the estimation of the complex mean vector and scatter matrix of a set of complex $t$-distributed random vectors is provided as an example of application."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.08505","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:52:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xtoDZCEc3I+cUOn6ZMWn+o4nMNu+lFNEfSCvI1n1GzbJe9l2CLp/Q5Ly33oVxJiV/TWEHw4r9HYHh+r6l2XgDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T12:40:09.062021Z"},"content_sha256":"8d6c26347a73684d4b56b1e3d42b48121be2453e7ec3749fc218a6ace89e2267","schema_version":"1.0","event_id":"sha256:8d6c26347a73684d4b56b1e3d42b48121be2453e7ec3749fc218a6ace89e2267"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/FJ67XDMWTKJQXFU2XHZS3TXBW6/bundle.json","state_url":"https://pith.science/pith/FJ67XDMWTKJQXFU2XHZS3TXBW6/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/FJ67XDMWTKJQXFU2XHZS3TXBW6/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":"2026-06-10T12:40:09Z","links":{"resolver":"https://pith.science/pith/FJ67XDMWTKJQXFU2XHZS3TXBW6","bundle":"https://pith.science/pith/FJ67XDMWTKJQXFU2XHZS3TXBW6/bundle.json","state":"https://pith.science/pith/FJ67XDMWTKJQXFU2XHZS3TXBW6/state.json","well_known_bundle":"https://pith.science/.well-known/pith/FJ67XDMWTKJQXFU2XHZS3TXBW6/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:FJ67XDMWTKJQXFU2XHZS3TXBW6","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":"4fad56b7cb44b6b3397a1b223d7c2951175ea1f47ccaa09e8ca56f6c42df93c7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"eess.SP","submitted_at":"2018-07-23T09:42:30Z","title_canon_sha256":"b00f6151256dec5ef2ff3b82e5c9fa043bcc7a9e5a696ef9f51ff925fb0c13f2"},"schema_version":"1.0","source":{"id":"1807.08505","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1807.08505","created_at":"2026-05-17T23:52:52Z"},{"alias_kind":"arxiv_version","alias_value":"1807.08505v2","created_at":"2026-05-17T23:52:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1807.08505","created_at":"2026-05-17T23:52:52Z"},{"alias_kind":"pith_short_12","alias_value":"FJ67XDMWTKJQ","created_at":"2026-05-18T12:32:22Z"},{"alias_kind":"pith_short_16","alias_value":"FJ67XDMWTKJQXFU2","created_at":"2026-05-18T12:32:22Z"},{"alias_kind":"pith_short_8","alias_value":"FJ67XDMW","created_at":"2026-05-18T12:32:22Z"}],"graph_snapshots":[{"event_id":"sha256:8d6c26347a73684d4b56b1e3d42b48121be2453e7ec3749fc218a6ace89e2267","target":"graph","created_at":"2026-05-17T23:52:52Z","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":"This letter aims at extending the Constrained Semiparametric Cramer-Rao Bound (CSCRB) for the joint estimation of mean vector and scatter matrix of Real Elliptically Symmetric (RES) distributions to Complex Elliptically Symmetric (CES) distributions. A closed form expression for the complex CSCRB (CCSCRB) is derived by exploiting the so-called \\textit{Wirtinger} or $\\mathbb{C}\\mathbb{R}$-\\textit{calculus}. Finally, the CCSCRB for the estimation of the complex mean vector and scatter matrix of a set of complex $t$-distributed random vectors is provided as an example of application.","authors_text":"Abdelhak M. Zoubir, Fulvio Gini, Maria S. Greco, Stefano Fortunati","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"eess.SP","submitted_at":"2018-07-23T09:42:30Z","title":"The Semiparametric Cram\\'er-Rao Bound for Complex Elliptically Symmetric Distributions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.08505","kind":"arxiv","version":2},"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":"sha256:0840aa41a9ce95e825e30881c6285d103141db3485f591ddd4acafac6c699eab","target":"record","created_at":"2026-05-17T23:52:52Z","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":"4fad56b7cb44b6b3397a1b223d7c2951175ea1f47ccaa09e8ca56f6c42df93c7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"eess.SP","submitted_at":"2018-07-23T09:42:30Z","title_canon_sha256":"b00f6151256dec5ef2ff3b82e5c9fa043bcc7a9e5a696ef9f51ff925fb0c13f2"},"schema_version":"1.0","source":{"id":"1807.08505","kind":"arxiv","version":2}},"canonical_sha256":"2a7dfb8d969a930b969ab9f32dcee1b78f4acac7ccb0a92605bda58ecae5bff5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2a7dfb8d969a930b969ab9f32dcee1b78f4acac7ccb0a92605bda58ecae5bff5","first_computed_at":"2026-05-17T23:52:52.639598Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:52:52.639598Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"iE/EAQlj4I3inrcZsjQ5bhEDQLrQuHzQjI+L4DRt+/OBv9q4fI6uoo21CqoZrK70lpPoeZAC/I6AW/KyCow7DA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:52:52.640376Z","signed_message":"canonical_sha256_bytes"},"source_id":"1807.08505","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0840aa41a9ce95e825e30881c6285d103141db3485f591ddd4acafac6c699eab","sha256:8d6c26347a73684d4b56b1e3d42b48121be2453e7ec3749fc218a6ace89e2267"],"state_sha256":"a2aba950970499b7167cce3121d79e4fc7615e2c66556fc5b9d7115015089aab"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"EI+TrJX7u75R4+oo2wkmxayhqgGFSK+LLpQynUVZ8g0zVWLdqS15gtap5dKI3qDvbY/k8PBgxqb6mPXPEOeQBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-10T12:40:09.064303Z","bundle_sha256":"8be465906304058ef8b1bcc65e87087d128d5e2083d4dbe1731a0c32d7c1728b"}}