{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2021:P3Q7HBZUM53URMQSAWBHDCQT6K","short_pith_number":"pith:P3Q7HBZU","canonical_record":{"source":{"id":"2110.03324","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2021-10-07T10:36:49Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"1f3092134c311e0fa78a0dc33959023d3c0926a7bec7ef18a0451290a6b29c25","abstract_canon_sha256":"b7a85fa76d9386e5fd9fa695f21f8ede2fb590e74cf06b2e7e25107189e30194"},"schema_version":"1.0"},"canonical_sha256":"7ee1f38734677748b2120582718a13f2bd56ddd87d3704426662cef0f726d4e8","source":{"kind":"arxiv","id":"2110.03324","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2110.03324","created_at":"2026-07-05T04:29:09Z"},{"alias_kind":"arxiv_version","alias_value":"2110.03324v2","created_at":"2026-07-05T04:29:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2110.03324","created_at":"2026-07-05T04:29:09Z"},{"alias_kind":"pith_short_12","alias_value":"P3Q7HBZUM53U","created_at":"2026-07-05T04:29:09Z"},{"alias_kind":"pith_short_16","alias_value":"P3Q7HBZUM53URMQS","created_at":"2026-07-05T04:29:09Z"},{"alias_kind":"pith_short_8","alias_value":"P3Q7HBZU","created_at":"2026-07-05T04:29:09Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2021:P3Q7HBZUM53URMQSAWBHDCQT6K","target":"record","payload":{"canonical_record":{"source":{"id":"2110.03324","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2021-10-07T10:36:49Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"1f3092134c311e0fa78a0dc33959023d3c0926a7bec7ef18a0451290a6b29c25","abstract_canon_sha256":"b7a85fa76d9386e5fd9fa695f21f8ede2fb590e74cf06b2e7e25107189e30194"},"schema_version":"1.0"},"canonical_sha256":"7ee1f38734677748b2120582718a13f2bd56ddd87d3704426662cef0f726d4e8","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T04:29:09.756415Z","signature_b64":"HWiX9ReDEc+/LsynE5a0lNgeizwUef8jNGln2tLP3W0CpBiIzpmpm0caHyEwlFiqX+KkQdF53kCkFkvKxSWcBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7ee1f38734677748b2120582718a13f2bd56ddd87d3704426662cef0f726d4e8","last_reissued_at":"2026-07-05T04:29:09.755870Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T04:29:09.755870Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2110.03324","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":"2026-07-05T04:29:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mL7GYPf5rOnNBgS8v+i+we4tT6osx72UdkBYct2tETGhpKbCUiRXHdDfhHPSvj3H4AeUmW89iN/6cEv6goTUBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-03T21:47:33.039900Z"},"content_sha256":"dd47e3405a5814f068a18b21f58e9eaacb65c6246b23251e799552bc3581c5b5","schema_version":"1.0","event_id":"sha256:dd47e3405a5814f068a18b21f58e9eaacb65c6246b23251e799552bc3581c5b5"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2021:P3Q7HBZUM53URMQSAWBHDCQT6K","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Structured Channel Covariance Estimation from Limited Samples for Large Antenna Arrays","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Giuseppe Caire, Mahdi Barzegar Khalilsarai, Saeid Haghighatshoar, Tianyu Yang","submitted_at":"2021-10-07T10:36:49Z","abstract_excerpt":"In massive multiple-input multiple-output (MIMO) systems, the knowledge of the users' channel covariance matrix is crucial for minimum mean square error (MMSE) channel estimation in the uplink as well as it plays an important role in several multiuser beamforming schemes in the downlink. Due to the large number of base station antennas in massive MIMO, accurate covariance estimation is challenging especially in the case where the number of samples is limited and thus comparable to the channel vector dimension. As a result, the standard sample covariance estimator may yield a too large estimati"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2110.03324","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2110.03324/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T04:29:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"F3ptdWXtytOAHvykSqET+KXzU0CU5czNZOS61eMvOsw+5F36ewNrU+O0Wv180rzJ6fFNGuUFWCrizxfROzBkDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-03T21:47:33.040442Z"},"content_sha256":"bb7ccc8d9ea43a7923e8d06c8160f5e09a7d1a216ab4e83b7e5659283d9edaa0","schema_version":"1.0","event_id":"sha256:bb7ccc8d9ea43a7923e8d06c8160f5e09a7d1a216ab4e83b7e5659283d9edaa0"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/P3Q7HBZUM53URMQSAWBHDCQT6K/bundle.json","state_url":"https://pith.science/pith/P3Q7HBZUM53URMQSAWBHDCQT6K/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/P3Q7HBZUM53URMQSAWBHDCQT6K/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":"2026-08-03T21:47:33Z","links":{"resolver":"https://pith.science/pith/P3Q7HBZUM53URMQSAWBHDCQT6K","bundle":"https://pith.science/pith/P3Q7HBZUM53URMQSAWBHDCQT6K/bundle.json","state":"https://pith.science/pith/P3Q7HBZUM53URMQSAWBHDCQT6K/state.json","well_known_bundle":"https://pith.science/.well-known/pith/P3Q7HBZUM53URMQSAWBHDCQT6K/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:P3Q7HBZUM53URMQSAWBHDCQT6K","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":"b7a85fa76d9386e5fd9fa695f21f8ede2fb590e74cf06b2e7e25107189e30194","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2021-10-07T10:36:49Z","title_canon_sha256":"1f3092134c311e0fa78a0dc33959023d3c0926a7bec7ef18a0451290a6b29c25"},"schema_version":"1.0","source":{"id":"2110.03324","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2110.03324","created_at":"2026-07-05T04:29:09Z"},{"alias_kind":"arxiv_version","alias_value":"2110.03324v2","created_at":"2026-07-05T04:29:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2110.03324","created_at":"2026-07-05T04:29:09Z"},{"alias_kind":"pith_short_12","alias_value":"P3Q7HBZUM53U","created_at":"2026-07-05T04:29:09Z"},{"alias_kind":"pith_short_16","alias_value":"P3Q7HBZUM53URMQS","created_at":"2026-07-05T04:29:09Z"},{"alias_kind":"pith_short_8","alias_value":"P3Q7HBZU","created_at":"2026-07-05T04:29:09Z"}],"graph_snapshots":[{"event_id":"sha256:bb7ccc8d9ea43a7923e8d06c8160f5e09a7d1a216ab4e83b7e5659283d9edaa0","target":"graph","created_at":"2026-07-05T04:29:09Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2110.03324/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In massive multiple-input multiple-output (MIMO) systems, the knowledge of the users' channel covariance matrix is crucial for minimum mean square error (MMSE) channel estimation in the uplink as well as it plays an important role in several multiuser beamforming schemes in the downlink. Due to the large number of base station antennas in massive MIMO, accurate covariance estimation is challenging especially in the case where the number of samples is limited and thus comparable to the channel vector dimension. As a result, the standard sample covariance estimator may yield a too large estimati","authors_text":"Giuseppe Caire, Mahdi Barzegar Khalilsarai, Saeid Haghighatshoar, Tianyu Yang","cross_cats":["math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2021-10-07T10:36:49Z","title":"Structured Channel Covariance Estimation from Limited Samples for Large Antenna Arrays"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2110.03324","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:dd47e3405a5814f068a18b21f58e9eaacb65c6246b23251e799552bc3581c5b5","target":"record","created_at":"2026-07-05T04:29:09Z","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":"b7a85fa76d9386e5fd9fa695f21f8ede2fb590e74cf06b2e7e25107189e30194","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2021-10-07T10:36:49Z","title_canon_sha256":"1f3092134c311e0fa78a0dc33959023d3c0926a7bec7ef18a0451290a6b29c25"},"schema_version":"1.0","source":{"id":"2110.03324","kind":"arxiv","version":2}},"canonical_sha256":"7ee1f38734677748b2120582718a13f2bd56ddd87d3704426662cef0f726d4e8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7ee1f38734677748b2120582718a13f2bd56ddd87d3704426662cef0f726d4e8","first_computed_at":"2026-07-05T04:29:09.755870Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T04:29:09.755870Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"HWiX9ReDEc+/LsynE5a0lNgeizwUef8jNGln2tLP3W0CpBiIzpmpm0caHyEwlFiqX+KkQdF53kCkFkvKxSWcBw==","signature_status":"signed_v1","signed_at":"2026-07-05T04:29:09.756415Z","signed_message":"canonical_sha256_bytes"},"source_id":"2110.03324","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:dd47e3405a5814f068a18b21f58e9eaacb65c6246b23251e799552bc3581c5b5","sha256:bb7ccc8d9ea43a7923e8d06c8160f5e09a7d1a216ab4e83b7e5659283d9edaa0"],"state_sha256":"40092e0379471973465124c9727283b075961cb65410aafc25f83fa73df10e84"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KVZ2JDsuP2/IlkQLEeoyGE99aquVU85uHkR8ChXF+ojohOw5KKJmO64VXzBLFXiELpAaUPQx/wUlSKv6yey4Aw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-03T21:47:33.045362Z","bundle_sha256":"b72cd12f12229da45305c24909d67ac31a14f5dc0173b93b933d9830d7a64245"}}