{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:3BETCMBNXIZA2VI5462FFXVINF","short_pith_number":"pith:3BETCMBN","canonical_record":{"source":{"id":"1212.0047","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2012-12-01T00:00:44Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"9da2b4ebf973d14be4112e53eae313c0788fdfca74d3dfd9e42a88b4fc48fe1a","abstract_canon_sha256":"76d118217f0b299aed55a6816a0bceeab74f50c5bb375ae2119b719cdcaa21a6"},"schema_version":"1.0"},"canonical_sha256":"d84931302dba320d551de7b452dea8697ae1257b89498eedbd841e3bde9c63e4","source":{"kind":"arxiv","id":"1212.0047","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1212.0047","created_at":"2026-05-18T00:58:42Z"},{"alias_kind":"arxiv_version","alias_value":"1212.0047v1","created_at":"2026-05-18T00:58:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1212.0047","created_at":"2026-05-18T00:58:42Z"},{"alias_kind":"pith_short_12","alias_value":"3BETCMBNXIZA","created_at":"2026-05-18T12:26:50Z"},{"alias_kind":"pith_short_16","alias_value":"3BETCMBNXIZA2VI5","created_at":"2026-05-18T12:26:50Z"},{"alias_kind":"pith_short_8","alias_value":"3BETCMBN","created_at":"2026-05-18T12:26:50Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:3BETCMBNXIZA2VI5462FFXVINF","target":"record","payload":{"canonical_record":{"source":{"id":"1212.0047","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2012-12-01T00:00:44Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"9da2b4ebf973d14be4112e53eae313c0788fdfca74d3dfd9e42a88b4fc48fe1a","abstract_canon_sha256":"76d118217f0b299aed55a6816a0bceeab74f50c5bb375ae2119b719cdcaa21a6"},"schema_version":"1.0"},"canonical_sha256":"d84931302dba320d551de7b452dea8697ae1257b89498eedbd841e3bde9c63e4","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:58:42.763948Z","signature_b64":"Qt7hm1uNhkxax9en3/V3pSEMBQRbF5hsFO2M4JFKlLOKiRbd2zcVS14S6ovKLfHlYl0mCE+AUi2QtrGd9qdvAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d84931302dba320d551de7b452dea8697ae1257b89498eedbd841e3bde9c63e4","last_reissued_at":"2026-05-18T00:58:42.763577Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:58:42.763577Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1212.0047","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:58:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"z8/VpcwuJQ7kWNbhOaCObfht3PE1nW84n1NOkduYQZDIShzSpTAaV86OugUHZ9GX1xW7+kb0D/UIavT+k+ouBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T02:33:35.674954Z"},"content_sha256":"d7f1e8ddf00696132e2cbc2641460872db8ea4242b0cdadc0dd91ea31c995578","schema_version":"1.0","event_id":"sha256:d7f1e8ddf00696132e2cbc2641460872db8ea4242b0cdadc0dd91ea31c995578"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:3BETCMBNXIZA2VI5462FFXVINF","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the capacity limit of wireless channels under colored scattering","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Dongwoon Bai, Inyup Kang, Jungwon Lee, Wooseok Nam","submitted_at":"2012-12-01T00:00:44Z","abstract_excerpt":"It has been generally believed that the multiple-input multiple-output (MIMO) channel capacity grows linearly with the size of antenna arrays. In terms of degrees of freedom, linear transmit and receive arrays of length $L$ in a scattering environment of total angular spread $|\\Omega|$ asymptotically have $|\\Omega| L$ degrees of freedom. In this paper, it is claimed that the linear increase in degrees of freedom may not be attained when scattered electromagnetic fields in the underlying scattering environment are statistically correlated. After introducing a model of correlated scattering, whi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.0047","kind":"arxiv","version":1},"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":"2026-05-18T00:58:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"BQPEc8gbIM4tToJeulO/eZsXaJ+Vgq/vmizEkWcBuHeOq366YHRsySlUJrbno8QYNw6eU5/7CLjvYh/USbyfDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T02:33:35.675599Z"},"content_sha256":"be3917a9f0f3ffef0c559f106e9688b6f9b14815e7565a7a023b6eebf9b6f529","schema_version":"1.0","event_id":"sha256:be3917a9f0f3ffef0c559f106e9688b6f9b14815e7565a7a023b6eebf9b6f529"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/3BETCMBNXIZA2VI5462FFXVINF/bundle.json","state_url":"https://pith.science/pith/3BETCMBNXIZA2VI5462FFXVINF/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/3BETCMBNXIZA2VI5462FFXVINF/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":"2026-05-27T02:33:35Z","links":{"resolver":"https://pith.science/pith/3BETCMBNXIZA2VI5462FFXVINF","bundle":"https://pith.science/pith/3BETCMBNXIZA2VI5462FFXVINF/bundle.json","state":"https://pith.science/pith/3BETCMBNXIZA2VI5462FFXVINF/state.json","well_known_bundle":"https://pith.science/.well-known/pith/3BETCMBNXIZA2VI5462FFXVINF/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:3BETCMBNXIZA2VI5462FFXVINF","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":"76d118217f0b299aed55a6816a0bceeab74f50c5bb375ae2119b719cdcaa21a6","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2012-12-01T00:00:44Z","title_canon_sha256":"9da2b4ebf973d14be4112e53eae313c0788fdfca74d3dfd9e42a88b4fc48fe1a"},"schema_version":"1.0","source":{"id":"1212.0047","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1212.0047","created_at":"2026-05-18T00:58:42Z"},{"alias_kind":"arxiv_version","alias_value":"1212.0047v1","created_at":"2026-05-18T00:58:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1212.0047","created_at":"2026-05-18T00:58:42Z"},{"alias_kind":"pith_short_12","alias_value":"3BETCMBNXIZA","created_at":"2026-05-18T12:26:50Z"},{"alias_kind":"pith_short_16","alias_value":"3BETCMBNXIZA2VI5","created_at":"2026-05-18T12:26:50Z"},{"alias_kind":"pith_short_8","alias_value":"3BETCMBN","created_at":"2026-05-18T12:26:50Z"}],"graph_snapshots":[{"event_id":"sha256:be3917a9f0f3ffef0c559f106e9688b6f9b14815e7565a7a023b6eebf9b6f529","target":"graph","created_at":"2026-05-18T00:58:42Z","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":"It has been generally believed that the multiple-input multiple-output (MIMO) channel capacity grows linearly with the size of antenna arrays. In terms of degrees of freedom, linear transmit and receive arrays of length $L$ in a scattering environment of total angular spread $|\\Omega|$ asymptotically have $|\\Omega| L$ degrees of freedom. In this paper, it is claimed that the linear increase in degrees of freedom may not be attained when scattered electromagnetic fields in the underlying scattering environment are statistically correlated. After introducing a model of correlated scattering, whi","authors_text":"Dongwoon Bai, Inyup Kang, Jungwon Lee, Wooseok Nam","cross_cats":["math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2012-12-01T00:00:44Z","title":"On the capacity limit of wireless channels under colored scattering"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.0047","kind":"arxiv","version":1},"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:d7f1e8ddf00696132e2cbc2641460872db8ea4242b0cdadc0dd91ea31c995578","target":"record","created_at":"2026-05-18T00:58:42Z","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":"76d118217f0b299aed55a6816a0bceeab74f50c5bb375ae2119b719cdcaa21a6","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2012-12-01T00:00:44Z","title_canon_sha256":"9da2b4ebf973d14be4112e53eae313c0788fdfca74d3dfd9e42a88b4fc48fe1a"},"schema_version":"1.0","source":{"id":"1212.0047","kind":"arxiv","version":1}},"canonical_sha256":"d84931302dba320d551de7b452dea8697ae1257b89498eedbd841e3bde9c63e4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d84931302dba320d551de7b452dea8697ae1257b89498eedbd841e3bde9c63e4","first_computed_at":"2026-05-18T00:58:42.763577Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:58:42.763577Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Qt7hm1uNhkxax9en3/V3pSEMBQRbF5hsFO2M4JFKlLOKiRbd2zcVS14S6ovKLfHlYl0mCE+AUi2QtrGd9qdvAg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:58:42.763948Z","signed_message":"canonical_sha256_bytes"},"source_id":"1212.0047","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d7f1e8ddf00696132e2cbc2641460872db8ea4242b0cdadc0dd91ea31c995578","sha256:be3917a9f0f3ffef0c559f106e9688b6f9b14815e7565a7a023b6eebf9b6f529"],"state_sha256":"c1eb09a6f680d4997cadfadcf03358ab41e3f57dbcc449736d48f266d86eefa0"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lRYWRqXc7OzE/TG5TDZVbzKmk7dcxwQ7jQHP7ElRk7IH54okVyO/qgnJLJSEFRGIsWI53FFEVAi0C9W75YngCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T02:33:35.678701Z","bundle_sha256":"a8c24e00259481011367e79c1038efdb35dd4ab06b076848b9c0156ed4b9fc97"}}