{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:SSV3YA7ZWZGX2M7IRAFI2YP5EL","short_pith_number":"pith:SSV3YA7Z","canonical_record":{"source":{"id":"1011.2196","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2010-11-09T20:48:49Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"64986a81a935806d0e9411590516cb61fb4155d9c6b19a5c3e425f8ba0639c0e","abstract_canon_sha256":"c1454e83e0bbf85e981eeaee0d753a113f666a71e2710108f1765b80bc1a87db"},"schema_version":"1.0"},"canonical_sha256":"94abbc03f9b64d7d33e8880a8d61fd22f0c2a820719cfb52aa09755a5c381ef4","source":{"kind":"arxiv","id":"1011.2196","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1011.2196","created_at":"2026-05-18T04:36:42Z"},{"alias_kind":"arxiv_version","alias_value":"1011.2196v1","created_at":"2026-05-18T04:36:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1011.2196","created_at":"2026-05-18T04:36:42Z"},{"alias_kind":"pith_short_12","alias_value":"SSV3YA7ZWZGX","created_at":"2026-05-18T12:26:13Z"},{"alias_kind":"pith_short_16","alias_value":"SSV3YA7ZWZGX2M7I","created_at":"2026-05-18T12:26:13Z"},{"alias_kind":"pith_short_8","alias_value":"SSV3YA7Z","created_at":"2026-05-18T12:26:13Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:SSV3YA7ZWZGX2M7IRAFI2YP5EL","target":"record","payload":{"canonical_record":{"source":{"id":"1011.2196","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2010-11-09T20:48:49Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"64986a81a935806d0e9411590516cb61fb4155d9c6b19a5c3e425f8ba0639c0e","abstract_canon_sha256":"c1454e83e0bbf85e981eeaee0d753a113f666a71e2710108f1765b80bc1a87db"},"schema_version":"1.0"},"canonical_sha256":"94abbc03f9b64d7d33e8880a8d61fd22f0c2a820719cfb52aa09755a5c381ef4","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:36:42.397792Z","signature_b64":"xRpe6f/PLjipo5ZuznNRYs6zDZErbzPYWOR39G1kcrHA7fD17GlQrBW+pkJLgutwzKWCtrt9gdb0Zhw7GioFAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"94abbc03f9b64d7d33e8880a8d61fd22f0c2a820719cfb52aa09755a5c381ef4","last_reissued_at":"2026-05-18T04:36:42.397350Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:36:42.397350Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1011.2196","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":"2026-05-18T04:36:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qsKEf63d4e48Ffvc+Gl6Tcgbzc8nyU7/d+FskP8YY0x2yb1ByZueerge2qXeeeaZYnmIkK1ISL6BAh7jEW/6CQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T12:43:24.857928Z"},"content_sha256":"82f47e1e71bb4a1a0afa4601eaed301891de775f8282ed3fc51b79eb59c3a460","schema_version":"1.0","event_id":"sha256:82f47e1e71bb4a1a0afa4601eaed301891de775f8282ed3fc51b79eb59c3a460"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:SSV3YA7ZWZGX2M7IRAFI2YP5EL","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Degrees of Freedom Regions of Two-User MIMO Z and Full Interference Channels: The Benefit of Reconfigurable Antennas","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Lei Ke, Zhengdao Wang","submitted_at":"2010-11-09T20:48:49Z","abstract_excerpt":"We study the degrees of freedom (DoF) regions of two-user multiple-input multiple-output (MIMO) Z and full interference channels in this paper. We assume that the receivers always have perfect channel state information. We first derive the DoF region of Z interference channel with channel state information at transmitter (CSIT). For full interference channel without CSIT, the DoF region has been fully characterized recently and it is shown that the previously known outer bound is not achievable. In this work, we investigate the no-CSIT case further by assuming that the transmitter has the abil"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1011.2196","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":"2026-05-18T04:36:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zutX2l3InuI4cav3NkCgwrQU61QEzdHL43LeIBlLM7IHkS5WpIxq/1VJZYozKLC+M9Na+u3XCrwF+Zkaz94HBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T12:43:24.858273Z"},"content_sha256":"7ed08362e0bdeaa2b2ba26b1a4af13c3114ac07ca4f2d6db3294034e26274b64","schema_version":"1.0","event_id":"sha256:7ed08362e0bdeaa2b2ba26b1a4af13c3114ac07ca4f2d6db3294034e26274b64"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/SSV3YA7ZWZGX2M7IRAFI2YP5EL/bundle.json","state_url":"https://pith.science/pith/SSV3YA7ZWZGX2M7IRAFI2YP5EL/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/SSV3YA7ZWZGX2M7IRAFI2YP5EL/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":"2026-06-26T12:43:24Z","links":{"resolver":"https://pith.science/pith/SSV3YA7ZWZGX2M7IRAFI2YP5EL","bundle":"https://pith.science/pith/SSV3YA7ZWZGX2M7IRAFI2YP5EL/bundle.json","state":"https://pith.science/pith/SSV3YA7ZWZGX2M7IRAFI2YP5EL/state.json","well_known_bundle":"https://pith.science/.well-known/pith/SSV3YA7ZWZGX2M7IRAFI2YP5EL/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:SSV3YA7ZWZGX2M7IRAFI2YP5EL","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":"c1454e83e0bbf85e981eeaee0d753a113f666a71e2710108f1765b80bc1a87db","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2010-11-09T20:48:49Z","title_canon_sha256":"64986a81a935806d0e9411590516cb61fb4155d9c6b19a5c3e425f8ba0639c0e"},"schema_version":"1.0","source":{"id":"1011.2196","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1011.2196","created_at":"2026-05-18T04:36:42Z"},{"alias_kind":"arxiv_version","alias_value":"1011.2196v1","created_at":"2026-05-18T04:36:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1011.2196","created_at":"2026-05-18T04:36:42Z"},{"alias_kind":"pith_short_12","alias_value":"SSV3YA7ZWZGX","created_at":"2026-05-18T12:26:13Z"},{"alias_kind":"pith_short_16","alias_value":"SSV3YA7ZWZGX2M7I","created_at":"2026-05-18T12:26:13Z"},{"alias_kind":"pith_short_8","alias_value":"SSV3YA7Z","created_at":"2026-05-18T12:26:13Z"}],"graph_snapshots":[{"event_id":"sha256:7ed08362e0bdeaa2b2ba26b1a4af13c3114ac07ca4f2d6db3294034e26274b64","target":"graph","created_at":"2026-05-18T04:36:42Z","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":"We study the degrees of freedom (DoF) regions of two-user multiple-input multiple-output (MIMO) Z and full interference channels in this paper. We assume that the receivers always have perfect channel state information. We first derive the DoF region of Z interference channel with channel state information at transmitter (CSIT). For full interference channel without CSIT, the DoF region has been fully characterized recently and it is shown that the previously known outer bound is not achievable. In this work, we investigate the no-CSIT case further by assuming that the transmitter has the abil","authors_text":"Lei Ke, Zhengdao Wang","cross_cats":["math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2010-11-09T20:48:49Z","title":"Degrees of Freedom Regions of Two-User MIMO Z and Full Interference Channels: The Benefit of Reconfigurable Antennas"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1011.2196","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":"sha256:82f47e1e71bb4a1a0afa4601eaed301891de775f8282ed3fc51b79eb59c3a460","target":"record","created_at":"2026-05-18T04:36:42Z","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":"c1454e83e0bbf85e981eeaee0d753a113f666a71e2710108f1765b80bc1a87db","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2010-11-09T20:48:49Z","title_canon_sha256":"64986a81a935806d0e9411590516cb61fb4155d9c6b19a5c3e425f8ba0639c0e"},"schema_version":"1.0","source":{"id":"1011.2196","kind":"arxiv","version":1}},"canonical_sha256":"94abbc03f9b64d7d33e8880a8d61fd22f0c2a820719cfb52aa09755a5c381ef4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"94abbc03f9b64d7d33e8880a8d61fd22f0c2a820719cfb52aa09755a5c381ef4","first_computed_at":"2026-05-18T04:36:42.397350Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:36:42.397350Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"xRpe6f/PLjipo5ZuznNRYs6zDZErbzPYWOR39G1kcrHA7fD17GlQrBW+pkJLgutwzKWCtrt9gdb0Zhw7GioFAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:36:42.397792Z","signed_message":"canonical_sha256_bytes"},"source_id":"1011.2196","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:82f47e1e71bb4a1a0afa4601eaed301891de775f8282ed3fc51b79eb59c3a460","sha256:7ed08362e0bdeaa2b2ba26b1a4af13c3114ac07ca4f2d6db3294034e26274b64"],"state_sha256":"1a38c3f114187bdfc6624f772031893f4a20261fc2d92df45a188ad131af16d4"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+HANPFmbrtQaZCGHLlZoinJIVM2qMfO40Z9hbQwDK++HK5QGE6zosxG3RRBrXDt+YrQWdb3E0MhrETSXZYS0BA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-26T12:43:24.860297Z","bundle_sha256":"f336a5e6d1b70b9a36d282c9424499910e72a19e417ed4c172aa183661ac3034"}}