{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:7OM3XXO2Y5FHZP6GKORRVYDMZN","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":"c646a346df1302dff553817842d0086d5f7b37b4fc74338aeb5bfa38f1e5e5ff","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2011-09-25T20:49:36Z","title_canon_sha256":"c803444235fec8d41fda091f56e9a1cb65910ec11602242f1666dce25ecda651"},"schema_version":"1.0","source":{"id":"1109.5396","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1109.5396","created_at":"2026-05-18T00:57:57Z"},{"alias_kind":"arxiv_version","alias_value":"1109.5396v1","created_at":"2026-05-18T00:57:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1109.5396","created_at":"2026-05-18T00:57:57Z"},{"alias_kind":"pith_short_12","alias_value":"7OM3XXO2Y5FH","created_at":"2026-05-18T12:26:22Z"},{"alias_kind":"pith_short_16","alias_value":"7OM3XXO2Y5FHZP6G","created_at":"2026-05-18T12:26:22Z"},{"alias_kind":"pith_short_8","alias_value":"7OM3XXO2","created_at":"2026-05-18T12:26:22Z"}],"graph_snapshots":[{"event_id":"sha256:0488d1c8406edefe4d71c13aaa3ee5b8d06cebe830d2b694dc1ca5ca186a7e5a","target":"graph","created_at":"2026-05-18T00:57:57Z","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) of the K-user interference channel with coordinated multi-point (CoMP) transmission and reception. Each message is jointly transmitted by M_t successive transmitters, and is jointly received by M_r successive receivers. We refer to this channel as the CoMP channel with a transmit cooperation order of M_t and receive cooperation order of M_r. Since the channel has a total of K transmit antennas and K receive antennas, the maximum possible DoF is equal to K. We show that the CoMP channel has K DoF if and only if M_t + M_r is greater than or equal to K+1. For","authors_text":"Aly El Gamal, Venugopal V. Veeravalli, V. Sreekanth Annapureddy","cross_cats":["math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2011-09-25T20:49:36Z","title":"Degrees of Freedom of Interference Channels with CoMP Transmission and Reception"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.5396","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":"sha256:554fd3100c6d73915a0165c3ad327985147fab4fb2356fdd57536d9ca0965bd7","target":"record","created_at":"2026-05-18T00:57:57Z","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":"c646a346df1302dff553817842d0086d5f7b37b4fc74338aeb5bfa38f1e5e5ff","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2011-09-25T20:49:36Z","title_canon_sha256":"c803444235fec8d41fda091f56e9a1cb65910ec11602242f1666dce25ecda651"},"schema_version":"1.0","source":{"id":"1109.5396","kind":"arxiv","version":1}},"canonical_sha256":"fb99bbdddac74a7cbfc653a31ae06ccb7de9d7300614bf93ea233ff9d81f28a3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fb99bbdddac74a7cbfc653a31ae06ccb7de9d7300614bf93ea233ff9d81f28a3","first_computed_at":"2026-05-18T00:57:57.218425Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:57:57.218425Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"MlbfM/pXYcDADSVeNtJp+8E70CATs5CqRy/y0LHT3oZTQ+2LIT6WCyc6WEfuNSktZ4+16sCdOD33EoKbC1EpAA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:57:57.218988Z","signed_message":"canonical_sha256_bytes"},"source_id":"1109.5396","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:554fd3100c6d73915a0165c3ad327985147fab4fb2356fdd57536d9ca0965bd7","sha256:0488d1c8406edefe4d71c13aaa3ee5b8d06cebe830d2b694dc1ca5ca186a7e5a"],"state_sha256":"9ad62f12647f3fc7b1e7571020e44d3f87a7028ed4151986a8a9e66cf96b4288"}