{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:C3S4NBGNA46BM7QHAT774UEO7I","short_pith_number":"pith:C3S4NBGN","canonical_record":{"source":{"id":"1510.00359","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2015-10-01T18:25:11Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"7fcfbb69773a1fcc14edc92dfbdecb0d4f4c5d10be9ca2e2eca3395c3d43e470","abstract_canon_sha256":"b660c441153362b9646a6bb28188fa4a1c97f019bdd39f0143e51cd5821979e3"},"schema_version":"1.0"},"canonical_sha256":"16e5c684cd073c167e0704fffe508efa144480d8d0417693dc70091d0dd2d4bd","source":{"kind":"arxiv","id":"1510.00359","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1510.00359","created_at":"2026-05-18T00:58:57Z"},{"alias_kind":"arxiv_version","alias_value":"1510.00359v3","created_at":"2026-05-18T00:58:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1510.00359","created_at":"2026-05-18T00:58:57Z"},{"alias_kind":"pith_short_12","alias_value":"C3S4NBGNA46B","created_at":"2026-05-18T12:29:14Z"},{"alias_kind":"pith_short_16","alias_value":"C3S4NBGNA46BM7QH","created_at":"2026-05-18T12:29:14Z"},{"alias_kind":"pith_short_8","alias_value":"C3S4NBGN","created_at":"2026-05-18T12:29:14Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:C3S4NBGNA46BM7QHAT774UEO7I","target":"record","payload":{"canonical_record":{"source":{"id":"1510.00359","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2015-10-01T18:25:11Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"7fcfbb69773a1fcc14edc92dfbdecb0d4f4c5d10be9ca2e2eca3395c3d43e470","abstract_canon_sha256":"b660c441153362b9646a6bb28188fa4a1c97f019bdd39f0143e51cd5821979e3"},"schema_version":"1.0"},"canonical_sha256":"16e5c684cd073c167e0704fffe508efa144480d8d0417693dc70091d0dd2d4bd","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:58:57.726997Z","signature_b64":"onJOXCNtBVQQJ4NSYD+SybvlBXArW6gYEaVaIOLw3eRHL4TNHvYnc1hfNRd4HuHC2XuYa/gZqrBNWPIASw+QAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"16e5c684cd073c167e0704fffe508efa144480d8d0417693dc70091d0dd2d4bd","last_reissued_at":"2026-05-18T00:58:57.726415Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:58:57.726415Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1510.00359","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:58:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rbwLZRHAs490aIXMRtxWSo+gT9+LmGW6GZNiLAfjjDNKa2rxQd15Dyl/BZ6UCSfoqRc+qMZZpsArrG3q6jfmBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T01:28:03.881886Z"},"content_sha256":"2846e65acd9c7455a48ec66cb978928d8be0a117e8daa0786f7043833ba003a1","schema_version":"1.0","event_id":"sha256:2846e65acd9c7455a48ec66cb978928d8be0a117e8daa0786f7043833ba003a1"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:C3S4NBGNA46BM7QHAT774UEO7I","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Achievable Degrees of Freedom on K-user MIMO Multi-way Relay Channel with Common and Private Messages","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Amr El-Keyi, Mohamed Salah, Mohammed Nafie, Yahya Mohasseb","submitted_at":"2015-10-01T18:25:11Z","abstract_excerpt":"This paper investigates the achievable total degrees of freedom (DoF) of the MIMO multi-way relay channel that consists of K users, where each user is equipped with M antennas, and a decode-and-forward relay equipped with N antennas. In this channel, each user wants to convey K-1 private messages to the other users in addition to a common message to all of them. Due to the absence of direct links between the users, communication occurs through the relay in two phases; a multiple access channel phase (MAC) and a broadcast (BC) phase. We drive cut-set bounds on the total DoF of the network, and "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.00359","kind":"arxiv","version":3},"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":"2026-05-18T00:58:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xlKA2FSA3144fUbCPF85DPDp5xfjk7SV2N0hLqpe4Xa9bKUmcgg4tJVNmqSnAppysEkpZzkj2ep/dTH5BKfsAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T01:28:03.882295Z"},"content_sha256":"10c0b77bccda86a356067c128c8815c770971bf35baa0ee16c3c78fc070c64dd","schema_version":"1.0","event_id":"sha256:10c0b77bccda86a356067c128c8815c770971bf35baa0ee16c3c78fc070c64dd"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/C3S4NBGNA46BM7QHAT774UEO7I/bundle.json","state_url":"https://pith.science/pith/C3S4NBGNA46BM7QHAT774UEO7I/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/C3S4NBGNA46BM7QHAT774UEO7I/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":"2026-06-11T01:28:03Z","links":{"resolver":"https://pith.science/pith/C3S4NBGNA46BM7QHAT774UEO7I","bundle":"https://pith.science/pith/C3S4NBGNA46BM7QHAT774UEO7I/bundle.json","state":"https://pith.science/pith/C3S4NBGNA46BM7QHAT774UEO7I/state.json","well_known_bundle":"https://pith.science/.well-known/pith/C3S4NBGNA46BM7QHAT774UEO7I/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:C3S4NBGNA46BM7QHAT774UEO7I","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":"b660c441153362b9646a6bb28188fa4a1c97f019bdd39f0143e51cd5821979e3","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2015-10-01T18:25:11Z","title_canon_sha256":"7fcfbb69773a1fcc14edc92dfbdecb0d4f4c5d10be9ca2e2eca3395c3d43e470"},"schema_version":"1.0","source":{"id":"1510.00359","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1510.00359","created_at":"2026-05-18T00:58:57Z"},{"alias_kind":"arxiv_version","alias_value":"1510.00359v3","created_at":"2026-05-18T00:58:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1510.00359","created_at":"2026-05-18T00:58:57Z"},{"alias_kind":"pith_short_12","alias_value":"C3S4NBGNA46B","created_at":"2026-05-18T12:29:14Z"},{"alias_kind":"pith_short_16","alias_value":"C3S4NBGNA46BM7QH","created_at":"2026-05-18T12:29:14Z"},{"alias_kind":"pith_short_8","alias_value":"C3S4NBGN","created_at":"2026-05-18T12:29:14Z"}],"graph_snapshots":[{"event_id":"sha256:10c0b77bccda86a356067c128c8815c770971bf35baa0ee16c3c78fc070c64dd","target":"graph","created_at":"2026-05-18T00:58:57Z","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":"This paper investigates the achievable total degrees of freedom (DoF) of the MIMO multi-way relay channel that consists of K users, where each user is equipped with M antennas, and a decode-and-forward relay equipped with N antennas. In this channel, each user wants to convey K-1 private messages to the other users in addition to a common message to all of them. Due to the absence of direct links between the users, communication occurs through the relay in two phases; a multiple access channel phase (MAC) and a broadcast (BC) phase. We drive cut-set bounds on the total DoF of the network, and ","authors_text":"Amr El-Keyi, Mohamed Salah, Mohammed Nafie, Yahya Mohasseb","cross_cats":["math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2015-10-01T18:25:11Z","title":"Achievable Degrees of Freedom on K-user MIMO Multi-way Relay Channel with Common and Private Messages"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.00359","kind":"arxiv","version":3},"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":"sha256:2846e65acd9c7455a48ec66cb978928d8be0a117e8daa0786f7043833ba003a1","target":"record","created_at":"2026-05-18T00:58:57Z","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":"b660c441153362b9646a6bb28188fa4a1c97f019bdd39f0143e51cd5821979e3","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2015-10-01T18:25:11Z","title_canon_sha256":"7fcfbb69773a1fcc14edc92dfbdecb0d4f4c5d10be9ca2e2eca3395c3d43e470"},"schema_version":"1.0","source":{"id":"1510.00359","kind":"arxiv","version":3}},"canonical_sha256":"16e5c684cd073c167e0704fffe508efa144480d8d0417693dc70091d0dd2d4bd","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"16e5c684cd073c167e0704fffe508efa144480d8d0417693dc70091d0dd2d4bd","first_computed_at":"2026-05-18T00:58:57.726415Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:58:57.726415Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"onJOXCNtBVQQJ4NSYD+SybvlBXArW6gYEaVaIOLw3eRHL4TNHvYnc1hfNRd4HuHC2XuYa/gZqrBNWPIASw+QAg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:58:57.726997Z","signed_message":"canonical_sha256_bytes"},"source_id":"1510.00359","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2846e65acd9c7455a48ec66cb978928d8be0a117e8daa0786f7043833ba003a1","sha256:10c0b77bccda86a356067c128c8815c770971bf35baa0ee16c3c78fc070c64dd"],"state_sha256":"1148cf5434f3f3ba12d640dd36df3ddd2c16edc57f8ae89e1b5c8beff0cdd4c9"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"30PESRO2uKCv/wWgin7AstaGFy9qatR4eEeXjkljI1M1Uj2iJYwto4u7hFrF/HwSSW7NK/VIgtw/azOwdoH7DQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-11T01:28:03.885512Z","bundle_sha256":"33e88c7984bba8456ea78d3569af905933cc18618c249d2ec3f9adf13fd787e8"}}