{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:OXZEGEZPUVTCKKZ5QDZLRDCIF7","short_pith_number":"pith:OXZEGEZP","canonical_record":{"source":{"id":"1001.4271","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2010-01-24T19:50:02Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"c8708b208426047dde6708d33ae1338c61a2e33debe4a7b84efcaa738345886e","abstract_canon_sha256":"5a31a285d597150f76c39155df00a75127e27ae0519efb82e7c4a41f5a2bca88"},"schema_version":"1.0"},"canonical_sha256":"75f243132fa566252b3d80f2b88c482fcc0bdf1a5ae46561f789c2994d2abadf","source":{"kind":"arxiv","id":"1001.4271","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1001.4271","created_at":"2026-05-18T00:58:19Z"},{"alias_kind":"arxiv_version","alias_value":"1001.4271v3","created_at":"2026-05-18T00:58:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1001.4271","created_at":"2026-05-18T00:58:19Z"},{"alias_kind":"pith_short_12","alias_value":"OXZEGEZPUVTC","created_at":"2026-05-18T12:26:12Z"},{"alias_kind":"pith_short_16","alias_value":"OXZEGEZPUVTCKKZ5","created_at":"2026-05-18T12:26:12Z"},{"alias_kind":"pith_short_8","alias_value":"OXZEGEZP","created_at":"2026-05-18T12:26:12Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:OXZEGEZPUVTCKKZ5QDZLRDCIF7","target":"record","payload":{"canonical_record":{"source":{"id":"1001.4271","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2010-01-24T19:50:02Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"c8708b208426047dde6708d33ae1338c61a2e33debe4a7b84efcaa738345886e","abstract_canon_sha256":"5a31a285d597150f76c39155df00a75127e27ae0519efb82e7c4a41f5a2bca88"},"schema_version":"1.0"},"canonical_sha256":"75f243132fa566252b3d80f2b88c482fcc0bdf1a5ae46561f789c2994d2abadf","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:58:19.770030Z","signature_b64":"HFCFzqhB0fW5N0kRcH2bulZueeGuguhjKZUM7HQoALjcnK/3BXtrpOredHudepc8fNCWOKbtinXQFosZcJr1CA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"75f243132fa566252b3d80f2b88c482fcc0bdf1a5ae46561f789c2994d2abadf","last_reissued_at":"2026-05-18T00:58:19.769366Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:58:19.769366Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1001.4271","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":"2026-05-18T00:58:19Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TxeOedGEjJCkbMzhf9strnnSIoRGUUDa3wjb6MoBb8xi1gkK0Lu9gs1PKQF/PNEFiGiLAPDX/pW8Lo58opNEDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T21:21:13.611511Z"},"content_sha256":"9c52f32dd3a92914b366c34e88b63c2d8241bdbb2ffb9069ed2636c74ea16c18","schema_version":"1.0","event_id":"sha256:9c52f32dd3a92914b366c34e88b63c2d8241bdbb2ffb9069ed2636c74ea16c18"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:OXZEGEZPUVTCKKZ5QDZLRDCIF7","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Divide-and-conquer: Approaching the capacity of the two-pair bidirectional Gaussian relay network","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"A. Salman Avestimehr, Aydin Sezgin, Babak Hassibi, M. Amin Khajehnejad","submitted_at":"2010-01-24T19:50:02Z","abstract_excerpt":"The capacity region of multi-pair bidirectional relay networks, in which a relay node facilitates the communication between multiple pairs of users, is studied. This problem is first examined in the context of the linear shift deterministic channel model. The capacity region of this network when the relay is operating at either full-duplex mode or half-duplex mode for arbitrary number of pairs is characterized. It is shown that the cut-set upper-bound is tight and the capacity region is achieved by a so called divide-and-conquer relaying strategy. The insights gained from the deterministic net"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1001.4271","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":"2026-05-18T00:58:19Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Erhglz9ndkdQ8eqIQshDztHdj+Dd9umOYW6o39OrPgZYYJ/KZl0Tim146iZWivNT4r6a/vKUpNMAOBIEUCJKCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T21:21:13.612219Z"},"content_sha256":"7707a5bfa37ad274c2abbf85b756d484021c601a983fbf64f1c1b3dbcc015088","schema_version":"1.0","event_id":"sha256:7707a5bfa37ad274c2abbf85b756d484021c601a983fbf64f1c1b3dbcc015088"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/OXZEGEZPUVTCKKZ5QDZLRDCIF7/bundle.json","state_url":"https://pith.science/pith/OXZEGEZPUVTCKKZ5QDZLRDCIF7/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/OXZEGEZPUVTCKKZ5QDZLRDCIF7/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":"2026-05-27T21:21:13Z","links":{"resolver":"https://pith.science/pith/OXZEGEZPUVTCKKZ5QDZLRDCIF7","bundle":"https://pith.science/pith/OXZEGEZPUVTCKKZ5QDZLRDCIF7/bundle.json","state":"https://pith.science/pith/OXZEGEZPUVTCKKZ5QDZLRDCIF7/state.json","well_known_bundle":"https://pith.science/.well-known/pith/OXZEGEZPUVTCKKZ5QDZLRDCIF7/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:OXZEGEZPUVTCKKZ5QDZLRDCIF7","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":"5a31a285d597150f76c39155df00a75127e27ae0519efb82e7c4a41f5a2bca88","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2010-01-24T19:50:02Z","title_canon_sha256":"c8708b208426047dde6708d33ae1338c61a2e33debe4a7b84efcaa738345886e"},"schema_version":"1.0","source":{"id":"1001.4271","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1001.4271","created_at":"2026-05-18T00:58:19Z"},{"alias_kind":"arxiv_version","alias_value":"1001.4271v3","created_at":"2026-05-18T00:58:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1001.4271","created_at":"2026-05-18T00:58:19Z"},{"alias_kind":"pith_short_12","alias_value":"OXZEGEZPUVTC","created_at":"2026-05-18T12:26:12Z"},{"alias_kind":"pith_short_16","alias_value":"OXZEGEZPUVTCKKZ5","created_at":"2026-05-18T12:26:12Z"},{"alias_kind":"pith_short_8","alias_value":"OXZEGEZP","created_at":"2026-05-18T12:26:12Z"}],"graph_snapshots":[{"event_id":"sha256:7707a5bfa37ad274c2abbf85b756d484021c601a983fbf64f1c1b3dbcc015088","target":"graph","created_at":"2026-05-18T00:58:19Z","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":"The capacity region of multi-pair bidirectional relay networks, in which a relay node facilitates the communication between multiple pairs of users, is studied. This problem is first examined in the context of the linear shift deterministic channel model. The capacity region of this network when the relay is operating at either full-duplex mode or half-duplex mode for arbitrary number of pairs is characterized. It is shown that the cut-set upper-bound is tight and the capacity region is achieved by a so called divide-and-conquer relaying strategy. The insights gained from the deterministic net","authors_text":"A. Salman Avestimehr, Aydin Sezgin, Babak Hassibi, M. Amin Khajehnejad","cross_cats":["math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2010-01-24T19:50:02Z","title":"Divide-and-conquer: Approaching the capacity of the two-pair bidirectional Gaussian relay network"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1001.4271","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":"sha256:9c52f32dd3a92914b366c34e88b63c2d8241bdbb2ffb9069ed2636c74ea16c18","target":"record","created_at":"2026-05-18T00:58:19Z","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":"5a31a285d597150f76c39155df00a75127e27ae0519efb82e7c4a41f5a2bca88","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2010-01-24T19:50:02Z","title_canon_sha256":"c8708b208426047dde6708d33ae1338c61a2e33debe4a7b84efcaa738345886e"},"schema_version":"1.0","source":{"id":"1001.4271","kind":"arxiv","version":3}},"canonical_sha256":"75f243132fa566252b3d80f2b88c482fcc0bdf1a5ae46561f789c2994d2abadf","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"75f243132fa566252b3d80f2b88c482fcc0bdf1a5ae46561f789c2994d2abadf","first_computed_at":"2026-05-18T00:58:19.769366Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:58:19.769366Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"HFCFzqhB0fW5N0kRcH2bulZueeGuguhjKZUM7HQoALjcnK/3BXtrpOredHudepc8fNCWOKbtinXQFosZcJr1CA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:58:19.770030Z","signed_message":"canonical_sha256_bytes"},"source_id":"1001.4271","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9c52f32dd3a92914b366c34e88b63c2d8241bdbb2ffb9069ed2636c74ea16c18","sha256:7707a5bfa37ad274c2abbf85b756d484021c601a983fbf64f1c1b3dbcc015088"],"state_sha256":"8204e2de647991c71476b7b675886ecc20721c1d3a392557cd264e9eed0d1262"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pkS3rO+Mk6p0lTkzxqCyANG+HqNNTDLNJUF0pKd28BCP0atoa1HSsFC6+MabJElrQhY9lFKyliCg5vUBk3mLDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T21:21:13.615940Z","bundle_sha256":"9a03625a560f26a1e525eaf515efec27db85ddeb18fe71225b3c74ce8199e103"}}