{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2008:3Z4RHMYMY2PHP6TZCXG2C5BVKK","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":"e79920c6853c4f05c47b28447796b6f5868e50dcad1e58007844de3048f83e6d","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2008-02-05T00:21:05Z","title_canon_sha256":"7152eae51ea2f52b6354a6f0077539198c98ed14cdad7b9db3c6a074b9d0a6a7"},"schema_version":"1.0","source":{"id":"0802.0534","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0802.0534","created_at":"2026-05-18T03:58:51Z"},{"alias_kind":"arxiv_version","alias_value":"0802.0534v1","created_at":"2026-05-18T03:58:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0802.0534","created_at":"2026-05-18T03:58:51Z"},{"alias_kind":"pith_short_12","alias_value":"3Z4RHMYMY2PH","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_16","alias_value":"3Z4RHMYMY2PHP6TZ","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_8","alias_value":"3Z4RHMYM","created_at":"2026-05-18T12:25:56Z"}],"graph_snapshots":[{"event_id":"sha256:63210b93c81e6cf016274c163222cd01ada47e89ef4b99fa19054d0154b1c7b5","target":"graph","created_at":"2026-05-18T03:58:51Z","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":"Recent work has characterized the sum capacity of time-varying/frequency-selective wireless interference networks and $X$ networks within $o(\\log({SNR}))$, i.e., with an accuracy approaching 100% at high SNR (signal to noise power ratio). In this paper, we seek similar capacity characterizations for wireless networks with relays, feedback, full duplex operation, and transmitter/receiver cooperation through noisy channels. First, we consider a network with $S$ source nodes, $R$ relay nodes and $D$ destination nodes with random time-varying/frequency-selective channel coefficients and global cha","authors_text":"Syed A. Jafar, Viveck R. Cadambe","cross_cats":["math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2008-02-05T00:21:05Z","title":"Capacity of Wireless Networks within o(log(SNR)) - the Impact of Relays, Feedback, Cooperation and Full-Duplex Operation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0802.0534","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:d040188b1799e4ac7e97dbb2673f206a9373cc5a7ffdab3d95cce5e544290826","target":"record","created_at":"2026-05-18T03:58:51Z","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":"e79920c6853c4f05c47b28447796b6f5868e50dcad1e58007844de3048f83e6d","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2008-02-05T00:21:05Z","title_canon_sha256":"7152eae51ea2f52b6354a6f0077539198c98ed14cdad7b9db3c6a074b9d0a6a7"},"schema_version":"1.0","source":{"id":"0802.0534","kind":"arxiv","version":1}},"canonical_sha256":"de7913b30cc69e77fa7915cda1743552aec7ba42ba96454d8a1ed9c3c5301acc","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"de7913b30cc69e77fa7915cda1743552aec7ba42ba96454d8a1ed9c3c5301acc","first_computed_at":"2026-05-18T03:58:51.984417Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:58:51.984417Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"PI04iXK1SkZxQ4OpmPciJYJlu50/edCfKL4UiSmKmF0ZMSQOKU0EYAY77hUKimDbNmWr1cUMN6L8FKD70LsjAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:58:51.984966Z","signed_message":"canonical_sha256_bytes"},"source_id":"0802.0534","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d040188b1799e4ac7e97dbb2673f206a9373cc5a7ffdab3d95cce5e544290826","sha256:63210b93c81e6cf016274c163222cd01ada47e89ef4b99fa19054d0154b1c7b5"],"state_sha256":"79be05300e4e846d438e182044bab0666cd3ea7e763aa9ab376011115ac96d2a"}