{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:OLB5PCQN72EWBH3H2GCQMGF6ND","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":"0ed0357a9f9345fa02c22338b3cf3fbbeba40a977522c5b858105b256884ad04","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2014-04-18T12:31:25Z","title_canon_sha256":"4b83e697376bc996291c1187d414e96e900b1f787706a2cc1b22eccc63bb88c0"},"schema_version":"1.0","source":{"id":"1404.4761","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1404.4761","created_at":"2026-05-18T00:59:03Z"},{"alias_kind":"arxiv_version","alias_value":"1404.4761v2","created_at":"2026-05-18T00:59:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1404.4761","created_at":"2026-05-18T00:59:03Z"},{"alias_kind":"pith_short_12","alias_value":"OLB5PCQN72EW","created_at":"2026-05-18T12:28:41Z"},{"alias_kind":"pith_short_16","alias_value":"OLB5PCQN72EWBH3H","created_at":"2026-05-18T12:28:41Z"},{"alias_kind":"pith_short_8","alias_value":"OLB5PCQN","created_at":"2026-05-18T12:28:41Z"}],"graph_snapshots":[{"event_id":"sha256:2edbde818d462800429ebd8788ce8dd15fd01c93e8a28c5f2bc726564b9373ee","target":"graph","created_at":"2026-05-18T00:59:03Z","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":"In this paper, we derive the capacity of the deterministic relay networks with relay messages. We consider a network which consists of five nodes, four of which can only communicate via the fifth one. However, the fifth node is not merely a relay as it may exchange private messages with the other network nodes. First, we develop an upper bound on the capacity region based on the notion of a single sided genie. In the course of the achievability proof, we also derive the deterministic capacity of a 4-user relay network (without private messages at the relay). The capacity achieving schemes use ","authors_text":"Ahmed A. Zewail, Hesham El Gamal, Mohammed Nafie, Yahya Mohasseb","cross_cats":["math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2014-04-18T12:31:25Z","title":"Using Network Coding to Achieve the Capacity of Deterministic Relay Networks with Relay Messages"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.4761","kind":"arxiv","version":2},"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":"sha256:58273fb2af74413d0de13713fac721f3596dcfa9e58c4808abf6c066cd240fe1","target":"record","created_at":"2026-05-18T00:59:03Z","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":"0ed0357a9f9345fa02c22338b3cf3fbbeba40a977522c5b858105b256884ad04","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2014-04-18T12:31:25Z","title_canon_sha256":"4b83e697376bc996291c1187d414e96e900b1f787706a2cc1b22eccc63bb88c0"},"schema_version":"1.0","source":{"id":"1404.4761","kind":"arxiv","version":2}},"canonical_sha256":"72c3d78a0dfe89609f67d1850618be68f2e6aa09831aaf35111f85d183e7d002","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"72c3d78a0dfe89609f67d1850618be68f2e6aa09831aaf35111f85d183e7d002","first_computed_at":"2026-05-18T00:59:03.110711Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:59:03.110711Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"PwMeLoi4wGFvsMgDIwS6y0U2C7p0yuBlHKANmcxu/fn3goAbdAhMgWs4xveMK39ZytAghTOx7K3IqInqcIqLDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:59:03.111306Z","signed_message":"canonical_sha256_bytes"},"source_id":"1404.4761","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:58273fb2af74413d0de13713fac721f3596dcfa9e58c4808abf6c066cd240fe1","sha256:2edbde818d462800429ebd8788ce8dd15fd01c93e8a28c5f2bc726564b9373ee"],"state_sha256":"e7fde8f906338eff177cd84634e6e4b1db7abb7acf173e91674afa7358a5ce94"}