{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:YPEYK5QZ4W3DXPHQOSU5MDHDKC","short_pith_number":"pith:YPEYK5QZ","canonical_record":{"source":{"id":"1304.4464","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2013-04-16T14:31:38Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"a954786140897ce54d5b03120c2a38f2d432d13bf1adb014dc395574f79e63d7","abstract_canon_sha256":"cfa92f32de4e3b1bdade965c39500bd4ca0439c23cded3de0ce1a6d50889cdc6"},"schema_version":"1.0"},"canonical_sha256":"c3c9857619e5b63bbcf074a9d60ce350b4e3c373feb2c0a9fb9380c8757f9505","source":{"kind":"arxiv","id":"1304.4464","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1304.4464","created_at":"2026-05-18T03:27:52Z"},{"alias_kind":"arxiv_version","alias_value":"1304.4464v1","created_at":"2026-05-18T03:27:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1304.4464","created_at":"2026-05-18T03:27:52Z"},{"alias_kind":"pith_short_12","alias_value":"YPEYK5QZ4W3D","created_at":"2026-05-18T12:28:09Z"},{"alias_kind":"pith_short_16","alias_value":"YPEYK5QZ4W3DXPHQ","created_at":"2026-05-18T12:28:09Z"},{"alias_kind":"pith_short_8","alias_value":"YPEYK5QZ","created_at":"2026-05-18T12:28:09Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:YPEYK5QZ4W3DXPHQOSU5MDHDKC","target":"record","payload":{"canonical_record":{"source":{"id":"1304.4464","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2013-04-16T14:31:38Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"a954786140897ce54d5b03120c2a38f2d432d13bf1adb014dc395574f79e63d7","abstract_canon_sha256":"cfa92f32de4e3b1bdade965c39500bd4ca0439c23cded3de0ce1a6d50889cdc6"},"schema_version":"1.0"},"canonical_sha256":"c3c9857619e5b63bbcf074a9d60ce350b4e3c373feb2c0a9fb9380c8757f9505","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:27:52.977740Z","signature_b64":"5iYAw/dwSrVKqkHFKU4V0+93FQ0Y8f0WSdFlv9vtAAriBGfXEwYmiChAzAAy0tQbkAkiwE5lqjTCvvsx0t4EDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c3c9857619e5b63bbcf074a9d60ce350b4e3c373feb2c0a9fb9380c8757f9505","last_reissued_at":"2026-05-18T03:27:52.977117Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:27:52.977117Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1304.4464","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:27:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KGS8dNWcMp9a66aKVTfXc6S1eZkaQ4RNyf+/EGULCjwc7ChBDr6dl9LVGFAoSrhE9VXRetmXsOeI8Fj1zBa6CQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T12:59:20.159931Z"},"content_sha256":"40128802224edb25cf1bc446f143ba3ee25f71d1250e74faa3ef2e33be7a91a2","schema_version":"1.0","event_id":"sha256:40128802224edb25cf1bc446f143ba3ee25f71d1250e74faa3ef2e33be7a91a2"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:YPEYK5QZ4W3DXPHQOSU5MDHDKC","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The Deterministic Multicast Capacity of 4-Node Relay Networks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Ahmed A. Zewail, H. El Gamal, M. Nafie, Y. Mohasseb","submitted_at":"2013-04-16T14:31:38Z","abstract_excerpt":"In this paper, we completely characterize the deterministic capacity region of a four-node relay network with no direct links between the nodes, where each node communicates with the three other nodes via a relay. Towards this end, we develop an upper bound on the deterministic capacity region, based on the notion of a one-sided genie. To establish achievability, we use the detour schemes that achieve the upper bound by routing specific bits via indirect paths instead of sending them directly."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.4464","kind":"arxiv","version":1},"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":"2026-05-18T03:27:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"c3CTiCzuaTgFU7GAQLV7Cj8FH/QtdqG6SkfoepBgIp560rBiA6lcmKD3W0069baklZ24dH93aZhv98d3+lYVDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T12:59:20.160597Z"},"content_sha256":"556f92260cddc37e883a0fbf5f5e39e2131cd0c41c443a428abe25ad166aaafe","schema_version":"1.0","event_id":"sha256:556f92260cddc37e883a0fbf5f5e39e2131cd0c41c443a428abe25ad166aaafe"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/YPEYK5QZ4W3DXPHQOSU5MDHDKC/bundle.json","state_url":"https://pith.science/pith/YPEYK5QZ4W3DXPHQOSU5MDHDKC/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/YPEYK5QZ4W3DXPHQOSU5MDHDKC/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":"2026-06-07T12:59:20Z","links":{"resolver":"https://pith.science/pith/YPEYK5QZ4W3DXPHQOSU5MDHDKC","bundle":"https://pith.science/pith/YPEYK5QZ4W3DXPHQOSU5MDHDKC/bundle.json","state":"https://pith.science/pith/YPEYK5QZ4W3DXPHQOSU5MDHDKC/state.json","well_known_bundle":"https://pith.science/.well-known/pith/YPEYK5QZ4W3DXPHQOSU5MDHDKC/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:YPEYK5QZ4W3DXPHQOSU5MDHDKC","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":"cfa92f32de4e3b1bdade965c39500bd4ca0439c23cded3de0ce1a6d50889cdc6","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2013-04-16T14:31:38Z","title_canon_sha256":"a954786140897ce54d5b03120c2a38f2d432d13bf1adb014dc395574f79e63d7"},"schema_version":"1.0","source":{"id":"1304.4464","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1304.4464","created_at":"2026-05-18T03:27:52Z"},{"alias_kind":"arxiv_version","alias_value":"1304.4464v1","created_at":"2026-05-18T03:27:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1304.4464","created_at":"2026-05-18T03:27:52Z"},{"alias_kind":"pith_short_12","alias_value":"YPEYK5QZ4W3D","created_at":"2026-05-18T12:28:09Z"},{"alias_kind":"pith_short_16","alias_value":"YPEYK5QZ4W3DXPHQ","created_at":"2026-05-18T12:28:09Z"},{"alias_kind":"pith_short_8","alias_value":"YPEYK5QZ","created_at":"2026-05-18T12:28:09Z"}],"graph_snapshots":[{"event_id":"sha256:556f92260cddc37e883a0fbf5f5e39e2131cd0c41c443a428abe25ad166aaafe","target":"graph","created_at":"2026-05-18T03:27:52Z","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 completely characterize the deterministic capacity region of a four-node relay network with no direct links between the nodes, where each node communicates with the three other nodes via a relay. Towards this end, we develop an upper bound on the deterministic capacity region, based on the notion of a one-sided genie. To establish achievability, we use the detour schemes that achieve the upper bound by routing specific bits via indirect paths instead of sending them directly.","authors_text":"Ahmed A. Zewail, H. El Gamal, M. Nafie, Y. Mohasseb","cross_cats":["math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2013-04-16T14:31:38Z","title":"The Deterministic Multicast Capacity of 4-Node Relay Networks"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.4464","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":"sha256:40128802224edb25cf1bc446f143ba3ee25f71d1250e74faa3ef2e33be7a91a2","target":"record","created_at":"2026-05-18T03:27:52Z","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":"cfa92f32de4e3b1bdade965c39500bd4ca0439c23cded3de0ce1a6d50889cdc6","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2013-04-16T14:31:38Z","title_canon_sha256":"a954786140897ce54d5b03120c2a38f2d432d13bf1adb014dc395574f79e63d7"},"schema_version":"1.0","source":{"id":"1304.4464","kind":"arxiv","version":1}},"canonical_sha256":"c3c9857619e5b63bbcf074a9d60ce350b4e3c373feb2c0a9fb9380c8757f9505","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c3c9857619e5b63bbcf074a9d60ce350b4e3c373feb2c0a9fb9380c8757f9505","first_computed_at":"2026-05-18T03:27:52.977117Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:27:52.977117Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"5iYAw/dwSrVKqkHFKU4V0+93FQ0Y8f0WSdFlv9vtAAriBGfXEwYmiChAzAAy0tQbkAkiwE5lqjTCvvsx0t4EDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:27:52.977740Z","signed_message":"canonical_sha256_bytes"},"source_id":"1304.4464","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:40128802224edb25cf1bc446f143ba3ee25f71d1250e74faa3ef2e33be7a91a2","sha256:556f92260cddc37e883a0fbf5f5e39e2131cd0c41c443a428abe25ad166aaafe"],"state_sha256":"5335446bf7c8ddc5ac610ca75a43de74333cba0765baa9d23d9064a5611cb021"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hnIAscuT86iNqK06V9rqdlHwANR1QdkfLS1zn2w/nuRQBbqdLSEo99922H37NJbgKKMqshicg+YnUOVQp+UOBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-07T12:59:20.164743Z","bundle_sha256":"c2686aea4157e21d80732aa32a37c3ee44f1e7e3c58027380a609cd4e8fe1014"}}