{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:VAXQFAKDG5ULDSPF56HZSVKCW7","short_pith_number":"pith:VAXQFAKD","canonical_record":{"source":{"id":"1310.1732","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2013-10-07T11:06:54Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"9a51138c18f8441023661a4769283acf5891ee83c97425548e4816ceae848cf8","abstract_canon_sha256":"57eba635b5dd865662077846b1b5f1766a8fe60461dbe77d160706045ca226c2"},"schema_version":"1.0"},"canonical_sha256":"a82f0281433768b1c9e5ef8f995542b7c1de5439207b1d4a28dbbddf22e9d467","source":{"kind":"arxiv","id":"1310.1732","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1310.1732","created_at":"2026-05-18T03:11:10Z"},{"alias_kind":"arxiv_version","alias_value":"1310.1732v1","created_at":"2026-05-18T03:11:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1310.1732","created_at":"2026-05-18T03:11:10Z"},{"alias_kind":"pith_short_12","alias_value":"VAXQFAKDG5UL","created_at":"2026-05-18T12:28:04Z"},{"alias_kind":"pith_short_16","alias_value":"VAXQFAKDG5ULDSPF","created_at":"2026-05-18T12:28:04Z"},{"alias_kind":"pith_short_8","alias_value":"VAXQFAKD","created_at":"2026-05-18T12:28:04Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:VAXQFAKDG5ULDSPF56HZSVKCW7","target":"record","payload":{"canonical_record":{"source":{"id":"1310.1732","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2013-10-07T11:06:54Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"9a51138c18f8441023661a4769283acf5891ee83c97425548e4816ceae848cf8","abstract_canon_sha256":"57eba635b5dd865662077846b1b5f1766a8fe60461dbe77d160706045ca226c2"},"schema_version":"1.0"},"canonical_sha256":"a82f0281433768b1c9e5ef8f995542b7c1de5439207b1d4a28dbbddf22e9d467","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:11:10.790649Z","signature_b64":"rXrVZbMARPS1NlYWqD2i2NvEk1KUgRNDIlkf6VP7yLxptPmnUtFOc3UjubZvV+JsPLpyV21Pob0Jzaxmyr35DA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a82f0281433768b1c9e5ef8f995542b7c1de5439207b1d4a28dbbddf22e9d467","last_reissued_at":"2026-05-18T03:11:10.789707Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:11:10.789707Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1310.1732","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":"2026-05-18T03:11:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4Bxm6Lla8BrQJ1RBYOFyWHJcQhThyB4qAlQHIokQxMXavDHRfxCrODFbYMXXx5E3kvnq3vTGkyeYwOmM31rMDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T20:17:39.745439Z"},"content_sha256":"2534555186c65217c514bda5d9cdebd7f62eefc3d08ed5322cc162e9f6ccd258","schema_version":"1.0","event_id":"sha256:2534555186c65217c514bda5d9cdebd7f62eefc3d08ed5322cc162e9f6ccd258"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:VAXQFAKDG5ULDSPF56HZSVKCW7","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The Approximate Capacity Region of the Gaussian Y-Channel","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Anas Chaaban, Aydin Sezgin","submitted_at":"2013-10-07T11:06:54Z","abstract_excerpt":"A full-duplex wireless network with three users that want to establish full message-exchange via a relay is considered. Thus, the network known as the Y-channel has a total of 6 messages, 2 outgoing and 2 incoming at each user. The users are not physically connected, and thus the relay is essential for their communication. The linear-shift deterministic Y-channel is considered first, its capacity region is characterized and shown not to be given by the cut-set bounds. The capacity achieving scheme has three different components (strategies): a bi-directional, a cyclic, and a uni-directional st"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.1732","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":"2026-05-18T03:11:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Qfimy+2R1rH0DqVzrvqMrNMw1ALTGcgyDKOfI1ZxwJHq8kCTnvucCumJksXapf/8ww2JYr5faDzf+SBRUewwCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T20:17:39.746291Z"},"content_sha256":"2c8825b39950b811c8759296d74d726e2a8bcbe109b4a6aec01a8809f616ed7f","schema_version":"1.0","event_id":"sha256:2c8825b39950b811c8759296d74d726e2a8bcbe109b4a6aec01a8809f616ed7f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/VAXQFAKDG5ULDSPF56HZSVKCW7/bundle.json","state_url":"https://pith.science/pith/VAXQFAKDG5ULDSPF56HZSVKCW7/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/VAXQFAKDG5ULDSPF56HZSVKCW7/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":"2026-05-25T20:17:39Z","links":{"resolver":"https://pith.science/pith/VAXQFAKDG5ULDSPF56HZSVKCW7","bundle":"https://pith.science/pith/VAXQFAKDG5ULDSPF56HZSVKCW7/bundle.json","state":"https://pith.science/pith/VAXQFAKDG5ULDSPF56HZSVKCW7/state.json","well_known_bundle":"https://pith.science/.well-known/pith/VAXQFAKDG5ULDSPF56HZSVKCW7/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:VAXQFAKDG5ULDSPF56HZSVKCW7","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":"57eba635b5dd865662077846b1b5f1766a8fe60461dbe77d160706045ca226c2","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2013-10-07T11:06:54Z","title_canon_sha256":"9a51138c18f8441023661a4769283acf5891ee83c97425548e4816ceae848cf8"},"schema_version":"1.0","source":{"id":"1310.1732","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1310.1732","created_at":"2026-05-18T03:11:10Z"},{"alias_kind":"arxiv_version","alias_value":"1310.1732v1","created_at":"2026-05-18T03:11:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1310.1732","created_at":"2026-05-18T03:11:10Z"},{"alias_kind":"pith_short_12","alias_value":"VAXQFAKDG5UL","created_at":"2026-05-18T12:28:04Z"},{"alias_kind":"pith_short_16","alias_value":"VAXQFAKDG5ULDSPF","created_at":"2026-05-18T12:28:04Z"},{"alias_kind":"pith_short_8","alias_value":"VAXQFAKD","created_at":"2026-05-18T12:28:04Z"}],"graph_snapshots":[{"event_id":"sha256:2c8825b39950b811c8759296d74d726e2a8bcbe109b4a6aec01a8809f616ed7f","target":"graph","created_at":"2026-05-18T03:11:10Z","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":"A full-duplex wireless network with three users that want to establish full message-exchange via a relay is considered. Thus, the network known as the Y-channel has a total of 6 messages, 2 outgoing and 2 incoming at each user. The users are not physically connected, and thus the relay is essential for their communication. The linear-shift deterministic Y-channel is considered first, its capacity region is characterized and shown not to be given by the cut-set bounds. The capacity achieving scheme has three different components (strategies): a bi-directional, a cyclic, and a uni-directional st","authors_text":"Anas Chaaban, Aydin Sezgin","cross_cats":["math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2013-10-07T11:06:54Z","title":"The Approximate Capacity Region of the Gaussian Y-Channel"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.1732","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":"sha256:2534555186c65217c514bda5d9cdebd7f62eefc3d08ed5322cc162e9f6ccd258","target":"record","created_at":"2026-05-18T03:11:10Z","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":"57eba635b5dd865662077846b1b5f1766a8fe60461dbe77d160706045ca226c2","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2013-10-07T11:06:54Z","title_canon_sha256":"9a51138c18f8441023661a4769283acf5891ee83c97425548e4816ceae848cf8"},"schema_version":"1.0","source":{"id":"1310.1732","kind":"arxiv","version":1}},"canonical_sha256":"a82f0281433768b1c9e5ef8f995542b7c1de5439207b1d4a28dbbddf22e9d467","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a82f0281433768b1c9e5ef8f995542b7c1de5439207b1d4a28dbbddf22e9d467","first_computed_at":"2026-05-18T03:11:10.789707Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:11:10.789707Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"rXrVZbMARPS1NlYWqD2i2NvEk1KUgRNDIlkf6VP7yLxptPmnUtFOc3UjubZvV+JsPLpyV21Pob0Jzaxmyr35DA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:11:10.790649Z","signed_message":"canonical_sha256_bytes"},"source_id":"1310.1732","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2534555186c65217c514bda5d9cdebd7f62eefc3d08ed5322cc162e9f6ccd258","sha256:2c8825b39950b811c8759296d74d726e2a8bcbe109b4a6aec01a8809f616ed7f"],"state_sha256":"54fc49ad94c713b44e22ec542ddd922ea2d0bc50b5f63c0e1719a56beb0ae2a0"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GPcaLZVfPpjX779BePVvCZeRawQyw0o/92VAFCQrsz1fne/h3kAoTIjQe5bu65bqWlj7ZyDb7/j8pZMijeygBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-25T20:17:39.750660Z","bundle_sha256":"f46a2e873e10bd80802d3bab4e7a7153bda1c4e40d2fed9141a353ea1baf1bac"}}