{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:D74QKCNV7PGKTNNB7MMSVXYC5E","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":"aa12b4c90a0f486a95f3a4036ceada185b1cac4afc1b5ca9856b29138708ac94","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2011-06-17T07:24:14Z","title_canon_sha256":"e06d456f273352a6fb7409ffccb62532b8eebce20580cc0d44a62ce195b86c58"},"schema_version":"1.0","source":{"id":"1106.3402","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1106.3402","created_at":"2026-05-18T02:21:43Z"},{"alias_kind":"arxiv_version","alias_value":"1106.3402v1","created_at":"2026-05-18T02:21:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1106.3402","created_at":"2026-05-18T02:21:43Z"},{"alias_kind":"pith_short_12","alias_value":"D74QKCNV7PGK","created_at":"2026-05-18T12:26:26Z"},{"alias_kind":"pith_short_16","alias_value":"D74QKCNV7PGKTNNB","created_at":"2026-05-18T12:26:26Z"},{"alias_kind":"pith_short_8","alias_value":"D74QKCNV","created_at":"2026-05-18T12:26:26Z"}],"graph_snapshots":[{"event_id":"sha256:d308edb1e0faa6f01fa2150585098fff5f57f988a36b0ab8ec1245e73d70ff6d","target":"graph","created_at":"2026-05-18T02:21:43Z","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 linear shift deterministic Y-channel is studied. That is, we have three users and one relay, where each user wishes to broadcast one message to each other user via the relay, resulting in a multi-way relaying setup. The cut-set bounds for this setup are shown to be not sufficient to characterize its capacity region. New upper bounds are derived, which when combined with the cut-set bounds provide an outer bound on the capacity region. It is shown that this outer bound is achievable, and as a result, the capacity region of the linear shift deterministic Y-channel is characterized.","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":"2011-06-17T07:24:14Z","title":"The Capacity Region of the Linear Shift Deterministic Y-Channel"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1106.3402","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:c869fb3a0502a9fe6d9acfcd532fd3af04f39c912b43f9dd2a79f0adcaaeee7b","target":"record","created_at":"2026-05-18T02:21:43Z","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":"aa12b4c90a0f486a95f3a4036ceada185b1cac4afc1b5ca9856b29138708ac94","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2011-06-17T07:24:14Z","title_canon_sha256":"e06d456f273352a6fb7409ffccb62532b8eebce20580cc0d44a62ce195b86c58"},"schema_version":"1.0","source":{"id":"1106.3402","kind":"arxiv","version":1}},"canonical_sha256":"1ff90509b5fbcca9b5a1fb192adf02e914976c6a9f3f7700b5ced0999bc5a6af","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1ff90509b5fbcca9b5a1fb192adf02e914976c6a9f3f7700b5ced0999bc5a6af","first_computed_at":"2026-05-18T02:21:43.890104Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:21:43.890104Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"1exTOGy5hZ7g4Kg4MRcD03RQLFBU0DRPRh3sQmUKNEUAt/7bAd7RVyVxF24BJEZyxlHCoOMr6r8Cdo8p4Vq2Cg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:21:43.890553Z","signed_message":"canonical_sha256_bytes"},"source_id":"1106.3402","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c869fb3a0502a9fe6d9acfcd532fd3af04f39c912b43f9dd2a79f0adcaaeee7b","sha256:d308edb1e0faa6f01fa2150585098fff5f57f988a36b0ab8ec1245e73d70ff6d"],"state_sha256":"75c294f9a169f469a49c02f86fe8babfdb79a310435b721549c41c02b86bed16"}