{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:75SAQWCCL3N232UTMMR6OV3SK3","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":"20fd4eb248fbe8259aba2c58c3b2b8112b9df4f0a813de6f871f5cf6cded079f","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2012-07-17T00:48:06Z","title_canon_sha256":"80cbb9a12eaa16fdf438b7eecb6b5c76ef59e86938770397372c9bc93a8961e6"},"schema_version":"1.0","source":{"id":"1207.3850","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1207.3850","created_at":"2026-05-18T03:39:28Z"},{"alias_kind":"arxiv_version","alias_value":"1207.3850v1","created_at":"2026-05-18T03:39:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1207.3850","created_at":"2026-05-18T03:39:28Z"},{"alias_kind":"pith_short_12","alias_value":"75SAQWCCL3N2","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_16","alias_value":"75SAQWCCL3N232UT","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_8","alias_value":"75SAQWCC","created_at":"2026-05-18T12:26:56Z"}],"graph_snapshots":[{"event_id":"sha256:b415e44286eb3a2ea29e7502e6054520740bed36ae58aed498343e2935ffcace","target":"graph","created_at":"2026-05-18T03:39:28Z","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":"We study the half-duplex multiple-relay channel (HD-MRC) where every node can either transmit or listen but cannot do both at the same time. We obtain a capacity upper bound based on a max-flow min-cut argument and achievable transmission rates based on the decode-forward (DF) coding strategy, for both the discrete memoryless HD-MRC and the phase-fading HD-MRC. We discover that both the upper bound and the achievable rates are functions of the transmit/listen state (a description of which nodes transmit and which receive). More precisely, they are functions of the time fraction of the differen","authors_text":"Lawrence Ong, Mehul Motani, Sarah J. Johnson","cross_cats":["math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2012-07-17T00:48:06Z","title":"On Capacity and Optimal Scheduling for the Half-Duplex Multiple-Relay Channel"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1207.3850","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":"sha256:994f31edc5e34c0901d40f71e365ca43cc7159dd245de8bf5f229c6558b957ff","target":"record","created_at":"2026-05-18T03:39:28Z","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":"20fd4eb248fbe8259aba2c58c3b2b8112b9df4f0a813de6f871f5cf6cded079f","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2012-07-17T00:48:06Z","title_canon_sha256":"80cbb9a12eaa16fdf438b7eecb6b5c76ef59e86938770397372c9bc93a8961e6"},"schema_version":"1.0","source":{"id":"1207.3850","kind":"arxiv","version":1}},"canonical_sha256":"ff640858425edbadea936323e7577256fa1fc806d54aba1709869fcfcea6375a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ff640858425edbadea936323e7577256fa1fc806d54aba1709869fcfcea6375a","first_computed_at":"2026-05-18T03:39:28.350843Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:39:28.350843Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"QrE85CXeLLZzUVRyqrFDEPjlffWGW/wOlM1krkQ2FmwZCKu25S5vwDuK0XOdbPSc3x3oN29qKWO8o84aVOtSCg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:39:28.351555Z","signed_message":"canonical_sha256_bytes"},"source_id":"1207.3850","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:994f31edc5e34c0901d40f71e365ca43cc7159dd245de8bf5f229c6558b957ff","sha256:b415e44286eb3a2ea29e7502e6054520740bed36ae58aed498343e2935ffcace"],"state_sha256":"c05f1451c40981a52a9766224e3f0205ddc954a120d952ad2fc8e77161cd31e9"}