{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:7K2PZI5MPU43RQ3BZNJCG7EOMA","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":"9222ed59917367213b67db296b850498630b96c0c2395bb4f9ec967d9a6c4be0","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2015-02-02T21:41:02Z","title_canon_sha256":"a1f50f8f6e332369ac8957e0a8c8ca1bf8aaf6c52f9751b1d8bb45392e8ed0ac"},"schema_version":"1.0","source":{"id":"1502.00656","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1502.00656","created_at":"2026-05-18T02:27:43Z"},{"alias_kind":"arxiv_version","alias_value":"1502.00656v2","created_at":"2026-05-18T02:27:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1502.00656","created_at":"2026-05-18T02:27:43Z"},{"alias_kind":"pith_short_12","alias_value":"7K2PZI5MPU43","created_at":"2026-05-18T12:29:10Z"},{"alias_kind":"pith_short_16","alias_value":"7K2PZI5MPU43RQ3B","created_at":"2026-05-18T12:29:10Z"},{"alias_kind":"pith_short_8","alias_value":"7K2PZI5M","created_at":"2026-05-18T12:29:10Z"}],"graph_snapshots":[{"event_id":"sha256:6b4fe5cf46f6b608ccb7a5f3386bd4714134c9ca20120bfee42557b23582bda3","target":"graph","created_at":"2026-05-18T02:27:43Z","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":"In this paper, we study the wireline two-unicast-Z communication network over directed acyclic graphs. The two-unicast-Z network is a two-unicast network where the destination intending to decode the second message has apriori side information of the first message. We make three contributions in this paper:\n  1. We describe a new linear network coding algorithm for two-unicast-Z networks over directed acyclic graphs. Our approach includes the idea of interference alignment as one of its key ingredients. For graphs of a bounded degree, our algorithm has linear complexity in terms of the number ","authors_text":"Muriel Medard, Viveck R. Cadambe, Weifei Zeng","cross_cats":["math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2015-02-02T21:41:02Z","title":"Alignment based Network Coding for Two-Unicast-Z Networks"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.00656","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":"sha256:27d0fd80443b72e0fe6c9b58cb010dcc68a22e74796dc1983e09ff740b7a73d4","target":"record","created_at":"2026-05-18T02:27:43Z","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":"9222ed59917367213b67db296b850498630b96c0c2395bb4f9ec967d9a6c4be0","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2015-02-02T21:41:02Z","title_canon_sha256":"a1f50f8f6e332369ac8957e0a8c8ca1bf8aaf6c52f9751b1d8bb45392e8ed0ac"},"schema_version":"1.0","source":{"id":"1502.00656","kind":"arxiv","version":2}},"canonical_sha256":"fab4fca3ac7d39b8c361cb52237c8e6023a6cfc51df35b345cc24031a6617008","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fab4fca3ac7d39b8c361cb52237c8e6023a6cfc51df35b345cc24031a6617008","first_computed_at":"2026-05-18T02:27:43.756979Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:27:43.756979Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"JBRy79Mj3EaQAs79Ah8B+nF/kXrI/alhAQpMNAdXD4hevqIh1nX+/5rvDVIMVdhMLVOF/meYbSWWvshQAdBfAg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:27:43.757526Z","signed_message":"canonical_sha256_bytes"},"source_id":"1502.00656","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:27d0fd80443b72e0fe6c9b58cb010dcc68a22e74796dc1983e09ff740b7a73d4","sha256:6b4fe5cf46f6b608ccb7a5f3386bd4714134c9ca20120bfee42557b23582bda3"],"state_sha256":"28b9a3af1db18ba1117626ce2340d524a890b7943511100b141d0c50f8cab36d"}