{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:7K2PZI5MPU43RQ3BZNJCG7EOMA","short_pith_number":"pith:7K2PZI5M","canonical_record":{"source":{"id":"1502.00656","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2015-02-02T21:41:02Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"a1f50f8f6e332369ac8957e0a8c8ca1bf8aaf6c52f9751b1d8bb45392e8ed0ac","abstract_canon_sha256":"9222ed59917367213b67db296b850498630b96c0c2395bb4f9ec967d9a6c4be0"},"schema_version":"1.0"},"canonical_sha256":"fab4fca3ac7d39b8c361cb52237c8e6023a6cfc51df35b345cc24031a6617008","source":{"kind":"arxiv","id":"1502.00656","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"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:7K2PZI5MPU43RQ3BZNJCG7EOMA","target":"record","payload":{"canonical_record":{"source":{"id":"1502.00656","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2015-02-02T21:41:02Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"a1f50f8f6e332369ac8957e0a8c8ca1bf8aaf6c52f9751b1d8bb45392e8ed0ac","abstract_canon_sha256":"9222ed59917367213b67db296b850498630b96c0c2395bb4f9ec967d9a6c4be0"},"schema_version":"1.0"},"canonical_sha256":"fab4fca3ac7d39b8c361cb52237c8e6023a6cfc51df35b345cc24031a6617008","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:27:43.757526Z","signature_b64":"JBRy79Mj3EaQAs79Ah8B+nF/kXrI/alhAQpMNAdXD4hevqIh1nX+/5rvDVIMVdhMLVOF/meYbSWWvshQAdBfAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fab4fca3ac7d39b8c361cb52237c8e6023a6cfc51df35b345cc24031a6617008","last_reissued_at":"2026-05-18T02:27:43.756979Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:27:43.756979Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1502.00656","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:27:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"s97J61QCCQyLBNCJ7JHT5xT0yUXpJ5Fu9n53GJhjoEc9u+ZUH3oSKw+ZfhgYkLHT/kM5tN3uestOLERP9q48Cw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-24T22:01:53.373090Z"},"content_sha256":"27d0fd80443b72e0fe6c9b58cb010dcc68a22e74796dc1983e09ff740b7a73d4","schema_version":"1.0","event_id":"sha256:27d0fd80443b72e0fe6c9b58cb010dcc68a22e74796dc1983e09ff740b7a73d4"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:7K2PZI5MPU43RQ3BZNJCG7EOMA","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Alignment based Network Coding for Two-Unicast-Z Networks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Muriel Medard, Viveck R. Cadambe, Weifei Zeng","submitted_at":"2015-02-02T21:41:02Z","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 "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.00656","kind":"arxiv","version":2},"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":"2026-05-18T02:27:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8xkLcyIoCrj6o6NLd8D2u7F0GWdH1ebX3+dUkLy+NwSbnWi7nNzNUsr5UIg98fgN7ZZamigfKj3kP9097mvZAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-24T22:01:53.373454Z"},"content_sha256":"6b4fe5cf46f6b608ccb7a5f3386bd4714134c9ca20120bfee42557b23582bda3","schema_version":"1.0","event_id":"sha256:6b4fe5cf46f6b608ccb7a5f3386bd4714134c9ca20120bfee42557b23582bda3"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/7K2PZI5MPU43RQ3BZNJCG7EOMA/bundle.json","state_url":"https://pith.science/pith/7K2PZI5MPU43RQ3BZNJCG7EOMA/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/7K2PZI5MPU43RQ3BZNJCG7EOMA/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":"2026-05-24T22:01:53Z","links":{"resolver":"https://pith.science/pith/7K2PZI5MPU43RQ3BZNJCG7EOMA","bundle":"https://pith.science/pith/7K2PZI5MPU43RQ3BZNJCG7EOMA/bundle.json","state":"https://pith.science/pith/7K2PZI5MPU43RQ3BZNJCG7EOMA/state.json","well_known_bundle":"https://pith.science/.well-known/pith/7K2PZI5MPU43RQ3BZNJCG7EOMA/bundle.json"},"state":{"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"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"v5Opq5qWjBuHJSLjb4h6vy2rf/IOpAyYdD3PPqqXgcl9VJrzzV44AWxvcXkpe5tro2Wfn/LN5SXeunjoF5xaCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-24T22:01:53.376033Z","bundle_sha256":"bfc880e8c658d94f555ea8f339ed9bbba0c7bac077430b24879c75a39e88a561"}}