{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:7HPVKR6KWGIJSZU5M2HHXMMMVG","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":"614f43187632198b8aa633070e6e3a559489b84c5c5ca2b103b52e125b4492f7","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2015-04-21T03:58:18Z","title_canon_sha256":"81b09b0e02a688dbef62a0a40333bd4b770480ffef0b48e26d88be678aadb424"},"schema_version":"1.0","source":{"id":"1504.05294","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1504.05294","created_at":"2026-05-18T01:26:57Z"},{"alias_kind":"arxiv_version","alias_value":"1504.05294v2","created_at":"2026-05-18T01:26:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1504.05294","created_at":"2026-05-18T01:26:57Z"},{"alias_kind":"pith_short_12","alias_value":"7HPVKR6KWGIJ","created_at":"2026-05-18T12:29:10Z"},{"alias_kind":"pith_short_16","alias_value":"7HPVKR6KWGIJSZU5","created_at":"2026-05-18T12:29:10Z"},{"alias_kind":"pith_short_8","alias_value":"7HPVKR6K","created_at":"2026-05-18T12:29:10Z"}],"graph_snapshots":[{"event_id":"sha256:b7232fbb6ba7bf08e359282f2ac67e155d6d57771b3ea0b5d5c2de6d9340a18a","target":"graph","created_at":"2026-05-18T01:26:57Z","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 upper bounds on the sum-rate of multiple-unicasts. We approximate the Generalized Network Sharing Bound (GNS cut) of the multiple-unicasts network coding problem with $k$ independent sources. Our approximation algorithm runs in polynomial time and yields an upper bound on the joint source entropy rate, which is within an $O(\\log^2 k)$ factor from the GNS cut. It further yields a vector-linear network code that achieves joint source entropy rate within an $O(\\log^2 k)$ factor from the GNS cut, but \\emph{not} with independent sources: the code induces a correlation pattern among the sou","authors_text":"Alexandros G. Dimakis, Karthikeyan Shanmugam, Megasthenis Asteris","cross_cats":["math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2015-04-21T03:58:18Z","title":"On Approximating the Sum-Rate for Multiple-Unicasts"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.05294","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:deb2ebbb63f4e25fc6241898a14bc9590392b3c80771ae527ffcb079c968e0f6","target":"record","created_at":"2026-05-18T01:26:57Z","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":"614f43187632198b8aa633070e6e3a559489b84c5c5ca2b103b52e125b4492f7","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2015-04-21T03:58:18Z","title_canon_sha256":"81b09b0e02a688dbef62a0a40333bd4b770480ffef0b48e26d88be678aadb424"},"schema_version":"1.0","source":{"id":"1504.05294","kind":"arxiv","version":2}},"canonical_sha256":"f9df5547cab19099669d668e7bb18ca9a5a038e9de79d2dda610a282e67bab08","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f9df5547cab19099669d668e7bb18ca9a5a038e9de79d2dda610a282e67bab08","first_computed_at":"2026-05-18T01:26:57.736976Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:26:57.736976Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"gCCQi0Bhz2NJREtS9UKJUeSuH2VIAWJGUoSE/bISX1hsYMYfp+RgJ9D4Q7cDuVSUKVuI8wfXAMnK4L3AnfVuAA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:26:57.737561Z","signed_message":"canonical_sha256_bytes"},"source_id":"1504.05294","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:deb2ebbb63f4e25fc6241898a14bc9590392b3c80771ae527ffcb079c968e0f6","sha256:b7232fbb6ba7bf08e359282f2ac67e155d6d57771b3ea0b5d5c2de6d9340a18a"],"state_sha256":"7dda0bb5e2159a53bc240ed31287d6745979d2afe42f51fe7008a9370ce2d2a5"}