{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:3TFYPFEXWTHV4VLJGUBVRFWCAA","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":"14214c6a0ff3d2dfdb84e369832a10372d66a7c55e96ccf122874e13d805d134","cross_cats_sorted":["math.IT"],"license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"cs.IT","submitted_at":"2015-02-03T07:27:34Z","title_canon_sha256":"b2513400e74216f53ade13530f3b96c7a0c02c9d4d379713fe036f2865d3d8d0"},"schema_version":"1.0","source":{"id":"1502.00762","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1502.00762","created_at":"2026-05-18T02:28:04Z"},{"alias_kind":"arxiv_version","alias_value":"1502.00762v1","created_at":"2026-05-18T02:28:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1502.00762","created_at":"2026-05-18T02:28:04Z"},{"alias_kind":"pith_short_12","alias_value":"3TFYPFEXWTHV","created_at":"2026-05-18T12:29:02Z"},{"alias_kind":"pith_short_16","alias_value":"3TFYPFEXWTHV4VLJ","created_at":"2026-05-18T12:29:02Z"},{"alias_kind":"pith_short_8","alias_value":"3TFYPFEX","created_at":"2026-05-18T12:29:02Z"}],"graph_snapshots":[{"event_id":"sha256:1fbae5e858ad75ee90784fa3b7f87ff4a543c706a04ed9800b8d38f830a24aa6","target":"graph","created_at":"2026-05-18T02:28:04Z","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 network coding problem of sum-networks with 3 sources and n terminals (3s/nt sum-network), for an arbitrary positive integer n, and derive a sufficient and necessary condition for the solvability of a family of so-called terminal-separable sum-network. Both the condition of terminal-separable and the solvability of a terminal-separable sum-network can be decided in polynomial time. Consequently, we give another necessary and sufficient condition, which yields a faster (O(|E|) time) algorithm than that of Shenvi and Dey ([18], (O(|E|^3) time), to determine the solvability of the 3s","authors_text":"Chau Yuen, Kai Cai, Rongquan Feng, Wentu Song","cross_cats":["math.IT"],"headline":"","license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"cs.IT","submitted_at":"2015-02-03T07:27:34Z","title":"On the Solvability of 3s/nt Sum-Network---A Region Decomposition and Weak Decentralized Code Method"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.00762","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":"sha256:17de7972e2f791f3b874e7bc450cf56f566a5fd704951c9b37dc649933419ff9","target":"record","created_at":"2026-05-18T02:28:04Z","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":"14214c6a0ff3d2dfdb84e369832a10372d66a7c55e96ccf122874e13d805d134","cross_cats_sorted":["math.IT"],"license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"cs.IT","submitted_at":"2015-02-03T07:27:34Z","title_canon_sha256":"b2513400e74216f53ade13530f3b96c7a0c02c9d4d379713fe036f2865d3d8d0"},"schema_version":"1.0","source":{"id":"1502.00762","kind":"arxiv","version":1}},"canonical_sha256":"dccb879497b4cf5e556935035896c200382531776e9c835c4b3c86cba7b9472f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"dccb879497b4cf5e556935035896c200382531776e9c835c4b3c86cba7b9472f","first_computed_at":"2026-05-18T02:28:04.376087Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:28:04.376087Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"AahkehuBUWhNVmjPO+WaMGsFKdXHZT9DhB+RtEGVEXv0FFURX/rNJOiMGNzE0+8CjesMdCvfDCX66uwH/RoxCA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:28:04.376488Z","signed_message":"canonical_sha256_bytes"},"source_id":"1502.00762","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:17de7972e2f791f3b874e7bc450cf56f566a5fd704951c9b37dc649933419ff9","sha256:1fbae5e858ad75ee90784fa3b7f87ff4a543c706a04ed9800b8d38f830a24aa6"],"state_sha256":"551463d866a8fc8ca4aaee5710ee62db1b0b61968f54a94cfcb81f0bce2ad388"}