{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:ODYOQSXD7XFKJGY2TIKEYCSABG","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":"eaf32ed3a8b61ccf785266e212aab5b2f309fb5345bbd1e4cdb27b1ec0b1676b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2018-11-29T07:23:44Z","title_canon_sha256":"ea3e3f1d3d42e210ea60331673303fba7c7437ef87c1f5ff0db7ecb7ecf8a880"},"schema_version":"1.0","source":{"id":"1812.01678","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1812.01678","created_at":"2026-05-17T23:49:16Z"},{"alias_kind":"arxiv_version","alias_value":"1812.01678v2","created_at":"2026-05-17T23:49:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1812.01678","created_at":"2026-05-17T23:49:16Z"},{"alias_kind":"pith_short_12","alias_value":"ODYOQSXD7XFK","created_at":"2026-05-18T12:32:43Z"},{"alias_kind":"pith_short_16","alias_value":"ODYOQSXD7XFKJGY2","created_at":"2026-05-18T12:32:43Z"},{"alias_kind":"pith_short_8","alias_value":"ODYOQSXD","created_at":"2026-05-18T12:32:43Z"}],"graph_snapshots":[{"event_id":"sha256:058cdfd4d180e830b9b555aa8294b552d9d7fc5210f77f0e2aa09fe81b16580b","target":"graph","created_at":"2026-05-17T23:49:16Z","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":"The Steiner tree problems are well-known NP-hard problems that have diverse applications. Duin et al. (2004) have intuitively proposed the widely-used transformation from the classical group Steiner tree problem to the classical Steiner tree problem in graphs. This transformation has not been rigorously proven so far. Specifically, the large M value that is used in this transformation has not been specified. In this paper, we address this issue by rigorously prove this transformation for a specific large M value.","authors_text":"Yahui Sun","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2018-11-29T07:23:44Z","title":"Solving group Steiner problems as Steiner problems: the rigorous proof"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.01678","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":"sha256:9e72535222e0ecf200ea7d37b7daf3bd0b5f20b8aa89a5cc354ddd7b3ba727a3","target":"record","created_at":"2026-05-17T23:49:16Z","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":"eaf32ed3a8b61ccf785266e212aab5b2f309fb5345bbd1e4cdb27b1ec0b1676b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2018-11-29T07:23:44Z","title_canon_sha256":"ea3e3f1d3d42e210ea60331673303fba7c7437ef87c1f5ff0db7ecb7ecf8a880"},"schema_version":"1.0","source":{"id":"1812.01678","kind":"arxiv","version":2}},"canonical_sha256":"70f0e84ae3fdcaa49b1a9a144c0a4009bcaf92dd33198f02b785ea974de22665","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"70f0e84ae3fdcaa49b1a9a144c0a4009bcaf92dd33198f02b785ea974de22665","first_computed_at":"2026-05-17T23:49:16.961565Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:49:16.961565Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"dBcO4rRU6hDKhqdZfW4eBy8MiDPbDGSwE5B36u5rl7yg1dAtk5hoOV4QDhBvnWCftJGbU/WAdHW5ozmj41pfCg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:49:16.962283Z","signed_message":"canonical_sha256_bytes"},"source_id":"1812.01678","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9e72535222e0ecf200ea7d37b7daf3bd0b5f20b8aa89a5cc354ddd7b3ba727a3","sha256:058cdfd4d180e830b9b555aa8294b552d9d7fc5210f77f0e2aa09fe81b16580b"],"state_sha256":"c20192a83bee586f04e219a67be19dc5912d892880e1e49e980bf435d5f6c63e"}