{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:7BTZNQ6DPR2RZYHVB7FBJR6WYP","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":"52a58a47904cb7ad79399c349ffb90c4076be97f84230eba7b818fabb0971b34","cross_cats_sorted":["cs.DM","math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-06-08T14:49:22Z","title_canon_sha256":"59326d3beab84f04a7d4e3f8d8fe60b504b61f785a5616c4c6d1ac908bef6404"},"schema_version":"1.0","source":{"id":"1306.1926","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1306.1926","created_at":"2026-05-18T00:51:07Z"},{"alias_kind":"arxiv_version","alias_value":"1306.1926v3","created_at":"2026-05-18T00:51:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1306.1926","created_at":"2026-05-18T00:51:07Z"},{"alias_kind":"pith_short_12","alias_value":"7BTZNQ6DPR2R","created_at":"2026-05-18T12:27:36Z"},{"alias_kind":"pith_short_16","alias_value":"7BTZNQ6DPR2RZYHV","created_at":"2026-05-18T12:27:36Z"},{"alias_kind":"pith_short_8","alias_value":"7BTZNQ6D","created_at":"2026-05-18T12:27:36Z"}],"graph_snapshots":[{"event_id":"sha256:0e1a5f73efc9d5c1a39a09b49de4fb8bb03b8c2cf0373682189b3140b74070eb","target":"graph","created_at":"2026-05-18T00:51:07Z","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":"Given an edge-weighted graph $G=(V,E)$ and a set $E_0\\subset E$, the incremental network design problem with minimum spanning trees asks for a sequence of edges $e'_1,\\ldots,e'_T\\in E\\setminus E_0$ minimizing $\\sum_{t=1}^Tw(X_t)$ where $w(X_t)$ is the weight of a minimum spanning tree $X_t$ for the subgraph $(V,E_0\\cup\\{e'_1,\\ldots,e'_t\\})$ and $T=\\lvert E\\setminus E_0\\rvert$. We prove that this problem can be solved by a greedy algorithm.","authors_text":"Konrad Engel, Martin W.P. Savelsbergh, Thomas Kalinowski","cross_cats":["cs.DM","math.OC"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-06-08T14:49:22Z","title":"Incremental Network Design with Minimum Spanning Trees"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1306.1926","kind":"arxiv","version":3},"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":"sha256:246212b3095a239dc20e47a0bfbb35eb57fa121833b8a89f5901d218fc4c0329","target":"record","created_at":"2026-05-18T00:51:07Z","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":"52a58a47904cb7ad79399c349ffb90c4076be97f84230eba7b818fabb0971b34","cross_cats_sorted":["cs.DM","math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-06-08T14:49:22Z","title_canon_sha256":"59326d3beab84f04a7d4e3f8d8fe60b504b61f785a5616c4c6d1ac908bef6404"},"schema_version":"1.0","source":{"id":"1306.1926","kind":"arxiv","version":3}},"canonical_sha256":"f86796c3c37c751ce0f50fca14c7d6c3e53d61084b64b2fb4a8a40a4217e95a1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f86796c3c37c751ce0f50fca14c7d6c3e53d61084b64b2fb4a8a40a4217e95a1","first_computed_at":"2026-05-18T00:51:07.731782Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:51:07.731782Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"myLypgvv5IayJu0ltfBrz07/BN9RedqFvxyL/LugkgAoZG/RXynXb95V3vvHLgVjl87dvUhtsp08j9yJ9gKaDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:51:07.732232Z","signed_message":"canonical_sha256_bytes"},"source_id":"1306.1926","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:246212b3095a239dc20e47a0bfbb35eb57fa121833b8a89f5901d218fc4c0329","sha256:0e1a5f73efc9d5c1a39a09b49de4fb8bb03b8c2cf0373682189b3140b74070eb"],"state_sha256":"0e7a583a0a782678b7cd72b61011a1be3b14c1e02f0b2f1db839cb0cd913c1c3"}