{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:YQRJJTGLO5JE2NJZ3GY7FWO2PZ","short_pith_number":"pith:YQRJJTGL","schema_version":"1.0","canonical_sha256":"c42294cccb77524d3539d9b1f2d9da7e52c087015eb0289d3aec340e4a6746b1","source":{"kind":"arxiv","id":"1702.01424","version":1},"attestation_state":"computed","paper":{"title":"On the Combinatorial Lower Bound for the Extension Complexity of the Spanning Tree Polytope","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OC"],"primary_cat":"cs.DM","authors_text":"Dirk Oliver Theis, Kaveh Khoshkhah","submitted_at":"2017-02-05T16:22:19Z","abstract_excerpt":"In the study of extensions of polytopes of combinatorial optimization problems, a notorious open question is that for the size of the smallest extended formulation of the Minimum Spanning Tree problem on a complete graph with $n$ nodes. The best known lower bound is the trival (dimension) bound, $\\Omega(n^2)$, the best known upper bound is the extended formulation by Wong (1980) of size $O(n^3)$ (also Martin, 1991).\n  In this note we give a nondeterministic communication protocol with cost $\\log_2(n^2\\log n)+O(1)$ for the support of the spanning tree slack matrix.\n  This means that the combina"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1702.01424","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2017-02-05T16:22:19Z","cross_cats_sorted":["math.OC"],"title_canon_sha256":"1287a2cdbc3a60c2976552b7b1ab0cee72cd2fdbda7b7db2e8dcb8365372d563","abstract_canon_sha256":"b6599dd0a37913f8cf3bb1d2853722632e4dd0800dc11cd026bba63862f5f382"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:51:23.481879Z","signature_b64":"asBPEWQbIf+oFjodiGtkfJZwqLniea6WG8KLlMhJ3ATu0ITSpgeSygq5g+JV9q/NPgDQOazKvqKwRwXYXnfsDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c42294cccb77524d3539d9b1f2d9da7e52c087015eb0289d3aec340e4a6746b1","last_reissued_at":"2026-05-18T00:51:23.481229Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:51:23.481229Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the Combinatorial Lower Bound for the Extension Complexity of the Spanning Tree Polytope","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OC"],"primary_cat":"cs.DM","authors_text":"Dirk Oliver Theis, Kaveh Khoshkhah","submitted_at":"2017-02-05T16:22:19Z","abstract_excerpt":"In the study of extensions of polytopes of combinatorial optimization problems, a notorious open question is that for the size of the smallest extended formulation of the Minimum Spanning Tree problem on a complete graph with $n$ nodes. The best known lower bound is the trival (dimension) bound, $\\Omega(n^2)$, the best known upper bound is the extended formulation by Wong (1980) of size $O(n^3)$ (also Martin, 1991).\n  In this note we give a nondeterministic communication protocol with cost $\\log_2(n^2\\log n)+O(1)$ for the support of the spanning tree slack matrix.\n  This means that the combina"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.01424","kind":"arxiv","version":1},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1702.01424","created_at":"2026-05-18T00:51:23.481309+00:00"},{"alias_kind":"arxiv_version","alias_value":"1702.01424v1","created_at":"2026-05-18T00:51:23.481309+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1702.01424","created_at":"2026-05-18T00:51:23.481309+00:00"},{"alias_kind":"pith_short_12","alias_value":"YQRJJTGLO5JE","created_at":"2026-05-18T12:31:56.362134+00:00"},{"alias_kind":"pith_short_16","alias_value":"YQRJJTGLO5JE2NJZ","created_at":"2026-05-18T12:31:56.362134+00:00"},{"alias_kind":"pith_short_8","alias_value":"YQRJJTGL","created_at":"2026-05-18T12:31:56.362134+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/YQRJJTGLO5JE2NJZ3GY7FWO2PZ","json":"https://pith.science/pith/YQRJJTGLO5JE2NJZ3GY7FWO2PZ.json","graph_json":"https://pith.science/api/pith-number/YQRJJTGLO5JE2NJZ3GY7FWO2PZ/graph.json","events_json":"https://pith.science/api/pith-number/YQRJJTGLO5JE2NJZ3GY7FWO2PZ/events.json","paper":"https://pith.science/paper/YQRJJTGL"},"agent_actions":{"view_html":"https://pith.science/pith/YQRJJTGLO5JE2NJZ3GY7FWO2PZ","download_json":"https://pith.science/pith/YQRJJTGLO5JE2NJZ3GY7FWO2PZ.json","view_paper":"https://pith.science/paper/YQRJJTGL","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1702.01424&json=true","fetch_graph":"https://pith.science/api/pith-number/YQRJJTGLO5JE2NJZ3GY7FWO2PZ/graph.json","fetch_events":"https://pith.science/api/pith-number/YQRJJTGLO5JE2NJZ3GY7FWO2PZ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/YQRJJTGLO5JE2NJZ3GY7FWO2PZ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/YQRJJTGLO5JE2NJZ3GY7FWO2PZ/action/storage_attestation","attest_author":"https://pith.science/pith/YQRJJTGLO5JE2NJZ3GY7FWO2PZ/action/author_attestation","sign_citation":"https://pith.science/pith/YQRJJTGLO5JE2NJZ3GY7FWO2PZ/action/citation_signature","submit_replication":"https://pith.science/pith/YQRJJTGLO5JE2NJZ3GY7FWO2PZ/action/replication_record"}},"created_at":"2026-05-18T00:51:23.481309+00:00","updated_at":"2026-05-18T00:51:23.481309+00:00"}