{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:7D54O2UM5VZBV2ERVWNN5OPHUK","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":"58feeb141713192d23322fe9f2fd9bb8757f86ab7369f504be7b4f6626dc9754","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-03-08T10:54:27Z","title_canon_sha256":"4685a99a617594bcaec4526774a65a2a7bb9d75e101d552c8d31f4a395f22644"},"schema_version":"1.0","source":{"id":"1603.02474","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1603.02474","created_at":"2026-05-18T00:25:21Z"},{"alias_kind":"arxiv_version","alias_value":"1603.02474v2","created_at":"2026-05-18T00:25:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1603.02474","created_at":"2026-05-18T00:25:21Z"},{"alias_kind":"pith_short_12","alias_value":"7D54O2UM5VZB","created_at":"2026-05-18T12:30:04Z"},{"alias_kind":"pith_short_16","alias_value":"7D54O2UM5VZBV2ER","created_at":"2026-05-18T12:30:04Z"},{"alias_kind":"pith_short_8","alias_value":"7D54O2UM","created_at":"2026-05-18T12:30:04Z"}],"graph_snapshots":[{"event_id":"sha256:84678da1f573de69ae18f4faeb96fba84675efebb92a11b1c541f1d0f96c4aee","target":"graph","created_at":"2026-05-18T00:25:21Z","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":"In 2009, Bang-Jensen asked whether there exists a function $g(k)$ such that every strongly $k$-connected $n$-vertex tournament contains a strongly $k$-connected spanning subgraph with at most $kn + g(k)$ arcs. In this paper, we answer the question by showing that every strongly $k$-connected $n$-vertex tournament contains a strongly $k$-connected spanning subgraph with at most $kn + 750k^2\\log(k+1)$ arcs.","authors_text":"Dong Yeap Kang, Geewon Suh, Jaehoon Kim, Younjin Kim","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-03-08T10:54:27Z","title":"Sparse spanning $k$-connected subgraphs in tournaments"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.02474","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:fd935a2a6d9cdbf18be983d1b57e2c109e371c07b0623b2c4f5c698fad89e1d2","target":"record","created_at":"2026-05-18T00:25:21Z","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":"58feeb141713192d23322fe9f2fd9bb8757f86ab7369f504be7b4f6626dc9754","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-03-08T10:54:27Z","title_canon_sha256":"4685a99a617594bcaec4526774a65a2a7bb9d75e101d552c8d31f4a395f22644"},"schema_version":"1.0","source":{"id":"1603.02474","kind":"arxiv","version":2}},"canonical_sha256":"f8fbc76a8ced721ae891ad9adeb9e7a292752d5757d4289984120b31bd388baa","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f8fbc76a8ced721ae891ad9adeb9e7a292752d5757d4289984120b31bd388baa","first_computed_at":"2026-05-18T00:25:21.492402Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:25:21.492402Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"0F7+bLOuM2pvSES8YF3U3m1k9iZ2yIVOzAU7wMw22+bYHutF0cfu0N2fDSnraqWwCJr1zjGEG3h4WGFCGOgtDw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:25:21.493032Z","signed_message":"canonical_sha256_bytes"},"source_id":"1603.02474","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fd935a2a6d9cdbf18be983d1b57e2c109e371c07b0623b2c4f5c698fad89e1d2","sha256:84678da1f573de69ae18f4faeb96fba84675efebb92a11b1c541f1d0f96c4aee"],"state_sha256":"c92b839bb7ebb4bf9513f6027dc3cb33d9309c7d887304306ef744c86c1d7678"}