{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:4YGYGUZVKNFEIOQC5WVBSZAF3N","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":"265e48e19039fd751f310036836cf6ae8315178ed4ffa4b104ec56e7ef6bb1c0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2017-04-11T03:50:11Z","title_canon_sha256":"4a8677410f02c8bc395213356aff780160e076972a66ec89e2f50ce21d905c41"},"schema_version":"1.0","source":{"id":"1704.03132","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1704.03132","created_at":"2026-05-18T00:08:23Z"},{"alias_kind":"arxiv_version","alias_value":"1704.03132v4","created_at":"2026-05-18T00:08:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1704.03132","created_at":"2026-05-18T00:08:23Z"},{"alias_kind":"pith_short_12","alias_value":"4YGYGUZVKNFE","created_at":"2026-05-18T12:31:00Z"},{"alias_kind":"pith_short_16","alias_value":"4YGYGUZVKNFEIOQC","created_at":"2026-05-18T12:31:00Z"},{"alias_kind":"pith_short_8","alias_value":"4YGYGUZV","created_at":"2026-05-18T12:31:00Z"}],"graph_snapshots":[{"event_id":"sha256:e6ba1ace2fc3278463f07b549d1fc43aa0fd1393def3535c33bf484dc4bcb212","target":"graph","created_at":"2026-05-18T00:08:23Z","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":"It is a long standing open problem whether Yao-Yao graphs $\\mathsf{YY}_{k}$ are all spanners [li2002sparse]. Bauer and Damian [bauer2013infinite] showed that all $\\mathsf{YY}_{6k}$ for $k \\geq 6$ are spanners. Li and Zhan [li2016almost] generalized their result and proved that all even Yao-Yao graphs $\\mathsf{YY}_{2k}$ are spanners (for $k\\geq 42$). However, their technique cannot be extended to odd Yao-Yao graphs, and whether they are spanners are still elusive. In this paper, we show that, surprisingly, for any integer $k \\geq 1$, there exist odd Yao-Yao graph $\\mathsf{YY}_{2k+1}$ instances,","authors_text":"Jian Li, Wei Zhan, Yifei Jin","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2017-04-11T03:50:11Z","title":"Odd Yao-Yao Graphs are Not Spanners"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.03132","kind":"arxiv","version":4},"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":"sha256:3436683dab6fc05d0059b8ddcd6391375326d5eca625cc41c78d7509a5cf6223","target":"record","created_at":"2026-05-18T00:08:23Z","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":"265e48e19039fd751f310036836cf6ae8315178ed4ffa4b104ec56e7ef6bb1c0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2017-04-11T03:50:11Z","title_canon_sha256":"4a8677410f02c8bc395213356aff780160e076972a66ec89e2f50ce21d905c41"},"schema_version":"1.0","source":{"id":"1704.03132","kind":"arxiv","version":4}},"canonical_sha256":"e60d835335534a443a02edaa196405db6b84a027c7fd4b24800790c4e321ac3e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e60d835335534a443a02edaa196405db6b84a027c7fd4b24800790c4e321ac3e","first_computed_at":"2026-05-18T00:08:23.717150Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:08:23.717150Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"MI1SsxV6vmDcoOd75i3NH405d3rFxy+AQEpRmD7pHrVFwgIGU0tpHmNpFwyotjNbiArnF2vF0MbzOPOOBXdjDA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:08:23.717789Z","signed_message":"canonical_sha256_bytes"},"source_id":"1704.03132","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3436683dab6fc05d0059b8ddcd6391375326d5eca625cc41c78d7509a5cf6223","sha256:e6ba1ace2fc3278463f07b549d1fc43aa0fd1393def3535c33bf484dc4bcb212"],"state_sha256":"c6bf4bd1026eb60a896843d995b4d207847f184799a2caa05749a7d0a3fdfbeb"}