{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:66A52ZCCNE3SQXG3JPD3SC6Q2U","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":"f8c7ef4f60a03ae8b3e770f2e078d4720763bf718e0f2cc6128884d527c1cd85","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-01-30T17:33:25Z","title_canon_sha256":"3e1686db1b31fc35915bc1335ab27cbc308749465a457ac6201951e903c58e1b"},"schema_version":"1.0","source":{"id":"1401.7931","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1401.7931","created_at":"2026-05-18T02:46:30Z"},{"alias_kind":"arxiv_version","alias_value":"1401.7931v2","created_at":"2026-05-18T02:46:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1401.7931","created_at":"2026-05-18T02:46:30Z"},{"alias_kind":"pith_short_12","alias_value":"66A52ZCCNE3S","created_at":"2026-05-18T12:28:16Z"},{"alias_kind":"pith_short_16","alias_value":"66A52ZCCNE3SQXG3","created_at":"2026-05-18T12:28:16Z"},{"alias_kind":"pith_short_8","alias_value":"66A52ZCC","created_at":"2026-05-18T12:28:16Z"}],"graph_snapshots":[{"event_id":"sha256:1b32c4e426aeeea8c4e74063d8eb35e18caa4f78c6817fbacc2be53d29db2817","target":"graph","created_at":"2026-05-18T02:46:30Z","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":"A graph on $2k$ vertices is path-pairable if for any pairing of the vertices the pairs can be joined by edge-disjoint paths. The so far known families of path-pairable graphs have diameter of length at most 3. In this paper we present an infinite family of path-pairable graphs with diameter $d(G)=O(\\sqrt{n})$ where $n$ denotes the number of vertices of the graph. We prove that our example is extremal up to a constant factor.","authors_text":"Gabor Meszaros","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-01-30T17:33:25Z","title":"Note on the Diameter of Path-Pairable Graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.7931","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:e80e02a814b86666f1363083f2cdb74ac1aeb5e3933592bdfecff0cbe6f40718","target":"record","created_at":"2026-05-18T02:46:30Z","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":"f8c7ef4f60a03ae8b3e770f2e078d4720763bf718e0f2cc6128884d527c1cd85","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-01-30T17:33:25Z","title_canon_sha256":"3e1686db1b31fc35915bc1335ab27cbc308749465a457ac6201951e903c58e1b"},"schema_version":"1.0","source":{"id":"1401.7931","kind":"arxiv","version":2}},"canonical_sha256":"f781dd64426937285cdb4bc7b90bd0d53e9848d0af89c52ca11cc4d83784f1ea","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f781dd64426937285cdb4bc7b90bd0d53e9848d0af89c52ca11cc4d83784f1ea","first_computed_at":"2026-05-18T02:46:30.945277Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:46:30.945277Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"4t+wGRBgLbppUnsSZ4DLL8Vc8XTjafF2jMUDWs/IDbzD3AwuUHgc+4iZE0CR9MkROc+oLYeBi5Zgfm86IGh2Aw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:46:30.945841Z","signed_message":"canonical_sha256_bytes"},"source_id":"1401.7931","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e80e02a814b86666f1363083f2cdb74ac1aeb5e3933592bdfecff0cbe6f40718","sha256:1b32c4e426aeeea8c4e74063d8eb35e18caa4f78c6817fbacc2be53d29db2817"],"state_sha256":"986753cd8aed021d0d0cf949c5c51003d3901945a5e9e984b5d411f4ace784d8"}