{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:FH4Y5C7L6SOQPWNU6FR4ROZIC3","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":"44a1309d1ac871dd656500584051bc23c88ea24835e3fe7f58c297641966b798","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-03-12T19:06:10Z","title_canon_sha256":"ddc2b90beabe877c53cd0ebf43dbe1f4b1100a24b97acf49e5b426321302bb04"},"schema_version":"1.0","source":{"id":"1803.04466","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1803.04466","created_at":"2026-05-17T23:51:56Z"},{"alias_kind":"arxiv_version","alias_value":"1803.04466v2","created_at":"2026-05-17T23:51:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1803.04466","created_at":"2026-05-17T23:51:56Z"},{"alias_kind":"pith_short_12","alias_value":"FH4Y5C7L6SOQ","created_at":"2026-05-18T12:32:22Z"},{"alias_kind":"pith_short_16","alias_value":"FH4Y5C7L6SOQPWNU","created_at":"2026-05-18T12:32:22Z"},{"alias_kind":"pith_short_8","alias_value":"FH4Y5C7L","created_at":"2026-05-18T12:32:22Z"}],"graph_snapshots":[{"event_id":"sha256:cced5324bb5e054fed08bb178a810a192680397ce3a94e5a65f8cd5458a99ebc","target":"graph","created_at":"2026-05-17T23:51:56Z","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":"Let $G$ be a graph, and $v\\in V(G)$ and $S\\subseteq V(G)\\backslash v$ of size at least $k$. An important result on graph connectivity due to Perfect states that, if $v$ and $S$ are $k$-linked, then a $(k-1)$-link between a vertex $v$ and $S$ can be extended to a $k$-link between $v$ and $S$ such that the endvertices of the $(k-1)$-link are also the endvertices of the $k$-link. We begin by proving a generalization of Perfect's result by showing that, if two disjoint sets $S_1$ and $S_2$ are $k$-linked, then a $t$-link ($t< k$) between two disjoint sets $S_1$ and $S_2$ can be extended to a $k$-l","authors_text":"Dong Ye, Ervin Gy\\H{o}ri, Michael D. Plummer, Xiaoya Zha","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-03-12T19:06:10Z","title":"Cycle Traversability for Claw-free Graphs and Polyhedral Maps"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.04466","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:b95d150bc7d902f0c7ec3a43952b00d2e8f70396a9f22cf6676f893ae2dca2b3","target":"record","created_at":"2026-05-17T23:51:56Z","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":"44a1309d1ac871dd656500584051bc23c88ea24835e3fe7f58c297641966b798","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-03-12T19:06:10Z","title_canon_sha256":"ddc2b90beabe877c53cd0ebf43dbe1f4b1100a24b97acf49e5b426321302bb04"},"schema_version":"1.0","source":{"id":"1803.04466","kind":"arxiv","version":2}},"canonical_sha256":"29f98e8bebf49d07d9b4f163c8bb2816dffd598ddf72a25c0102b9339eec096f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"29f98e8bebf49d07d9b4f163c8bb2816dffd598ddf72a25c0102b9339eec096f","first_computed_at":"2026-05-17T23:51:56.026759Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:51:56.026759Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"hvbupVJL13vhsDQ7nzW3gnsjcOHQY6sh1dAS0ZVZ4EyDwCz9rmLC0TeTACP+4eTLoc/oUEp15ql05oqhgXObCg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:51:56.027233Z","signed_message":"canonical_sha256_bytes"},"source_id":"1803.04466","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b95d150bc7d902f0c7ec3a43952b00d2e8f70396a9f22cf6676f893ae2dca2b3","sha256:cced5324bb5e054fed08bb178a810a192680397ce3a94e5a65f8cd5458a99ebc"],"state_sha256":"8ca4e47171ceb8755a181788363df82d400e581a22ecfc2b75641af67b6438d5"}