{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:HOV425YM7VZRHKJ7FZKFNR7ZCF","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":"eca0de62126a532a61acae34141d01899fe6baa3d9ee6f1bfc0806701fd55871","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2014-10-01T17:58:13Z","title_canon_sha256":"d54132e8dec5a7f3c2e2942671ad493f6b679aa8935aed0425a580370a8ec10c"},"schema_version":"1.0","source":{"id":"1410.0309","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1410.0309","created_at":"2026-05-18T01:55:53Z"},{"alias_kind":"arxiv_version","alias_value":"1410.0309v4","created_at":"2026-05-18T01:55:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1410.0309","created_at":"2026-05-18T01:55:53Z"},{"alias_kind":"pith_short_12","alias_value":"HOV425YM7VZR","created_at":"2026-05-18T12:28:30Z"},{"alias_kind":"pith_short_16","alias_value":"HOV425YM7VZRHKJ7","created_at":"2026-05-18T12:28:30Z"},{"alias_kind":"pith_short_8","alias_value":"HOV425YM","created_at":"2026-05-18T12:28:30Z"}],"graph_snapshots":[{"event_id":"sha256:7bf9b80d73d6eb51cb2c1349eb48380767eedea22d52a6bd1f9b3aac09152764","target":"graph","created_at":"2026-05-18T01:55:53Z","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":"Given a set $S$ of points in the plane, the $k$-Gabriel graph of $S$ is the geometric graph with vertex set $S$, where $p_i,p_j\\in S$ are connected by an edge if and only if the closed disk having segment $\\bar{p_ip_j}$ as diameter contains at most $k$ points of $S \\setminus \\{p_i,p_j\\}$. We consider the following question: What is the minimum value of $k$ such that the $k$-Gabriel graph of every point set $S$ contains a Hamiltonian cycle? For this value, we give an upper bound of 10 and a lower bound of 2. The best previously known values were 15 and 1, respectively.","authors_text":"Maria Saumell, Nico Van Cleemput, Tom\\'a\\v{s} Kaiser","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2014-10-01T17:58:13Z","title":"10-Gabriel graphs are Hamiltonian"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.0309","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":"sha256:36ff3f57dfa1ccf3aa2df79d5af44ce3686f96769e1e2ae80bed64454cf5b59a","target":"record","created_at":"2026-05-18T01:55:53Z","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":"eca0de62126a532a61acae34141d01899fe6baa3d9ee6f1bfc0806701fd55871","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2014-10-01T17:58:13Z","title_canon_sha256":"d54132e8dec5a7f3c2e2942671ad493f6b679aa8935aed0425a580370a8ec10c"},"schema_version":"1.0","source":{"id":"1410.0309","kind":"arxiv","version":4}},"canonical_sha256":"3babcd770cfd7313a93f2e5456c7f91146654c721d0549887efb78f68ca77734","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3babcd770cfd7313a93f2e5456c7f91146654c721d0549887efb78f68ca77734","first_computed_at":"2026-05-18T01:55:53.125795Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:55:53.125795Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"pam6q1aBHMj5SSwtwJ6tr4UuKKdbtn+JHLJJ4Rw/mCSKuM/bWDz2Xx3xU6Z9lNP96StpAN531AR1hAq0vmSBBg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:55:53.126260Z","signed_message":"canonical_sha256_bytes"},"source_id":"1410.0309","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:36ff3f57dfa1ccf3aa2df79d5af44ce3686f96769e1e2ae80bed64454cf5b59a","sha256:7bf9b80d73d6eb51cb2c1349eb48380767eedea22d52a6bd1f9b3aac09152764"],"state_sha256":"3bf6ae1ae6d8e9276e5f0fb14c9e59489cfd18060d438776036a9b876dac09da"}