{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:IWHZQ6WM32Y2YAUNIEBI2EOFVN","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":"bce3cf005171a6e40c5764745dce4c40b4c68fb8fa23e80693af2ae7e1bed993","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2012-12-14T23:54:55Z","title_canon_sha256":"14e0d7e9977d166c506c7d29ba2dbbf9e5c938300ff90106330156268941013c"},"schema_version":"1.0","source":{"id":"1212.3641","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1212.3641","created_at":"2026-05-18T03:38:22Z"},{"alias_kind":"arxiv_version","alias_value":"1212.3641v1","created_at":"2026-05-18T03:38:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1212.3641","created_at":"2026-05-18T03:38:22Z"},{"alias_kind":"pith_short_12","alias_value":"IWHZQ6WM32Y2","created_at":"2026-05-18T12:27:09Z"},{"alias_kind":"pith_short_16","alias_value":"IWHZQ6WM32Y2YAUN","created_at":"2026-05-18T12:27:09Z"},{"alias_kind":"pith_short_8","alias_value":"IWHZQ6WM","created_at":"2026-05-18T12:27:09Z"}],"graph_snapshots":[{"event_id":"sha256:6684fb81b340203c07cc6bdffb7346232dbe3e03c636c8d4ce8a256155033439","target":"graph","created_at":"2026-05-18T03:38:22Z","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":"We estimate the minimum number of vertices of a cubic graph with given oddness and cyclic connectivity. We prove that a bridgeless cubic graph $G$ with oddness $\\omega(G)$ other than the Petersen graph has at least $5.41\\cdot\\omega(G)$ vertices, and for each integer $k$ with $2\\le k\\le 6$ we construct an infinite family of cubic graphs with cyclic connectivity $k$ and small oddness ratio $|V(G)|/\\omega(G)$. In particular, for cyclic connectivity 2, 4, 5, and 6 we improve the upper bounds on the oddness ratio of snarks to 7.5, 13, 25, and 99 from the known values 9, 15, 76, and 118, respectivel","authors_text":"Edita Macajova, Jan Mazak, Martin Skoviera, Robert Lukotka","cross_cats":["math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2012-12-14T23:54:55Z","title":"Small snarks with large oddness"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.3641","kind":"arxiv","version":1},"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":"sha256:33da2fc639a6cf12fc5d750e64150473a3fc6ffc26457e2c6283a9d7da2bff9b","target":"record","created_at":"2026-05-18T03:38:22Z","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":"bce3cf005171a6e40c5764745dce4c40b4c68fb8fa23e80693af2ae7e1bed993","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2012-12-14T23:54:55Z","title_canon_sha256":"14e0d7e9977d166c506c7d29ba2dbbf9e5c938300ff90106330156268941013c"},"schema_version":"1.0","source":{"id":"1212.3641","kind":"arxiv","version":1}},"canonical_sha256":"458f987accdeb1ac028d41028d11c5ab6fd2b5ad6c7edb9cec4ba2fc2a5b6fac","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"458f987accdeb1ac028d41028d11c5ab6fd2b5ad6c7edb9cec4ba2fc2a5b6fac","first_computed_at":"2026-05-18T03:38:22.777817Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:38:22.777817Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"hjpZu5oQjgVn9BK+gHki6PNjReCHtDAlF+aP1aqgbLfIGBj+oo+Im8O6hYReeq7ImMg5Urtw4rVriviQSc79Bw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:38:22.778208Z","signed_message":"canonical_sha256_bytes"},"source_id":"1212.3641","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:33da2fc639a6cf12fc5d750e64150473a3fc6ffc26457e2c6283a9d7da2bff9b","sha256:6684fb81b340203c07cc6bdffb7346232dbe3e03c636c8d4ce8a256155033439"],"state_sha256":"2b034707c2c1d550a8b4e9af69b451f33974a145524a5e8f7606793dd5b70e8a"}