{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:GTACAI7RMXMCV77PZWXMGLUJKA","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":"985014a0ee79c3782c673aa19e6ed4ca0a34ec0f060f7cfd45b1db3404dd985d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-09-23T20:04:29Z","title_canon_sha256":"ce59a0b929b78b9bf65a57ed66651dee14401dc41c221bdffa5ece0b1c2422b7"},"schema_version":"1.0","source":{"id":"1709.08111","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1709.08111","created_at":"2026-05-18T00:34:27Z"},{"alias_kind":"arxiv_version","alias_value":"1709.08111v1","created_at":"2026-05-18T00:34:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1709.08111","created_at":"2026-05-18T00:34:27Z"},{"alias_kind":"pith_short_12","alias_value":"GTACAI7RMXMC","created_at":"2026-05-18T12:31:18Z"},{"alias_kind":"pith_short_16","alias_value":"GTACAI7RMXMCV77P","created_at":"2026-05-18T12:31:18Z"},{"alias_kind":"pith_short_8","alias_value":"GTACAI7R","created_at":"2026-05-18T12:31:18Z"}],"graph_snapshots":[{"event_id":"sha256:65fdff3a7b0a34d5a397dc37513aa9e42b75008be7d1baaa4ff0f0963ae61069","target":"graph","created_at":"2026-05-18T00:34:27Z","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":"Over the past twenty years, critical and bicritical snarks have been appearing in the literature in various forms and in different contexts. Two main variants of criticality of snarks have been studied: criticality with respect to the non-existence of a $3$-edge-colouring and criticality with respect to the non-existence of a nowhere-zero $4$-flow. In this paper we show that these two kinds of criticality coincide, thereby completing previous partial results of de Freitas et al. [Electron. Notes Discrete Math. 50 (2015), 199--204] and Fiol et al. [ arXiv:1702.07156v1 (2017)].","authors_text":"Edita M\\'a\\v{c}ajov\\'a, Martin \\v{S}koviera","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-09-23T20:04:29Z","title":"Critical and flow-critical snarks coincide"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.08111","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":"sha256:6718b6bda7bbf5a00434e6f6ef0144fa4c70f6288f9cbe9e42fb4e92ff21c210","target":"record","created_at":"2026-05-18T00:34:27Z","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":"985014a0ee79c3782c673aa19e6ed4ca0a34ec0f060f7cfd45b1db3404dd985d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-09-23T20:04:29Z","title_canon_sha256":"ce59a0b929b78b9bf65a57ed66651dee14401dc41c221bdffa5ece0b1c2422b7"},"schema_version":"1.0","source":{"id":"1709.08111","kind":"arxiv","version":1}},"canonical_sha256":"34c02023f165d82affefcdaec32e895006aa5f434bd94be87c756baf1135372e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"34c02023f165d82affefcdaec32e895006aa5f434bd94be87c756baf1135372e","first_computed_at":"2026-05-18T00:34:27.962379Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:34:27.962379Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"pVtDI9OixW6W9TxcLeylEFabxpe2yRG5QC0jCz4GDix4GXtR6ZloBuiVpvn4R3vIH2aSdp9emdka+AoeeBUgBA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:34:27.962852Z","signed_message":"canonical_sha256_bytes"},"source_id":"1709.08111","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6718b6bda7bbf5a00434e6f6ef0144fa4c70f6288f9cbe9e42fb4e92ff21c210","sha256:65fdff3a7b0a34d5a397dc37513aa9e42b75008be7d1baaa4ff0f0963ae61069"],"state_sha256":"e4411862cc690e92dc5705345f7ee5d78dfa6bee263f1780d26f4e458239e4cc"}