{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:7MNXWCVSDTCE4JIYLYCZ45E3QX","short_pith_number":"pith:7MNXWCVS","canonical_record":{"source":{"id":"1302.2158","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-02-08T21:25:22Z","cross_cats_sorted":["cs.DM"],"title_canon_sha256":"131a0ea3f327d6f46fb3858257fbadcae8d5c9ae64cb7a3607ad3e70691e2d88","abstract_canon_sha256":"4bd440982cddcdfb252b004c7120f35851b97d5f08afd4e51a0b5ef684b4b3f4"},"schema_version":"1.0"},"canonical_sha256":"fb1b7b0ab21cc44e25185e059e749b85e9a0df3a2c9a169864dbdb7fc412668f","source":{"kind":"arxiv","id":"1302.2158","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1302.2158","created_at":"2026-05-18T00:40:52Z"},{"alias_kind":"arxiv_version","alias_value":"1302.2158v4","created_at":"2026-05-18T00:40:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1302.2158","created_at":"2026-05-18T00:40:52Z"},{"alias_kind":"pith_short_12","alias_value":"7MNXWCVSDTCE","created_at":"2026-05-18T12:27:36Z"},{"alias_kind":"pith_short_16","alias_value":"7MNXWCVSDTCE4JIY","created_at":"2026-05-18T12:27:36Z"},{"alias_kind":"pith_short_8","alias_value":"7MNXWCVS","created_at":"2026-05-18T12:27:36Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:7MNXWCVSDTCE4JIYLYCZ45E3QX","target":"record","payload":{"canonical_record":{"source":{"id":"1302.2158","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-02-08T21:25:22Z","cross_cats_sorted":["cs.DM"],"title_canon_sha256":"131a0ea3f327d6f46fb3858257fbadcae8d5c9ae64cb7a3607ad3e70691e2d88","abstract_canon_sha256":"4bd440982cddcdfb252b004c7120f35851b97d5f08afd4e51a0b5ef684b4b3f4"},"schema_version":"1.0"},"canonical_sha256":"fb1b7b0ab21cc44e25185e059e749b85e9a0df3a2c9a169864dbdb7fc412668f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:40:52.185759Z","signature_b64":"WZGucrAk4+V/Ejp5IIQ4Wk8yi7sIbN8EV8cTzbXuvGEbHOnsdDL+j54lHXE/inKkd1Z3upN6/aMD/tQ42HlhBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fb1b7b0ab21cc44e25185e059e749b85e9a0df3a2c9a169864dbdb7fc412668f","last_reissued_at":"2026-05-18T00:40:52.185127Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:40:52.185127Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1302.2158","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:40:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JGb/7cYatrt9L5YCyqtUojR20+KaC4B2xiJY8v75nRNC2usrBo8mETuEs6917H+QKIglWrktoGc46vvv0x0eCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T03:03:11.660084Z"},"content_sha256":"055819459adfedb667f3da3f570507fb4c19d83b51566c38cdb955816e4731e8","schema_version":"1.0","event_id":"sha256:055819459adfedb667f3da3f570507fb4c19d83b51566c38cdb955816e4731e8"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:7MNXWCVSDTCE4JIYLYCZ45E3QX","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Three-coloring triangle-free graphs on surfaces II. 4-critical graphs in a disk","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM"],"primary_cat":"math.CO","authors_text":"Daniel Kral, Robin Thomas, Zdenek Dvorak","submitted_at":"2013-02-08T21:25:22Z","abstract_excerpt":"Let G be a plane graph of girth at least five. We show that if there exists a 3-coloring phi of a cycle C of G that does not extend to a 3-coloring of G, then G has a subgraph H on O(|C|) vertices that also has no 3-coloring extending phi. This is asymptotically best possible and improves a previous bound of Thomassen. In the next paper of the series we will use this result and the attendant theory to prove a generalization to graphs on surfaces with several precolored cycles."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.2158","kind":"arxiv","version":4},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:40:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JoEkTrGug7A5lUgt4lwzht3ghot0gz5NOx5kGwY1+j1eEkuLSTUU7MxgyxEsS9bK8lAyJStzTkbfnnEY9dfQCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T03:03:11.660697Z"},"content_sha256":"66b834d4ebc7bc06ba60d35fad946104df9d244560a72c5c593e8cd73207008c","schema_version":"1.0","event_id":"sha256:66b834d4ebc7bc06ba60d35fad946104df9d244560a72c5c593e8cd73207008c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/7MNXWCVSDTCE4JIYLYCZ45E3QX/bundle.json","state_url":"https://pith.science/pith/7MNXWCVSDTCE4JIYLYCZ45E3QX/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/7MNXWCVSDTCE4JIYLYCZ45E3QX/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-05-27T03:03:11Z","links":{"resolver":"https://pith.science/pith/7MNXWCVSDTCE4JIYLYCZ45E3QX","bundle":"https://pith.science/pith/7MNXWCVSDTCE4JIYLYCZ45E3QX/bundle.json","state":"https://pith.science/pith/7MNXWCVSDTCE4JIYLYCZ45E3QX/state.json","well_known_bundle":"https://pith.science/.well-known/pith/7MNXWCVSDTCE4JIYLYCZ45E3QX/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:7MNXWCVSDTCE4JIYLYCZ45E3QX","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":"4bd440982cddcdfb252b004c7120f35851b97d5f08afd4e51a0b5ef684b4b3f4","cross_cats_sorted":["cs.DM"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-02-08T21:25:22Z","title_canon_sha256":"131a0ea3f327d6f46fb3858257fbadcae8d5c9ae64cb7a3607ad3e70691e2d88"},"schema_version":"1.0","source":{"id":"1302.2158","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1302.2158","created_at":"2026-05-18T00:40:52Z"},{"alias_kind":"arxiv_version","alias_value":"1302.2158v4","created_at":"2026-05-18T00:40:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1302.2158","created_at":"2026-05-18T00:40:52Z"},{"alias_kind":"pith_short_12","alias_value":"7MNXWCVSDTCE","created_at":"2026-05-18T12:27:36Z"},{"alias_kind":"pith_short_16","alias_value":"7MNXWCVSDTCE4JIY","created_at":"2026-05-18T12:27:36Z"},{"alias_kind":"pith_short_8","alias_value":"7MNXWCVS","created_at":"2026-05-18T12:27:36Z"}],"graph_snapshots":[{"event_id":"sha256:66b834d4ebc7bc06ba60d35fad946104df9d244560a72c5c593e8cd73207008c","target":"graph","created_at":"2026-05-18T00:40:52Z","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 plane graph of girth at least five. We show that if there exists a 3-coloring phi of a cycle C of G that does not extend to a 3-coloring of G, then G has a subgraph H on O(|C|) vertices that also has no 3-coloring extending phi. This is asymptotically best possible and improves a previous bound of Thomassen. In the next paper of the series we will use this result and the attendant theory to prove a generalization to graphs on surfaces with several precolored cycles.","authors_text":"Daniel Kral, Robin Thomas, Zdenek Dvorak","cross_cats":["cs.DM"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-02-08T21:25:22Z","title":"Three-coloring triangle-free graphs on surfaces II. 4-critical graphs in a disk"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.2158","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":"sha256:055819459adfedb667f3da3f570507fb4c19d83b51566c38cdb955816e4731e8","target":"record","created_at":"2026-05-18T00:40:52Z","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":"4bd440982cddcdfb252b004c7120f35851b97d5f08afd4e51a0b5ef684b4b3f4","cross_cats_sorted":["cs.DM"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-02-08T21:25:22Z","title_canon_sha256":"131a0ea3f327d6f46fb3858257fbadcae8d5c9ae64cb7a3607ad3e70691e2d88"},"schema_version":"1.0","source":{"id":"1302.2158","kind":"arxiv","version":4}},"canonical_sha256":"fb1b7b0ab21cc44e25185e059e749b85e9a0df3a2c9a169864dbdb7fc412668f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fb1b7b0ab21cc44e25185e059e749b85e9a0df3a2c9a169864dbdb7fc412668f","first_computed_at":"2026-05-18T00:40:52.185127Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:40:52.185127Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"WZGucrAk4+V/Ejp5IIQ4Wk8yi7sIbN8EV8cTzbXuvGEbHOnsdDL+j54lHXE/inKkd1Z3upN6/aMD/tQ42HlhBw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:40:52.185759Z","signed_message":"canonical_sha256_bytes"},"source_id":"1302.2158","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:055819459adfedb667f3da3f570507fb4c19d83b51566c38cdb955816e4731e8","sha256:66b834d4ebc7bc06ba60d35fad946104df9d244560a72c5c593e8cd73207008c"],"state_sha256":"7da2a5033211b4b8b84872df08abb0e616392823e1859579e304dba00ae17bcd"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jvod5kR7LMitj+CCQmbX5BUcwFDDLjCUbyHRtqcwBvyhNuwVETeZCtLen+KIKindlCLPtRZRD5EuoiVVGF85Bw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T03:03:11.664692Z","bundle_sha256":"338cf83663210b8ff325f5d24678a3d3b5df71374d60029db0c7bd4506d0fac3"}}