{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:KNR5MZGFIHUY3F7H2YNNPLXRNU","short_pith_number":"pith:KNR5MZGF","canonical_record":{"source":{"id":"1105.1023","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-05-05T09:41:59Z","cross_cats_sorted":[],"title_canon_sha256":"da325d1fa775fb2420f15ccb5118bb97854b7737ed5160b5d881965b8491b97f","abstract_canon_sha256":"f02efa066527c5e758d099084f71e3ac60be407691a8e25d56a5442a9301df04"},"schema_version":"1.0"},"canonical_sha256":"5363d664c541e98d97e7d61ad7aef16d1a15e5d160e1bf1e65cd23a83ceb2338","source":{"kind":"arxiv","id":"1105.1023","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1105.1023","created_at":"2026-05-18T03:46:18Z"},{"alias_kind":"arxiv_version","alias_value":"1105.1023v1","created_at":"2026-05-18T03:46:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1105.1023","created_at":"2026-05-18T03:46:18Z"},{"alias_kind":"pith_short_12","alias_value":"KNR5MZGFIHUY","created_at":"2026-05-18T12:26:32Z"},{"alias_kind":"pith_short_16","alias_value":"KNR5MZGFIHUY3F7H","created_at":"2026-05-18T12:26:32Z"},{"alias_kind":"pith_short_8","alias_value":"KNR5MZGF","created_at":"2026-05-18T12:26:32Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:KNR5MZGFIHUY3F7H2YNNPLXRNU","target":"record","payload":{"canonical_record":{"source":{"id":"1105.1023","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-05-05T09:41:59Z","cross_cats_sorted":[],"title_canon_sha256":"da325d1fa775fb2420f15ccb5118bb97854b7737ed5160b5d881965b8491b97f","abstract_canon_sha256":"f02efa066527c5e758d099084f71e3ac60be407691a8e25d56a5442a9301df04"},"schema_version":"1.0"},"canonical_sha256":"5363d664c541e98d97e7d61ad7aef16d1a15e5d160e1bf1e65cd23a83ceb2338","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:46:18.656328Z","signature_b64":"67gXrBVvJ+qCVWPy22Zj7/YYV8utaRKlwsJjHSsqz22chBQzfBSdwFGVSY5CwArG3iCk0X/likXRYwwxafvNCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5363d664c541e98d97e7d61ad7aef16d1a15e5d160e1bf1e65cd23a83ceb2338","last_reissued_at":"2026-05-18T03:46:18.655341Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:46:18.655341Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1105.1023","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:46:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wtmRMOlCjrc2kGZitPy+zSKrOeTSKoWVKlhnC9El7wedA1otzhcAhttMyAU9tr2h6IKVn5hs//4O2ngsukv5BA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T10:40:43.422841Z"},"content_sha256":"88ef166bb4d4b4cb49ba2855e2d55e7508ffbb5b6c1ed1927812e58d50ed14b1","schema_version":"1.0","event_id":"sha256:88ef166bb4d4b4cb49ba2855e2d55e7508ffbb5b6c1ed1927812e58d50ed14b1"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:KNR5MZGFIHUY3F7H2YNNPLXRNU","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Vertex coloring of plane graphs with nonrepetitive boundary paths","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"J\\'anos Bar\\'at, J\\'ulius Czap","submitted_at":"2011-05-05T09:41:59Z","abstract_excerpt":"A sequence $s_1,s_2,...,s_k,s_1,s_2,...,s_k$ is a repetition. A sequence $S$ is nonrepetitive, if no subsequence of consecutive terms of $S$ form a repetition. Let $G$ be a vertex colored graph. A path of $G$ is nonrepetitive, if the sequence of colors on its vertices is nonrepetitive. If $G$ is a plane graph, then a facial nonrepetitive vertex coloring of $G$ is a vertex coloring such that any facial path is nonrepetitive. Let $\\pi_f(G)$ denote the minimum number of colors of a facial nonrepetitive vertex coloring of $G$. Jendro\\vl and Harant posed a conjecture that $\\pi_f(G)$ can be bounded "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1105.1023","kind":"arxiv","version":1},"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":"2026-05-18T03:46:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"onP6sWD0jutezmByKfCZzTLdUdBJzO1A36a66Lk7R4FiYzREGSLEL16b0aTspm21JctdZNmq5a9t7GIawdZ+Dg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T10:40:43.423168Z"},"content_sha256":"8d169861f89ca7350ee9b1f6ed0ea7570fd7ae02af17f8d1505bef63dbc78198","schema_version":"1.0","event_id":"sha256:8d169861f89ca7350ee9b1f6ed0ea7570fd7ae02af17f8d1505bef63dbc78198"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/KNR5MZGFIHUY3F7H2YNNPLXRNU/bundle.json","state_url":"https://pith.science/pith/KNR5MZGFIHUY3F7H2YNNPLXRNU/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/KNR5MZGFIHUY3F7H2YNNPLXRNU/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":"2026-06-03T10:40:43Z","links":{"resolver":"https://pith.science/pith/KNR5MZGFIHUY3F7H2YNNPLXRNU","bundle":"https://pith.science/pith/KNR5MZGFIHUY3F7H2YNNPLXRNU/bundle.json","state":"https://pith.science/pith/KNR5MZGFIHUY3F7H2YNNPLXRNU/state.json","well_known_bundle":"https://pith.science/.well-known/pith/KNR5MZGFIHUY3F7H2YNNPLXRNU/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:KNR5MZGFIHUY3F7H2YNNPLXRNU","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":"f02efa066527c5e758d099084f71e3ac60be407691a8e25d56a5442a9301df04","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-05-05T09:41:59Z","title_canon_sha256":"da325d1fa775fb2420f15ccb5118bb97854b7737ed5160b5d881965b8491b97f"},"schema_version":"1.0","source":{"id":"1105.1023","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1105.1023","created_at":"2026-05-18T03:46:18Z"},{"alias_kind":"arxiv_version","alias_value":"1105.1023v1","created_at":"2026-05-18T03:46:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1105.1023","created_at":"2026-05-18T03:46:18Z"},{"alias_kind":"pith_short_12","alias_value":"KNR5MZGFIHUY","created_at":"2026-05-18T12:26:32Z"},{"alias_kind":"pith_short_16","alias_value":"KNR5MZGFIHUY3F7H","created_at":"2026-05-18T12:26:32Z"},{"alias_kind":"pith_short_8","alias_value":"KNR5MZGF","created_at":"2026-05-18T12:26:32Z"}],"graph_snapshots":[{"event_id":"sha256:8d169861f89ca7350ee9b1f6ed0ea7570fd7ae02af17f8d1505bef63dbc78198","target":"graph","created_at":"2026-05-18T03:46:18Z","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":"A sequence $s_1,s_2,...,s_k,s_1,s_2,...,s_k$ is a repetition. A sequence $S$ is nonrepetitive, if no subsequence of consecutive terms of $S$ form a repetition. Let $G$ be a vertex colored graph. A path of $G$ is nonrepetitive, if the sequence of colors on its vertices is nonrepetitive. If $G$ is a plane graph, then a facial nonrepetitive vertex coloring of $G$ is a vertex coloring such that any facial path is nonrepetitive. Let $\\pi_f(G)$ denote the minimum number of colors of a facial nonrepetitive vertex coloring of $G$. Jendro\\vl and Harant posed a conjecture that $\\pi_f(G)$ can be bounded ","authors_text":"J\\'anos Bar\\'at, J\\'ulius Czap","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-05-05T09:41:59Z","title":"Vertex coloring of plane graphs with nonrepetitive boundary paths"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1105.1023","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":"sha256:88ef166bb4d4b4cb49ba2855e2d55e7508ffbb5b6c1ed1927812e58d50ed14b1","target":"record","created_at":"2026-05-18T03:46:18Z","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":"f02efa066527c5e758d099084f71e3ac60be407691a8e25d56a5442a9301df04","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-05-05T09:41:59Z","title_canon_sha256":"da325d1fa775fb2420f15ccb5118bb97854b7737ed5160b5d881965b8491b97f"},"schema_version":"1.0","source":{"id":"1105.1023","kind":"arxiv","version":1}},"canonical_sha256":"5363d664c541e98d97e7d61ad7aef16d1a15e5d160e1bf1e65cd23a83ceb2338","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5363d664c541e98d97e7d61ad7aef16d1a15e5d160e1bf1e65cd23a83ceb2338","first_computed_at":"2026-05-18T03:46:18.655341Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:46:18.655341Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"67gXrBVvJ+qCVWPy22Zj7/YYV8utaRKlwsJjHSsqz22chBQzfBSdwFGVSY5CwArG3iCk0X/likXRYwwxafvNCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:46:18.656328Z","signed_message":"canonical_sha256_bytes"},"source_id":"1105.1023","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:88ef166bb4d4b4cb49ba2855e2d55e7508ffbb5b6c1ed1927812e58d50ed14b1","sha256:8d169861f89ca7350ee9b1f6ed0ea7570fd7ae02af17f8d1505bef63dbc78198"],"state_sha256":"9e184219562eddaa214141cbb02d8532ebd638e7441e903441710c9f334fc362"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ONfSfoH4Z4XzxMjmxKqEnbeta5Nr5GT3W4FvqCVPY8dwaljGSQ+e3Qc0RxDdljJf3ICZOt8XFEkJc/+DE1S1CQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T10:40:43.425328Z","bundle_sha256":"cccfb3d1274acbd96c58d0fb3335945ac4aead390c305eb4db99254b0dd216e8"}}