{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:IR6KPFUBYZAPY2APZ7PTM6GRHT","short_pith_number":"pith:IR6KPFUB","canonical_record":{"source":{"id":"1209.0366","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-09-03T14:42:43Z","cross_cats_sorted":["cs.DM"],"title_canon_sha256":"0345a85967bd4115d9037902532e8d3582b5d1ca3fb7da0f2cf08de00c8c00e9","abstract_canon_sha256":"2199d68c7f90b97213f7f67e85c51d8c18d7ed96aaa5d4ca3ede912e412cb69d"},"schema_version":"1.0"},"canonical_sha256":"447ca79681c640fc680fcfdf3678d13ce592d17d41cb26d4e36cbdc8e6d6ef40","source":{"kind":"arxiv","id":"1209.0366","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1209.0366","created_at":"2026-05-18T00:54:58Z"},{"alias_kind":"arxiv_version","alias_value":"1209.0366v2","created_at":"2026-05-18T00:54:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1209.0366","created_at":"2026-05-18T00:54:58Z"},{"alias_kind":"pith_short_12","alias_value":"IR6KPFUBYZAP","created_at":"2026-05-18T12:27:09Z"},{"alias_kind":"pith_short_16","alias_value":"IR6KPFUBYZAPY2AP","created_at":"2026-05-18T12:27:09Z"},{"alias_kind":"pith_short_8","alias_value":"IR6KPFUB","created_at":"2026-05-18T12:27:09Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:IR6KPFUBYZAPY2APZ7PTM6GRHT","target":"record","payload":{"canonical_record":{"source":{"id":"1209.0366","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-09-03T14:42:43Z","cross_cats_sorted":["cs.DM"],"title_canon_sha256":"0345a85967bd4115d9037902532e8d3582b5d1ca3fb7da0f2cf08de00c8c00e9","abstract_canon_sha256":"2199d68c7f90b97213f7f67e85c51d8c18d7ed96aaa5d4ca3ede912e412cb69d"},"schema_version":"1.0"},"canonical_sha256":"447ca79681c640fc680fcfdf3678d13ce592d17d41cb26d4e36cbdc8e6d6ef40","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:54:58.464801Z","signature_b64":"uaLzelShah3FafukVfqyoWdDtOTCOdQadEzzmyaOGWPC64fakGD2Gq4eHHVblaPDSBv5IMZ+w68EmmtORByQCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"447ca79681c640fc680fcfdf3678d13ce592d17d41cb26d4e36cbdc8e6d6ef40","last_reissued_at":"2026-05-18T00:54:58.464163Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:54:58.464163Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1209.0366","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:54:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0lS6FdYJ+PMnmBaPLPxnOqfmtSHSjAIBcEh6dmIWJBR6D3vZ7deWcEo3UhKpIowfujGZYqVI7SoGGW3TJlasDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T19:15:26.344083Z"},"content_sha256":"60b6c83c52963bf3bc74d256ea89ada630c780f687efd3fe2726d3fb823d7255","schema_version":"1.0","event_id":"sha256:60b6c83c52963bf3bc74d256ea89ada630c780f687efd3fe2726d3fb823d7255"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:IR6KPFUBYZAPY2APZ7PTM6GRHT","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"5-list-coloring planar graphs with distant precolored vertices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM"],"primary_cat":"math.CO","authors_text":"Bernard Lidicky, Bojan Mohar, Luke Postle, Zdenek Dvorak","submitted_at":"2012-09-03T14:42:43Z","abstract_excerpt":"We answer positively the question of Albertson asking whether every planar graph can be $5$-list-colored even if it contains precolored vertices, as long as they are sufficiently far apart from each other. In order to prove this claim, we also give bounds on the sizes of graphs critical with respect to 5-list coloring. In particular, if G is a planar graph, H is a connected subgraph of G and L is an assignment of lists of colors to the vertices of G such that |L(v)| >= 5 for every v in V(G)-V(H) and G is not L-colorable, then G contains a subgraph with O(|H|^2) vertices that is not L-colorable"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1209.0366","kind":"arxiv","version":2},"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":"2026-05-18T00:54:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"CQUUmcMhqvUwtz6adeA7Qj3W3kDQCw0iQmIW8VgfS9WRJA90R4IZf6nsgniFyurTpLWLgw8fy49JVeXINYR7CA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T19:15:26.344713Z"},"content_sha256":"fffc358800f05ebd303ec97f58976042acd7adc5104c368fce5ea2b697b5874b","schema_version":"1.0","event_id":"sha256:fffc358800f05ebd303ec97f58976042acd7adc5104c368fce5ea2b697b5874b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/IR6KPFUBYZAPY2APZ7PTM6GRHT/bundle.json","state_url":"https://pith.science/pith/IR6KPFUBYZAPY2APZ7PTM6GRHT/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/IR6KPFUBYZAPY2APZ7PTM6GRHT/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":"2026-05-25T19:15:26Z","links":{"resolver":"https://pith.science/pith/IR6KPFUBYZAPY2APZ7PTM6GRHT","bundle":"https://pith.science/pith/IR6KPFUBYZAPY2APZ7PTM6GRHT/bundle.json","state":"https://pith.science/pith/IR6KPFUBYZAPY2APZ7PTM6GRHT/state.json","well_known_bundle":"https://pith.science/.well-known/pith/IR6KPFUBYZAPY2APZ7PTM6GRHT/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:IR6KPFUBYZAPY2APZ7PTM6GRHT","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":"2199d68c7f90b97213f7f67e85c51d8c18d7ed96aaa5d4ca3ede912e412cb69d","cross_cats_sorted":["cs.DM"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-09-03T14:42:43Z","title_canon_sha256":"0345a85967bd4115d9037902532e8d3582b5d1ca3fb7da0f2cf08de00c8c00e9"},"schema_version":"1.0","source":{"id":"1209.0366","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1209.0366","created_at":"2026-05-18T00:54:58Z"},{"alias_kind":"arxiv_version","alias_value":"1209.0366v2","created_at":"2026-05-18T00:54:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1209.0366","created_at":"2026-05-18T00:54:58Z"},{"alias_kind":"pith_short_12","alias_value":"IR6KPFUBYZAP","created_at":"2026-05-18T12:27:09Z"},{"alias_kind":"pith_short_16","alias_value":"IR6KPFUBYZAPY2AP","created_at":"2026-05-18T12:27:09Z"},{"alias_kind":"pith_short_8","alias_value":"IR6KPFUB","created_at":"2026-05-18T12:27:09Z"}],"graph_snapshots":[{"event_id":"sha256:fffc358800f05ebd303ec97f58976042acd7adc5104c368fce5ea2b697b5874b","target":"graph","created_at":"2026-05-18T00:54:58Z","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 answer positively the question of Albertson asking whether every planar graph can be $5$-list-colored even if it contains precolored vertices, as long as they are sufficiently far apart from each other. In order to prove this claim, we also give bounds on the sizes of graphs critical with respect to 5-list coloring. In particular, if G is a planar graph, H is a connected subgraph of G and L is an assignment of lists of colors to the vertices of G such that |L(v)| >= 5 for every v in V(G)-V(H) and G is not L-colorable, then G contains a subgraph with O(|H|^2) vertices that is not L-colorable","authors_text":"Bernard Lidicky, Bojan Mohar, Luke Postle, Zdenek Dvorak","cross_cats":["cs.DM"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-09-03T14:42:43Z","title":"5-list-coloring planar graphs with distant precolored vertices"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1209.0366","kind":"arxiv","version":2},"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":"sha256:60b6c83c52963bf3bc74d256ea89ada630c780f687efd3fe2726d3fb823d7255","target":"record","created_at":"2026-05-18T00:54:58Z","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":"2199d68c7f90b97213f7f67e85c51d8c18d7ed96aaa5d4ca3ede912e412cb69d","cross_cats_sorted":["cs.DM"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-09-03T14:42:43Z","title_canon_sha256":"0345a85967bd4115d9037902532e8d3582b5d1ca3fb7da0f2cf08de00c8c00e9"},"schema_version":"1.0","source":{"id":"1209.0366","kind":"arxiv","version":2}},"canonical_sha256":"447ca79681c640fc680fcfdf3678d13ce592d17d41cb26d4e36cbdc8e6d6ef40","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"447ca79681c640fc680fcfdf3678d13ce592d17d41cb26d4e36cbdc8e6d6ef40","first_computed_at":"2026-05-18T00:54:58.464163Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:54:58.464163Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"uaLzelShah3FafukVfqyoWdDtOTCOdQadEzzmyaOGWPC64fakGD2Gq4eHHVblaPDSBv5IMZ+w68EmmtORByQCA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:54:58.464801Z","signed_message":"canonical_sha256_bytes"},"source_id":"1209.0366","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:60b6c83c52963bf3bc74d256ea89ada630c780f687efd3fe2726d3fb823d7255","sha256:fffc358800f05ebd303ec97f58976042acd7adc5104c368fce5ea2b697b5874b"],"state_sha256":"cc11da7dff67cd0ca206a5cf649a201fecb8fb75a7323caa6c56a7fde258080f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hYisSKTC2Lj2D0pej5bqHkp/90wmVZXO5oP9BisBw7Gs24f328nC/1AjrARBxuEDXYw5wQ5pOmCJWu3hXoEABg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-25T19:15:26.348656Z","bundle_sha256":"3fe5299e0c9386ceaa2e079199800d8afdfb8acbb400cf9df58cf70f575e8be8"}}