{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:Z2IRFSRWIVC2XTDPYIUQSURHTD","short_pith_number":"pith:Z2IRFSRW","canonical_record":{"source":{"id":"1508.03437","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-08-14T08:25:53Z","cross_cats_sorted":[],"title_canon_sha256":"95491bf089b1244358b01a3f594022cc52153c67ac278c4f0151b08aa5d17433","abstract_canon_sha256":"d41821679b65c6aa281b8f8fb82f294bbe11c26536ef5bab47c20e82ee5a9bdc"},"schema_version":"1.0"},"canonical_sha256":"ce9112ca364545abcc6fc22909522798faf06d87104d0b8bfcda181c0d3b85a8","source":{"kind":"arxiv","id":"1508.03437","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1508.03437","created_at":"2026-05-18T01:02:56Z"},{"alias_kind":"arxiv_version","alias_value":"1508.03437v2","created_at":"2026-05-18T01:02:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1508.03437","created_at":"2026-05-18T01:02:56Z"},{"alias_kind":"pith_short_12","alias_value":"Z2IRFSRWIVC2","created_at":"2026-05-18T12:29:52Z"},{"alias_kind":"pith_short_16","alias_value":"Z2IRFSRWIVC2XTDP","created_at":"2026-05-18T12:29:52Z"},{"alias_kind":"pith_short_8","alias_value":"Z2IRFSRW","created_at":"2026-05-18T12:29:52Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:Z2IRFSRWIVC2XTDPYIUQSURHTD","target":"record","payload":{"canonical_record":{"source":{"id":"1508.03437","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-08-14T08:25:53Z","cross_cats_sorted":[],"title_canon_sha256":"95491bf089b1244358b01a3f594022cc52153c67ac278c4f0151b08aa5d17433","abstract_canon_sha256":"d41821679b65c6aa281b8f8fb82f294bbe11c26536ef5bab47c20e82ee5a9bdc"},"schema_version":"1.0"},"canonical_sha256":"ce9112ca364545abcc6fc22909522798faf06d87104d0b8bfcda181c0d3b85a8","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:02:56.896297Z","signature_b64":"ZgibY9HNFAJZ8qrRezT7E8KtH4U5tIJsILerSrr09Un4UOUmIaPjt2zMQM0WmFS/qQJUEVJYv5g4hJ94810kBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ce9112ca364545abcc6fc22909522798faf06d87104d0b8bfcda181c0d3b85a8","last_reissued_at":"2026-05-18T01:02:56.895807Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:02:56.895807Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1508.03437","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":"2026-05-18T01:02:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gxKDDbKnCoSM+akcpFqeT/jpJPVW7yz3aGZUDC5HKNPDwwz9MP03vK/AyGT54fsELTMaJFoeiJQ1L+IcuExNCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T21:54:17.599434Z"},"content_sha256":"981f2d2cee5413cd540e8e8411e6f1eb4aef6bd6256f0ea765357f4a03e0e8ea","schema_version":"1.0","event_id":"sha256:981f2d2cee5413cd540e8e8411e6f1eb4aef6bd6256f0ea765357f4a03e0e8ea"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:Z2IRFSRWIVC2XTDPYIUQSURHTD","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Correspondence coloring and its application to list-coloring planar graphs without cycles of lengths 4 to 8","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Luke Postle, Zdenek Dvorak","submitted_at":"2015-08-14T08:25:53Z","abstract_excerpt":"We introduce a new variant of graph coloring called correspondence coloring which generalizes list coloring and allows for reductions previously only possible for ordinary coloring. Using this tool, we prove that excluding cycles of lengths 4 to 8 is sufficient to guarantee 3-choosability of a planar graph, thus answering a question of Borodin."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.03437","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":"2026-05-18T01:02:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+6iwaySFm1GHS/F17KjlkIZ9RabG2NHqhl9g6HdRHPTpC/p7SvFY5gke9mGMlnjIaZ9RoMOcm5fu986atVrgAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T21:54:17.600074Z"},"content_sha256":"eac02ab00bceacf1fc45f562677be4135c2b5706d550f11a7811f20b5a4b3644","schema_version":"1.0","event_id":"sha256:eac02ab00bceacf1fc45f562677be4135c2b5706d550f11a7811f20b5a4b3644"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/Z2IRFSRWIVC2XTDPYIUQSURHTD/bundle.json","state_url":"https://pith.science/pith/Z2IRFSRWIVC2XTDPYIUQSURHTD/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/Z2IRFSRWIVC2XTDPYIUQSURHTD/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":"2026-05-25T21:54:17Z","links":{"resolver":"https://pith.science/pith/Z2IRFSRWIVC2XTDPYIUQSURHTD","bundle":"https://pith.science/pith/Z2IRFSRWIVC2XTDPYIUQSURHTD/bundle.json","state":"https://pith.science/pith/Z2IRFSRWIVC2XTDPYIUQSURHTD/state.json","well_known_bundle":"https://pith.science/.well-known/pith/Z2IRFSRWIVC2XTDPYIUQSURHTD/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:Z2IRFSRWIVC2XTDPYIUQSURHTD","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":"d41821679b65c6aa281b8f8fb82f294bbe11c26536ef5bab47c20e82ee5a9bdc","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-08-14T08:25:53Z","title_canon_sha256":"95491bf089b1244358b01a3f594022cc52153c67ac278c4f0151b08aa5d17433"},"schema_version":"1.0","source":{"id":"1508.03437","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1508.03437","created_at":"2026-05-18T01:02:56Z"},{"alias_kind":"arxiv_version","alias_value":"1508.03437v2","created_at":"2026-05-18T01:02:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1508.03437","created_at":"2026-05-18T01:02:56Z"},{"alias_kind":"pith_short_12","alias_value":"Z2IRFSRWIVC2","created_at":"2026-05-18T12:29:52Z"},{"alias_kind":"pith_short_16","alias_value":"Z2IRFSRWIVC2XTDP","created_at":"2026-05-18T12:29:52Z"},{"alias_kind":"pith_short_8","alias_value":"Z2IRFSRW","created_at":"2026-05-18T12:29:52Z"}],"graph_snapshots":[{"event_id":"sha256:eac02ab00bceacf1fc45f562677be4135c2b5706d550f11a7811f20b5a4b3644","target":"graph","created_at":"2026-05-18T01:02:56Z","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 introduce a new variant of graph coloring called correspondence coloring which generalizes list coloring and allows for reductions previously only possible for ordinary coloring. Using this tool, we prove that excluding cycles of lengths 4 to 8 is sufficient to guarantee 3-choosability of a planar graph, thus answering a question of Borodin.","authors_text":"Luke Postle, Zdenek Dvorak","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-08-14T08:25:53Z","title":"Correspondence coloring and its application to list-coloring planar graphs without cycles of lengths 4 to 8"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.03437","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":"sha256:981f2d2cee5413cd540e8e8411e6f1eb4aef6bd6256f0ea765357f4a03e0e8ea","target":"record","created_at":"2026-05-18T01:02:56Z","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":"d41821679b65c6aa281b8f8fb82f294bbe11c26536ef5bab47c20e82ee5a9bdc","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-08-14T08:25:53Z","title_canon_sha256":"95491bf089b1244358b01a3f594022cc52153c67ac278c4f0151b08aa5d17433"},"schema_version":"1.0","source":{"id":"1508.03437","kind":"arxiv","version":2}},"canonical_sha256":"ce9112ca364545abcc6fc22909522798faf06d87104d0b8bfcda181c0d3b85a8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ce9112ca364545abcc6fc22909522798faf06d87104d0b8bfcda181c0d3b85a8","first_computed_at":"2026-05-18T01:02:56.895807Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:02:56.895807Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ZgibY9HNFAJZ8qrRezT7E8KtH4U5tIJsILerSrr09Un4UOUmIaPjt2zMQM0WmFS/qQJUEVJYv5g4hJ94810kBw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:02:56.896297Z","signed_message":"canonical_sha256_bytes"},"source_id":"1508.03437","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:981f2d2cee5413cd540e8e8411e6f1eb4aef6bd6256f0ea765357f4a03e0e8ea","sha256:eac02ab00bceacf1fc45f562677be4135c2b5706d550f11a7811f20b5a4b3644"],"state_sha256":"f2def438bb42d4ab0f47dd9ac7735a6732762ae9b8ba637fb74fa4f0cc6f33cd"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"e0+gyP85FeCRZBbTJwQRrGwalmkmSPpyEDcR7ysecWou/DYAXY1tpQ52OYeZJBybJXJzBpPQ3hVvQoEWTRAGBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-25T21:54:17.603025Z","bundle_sha256":"a4414faec3ea8f9f467a607e44fc5ca2bb6c56fa91cee33097e58835a35f3b26"}}