{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:SUTJLLJZDXTHTRKNUYSL26ACN5","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":"063a23bf3ffca4770807e01386d346691bdb71926d0d016cffe6db0c73cd6e19","cross_cats_sorted":["cs.DM"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-05-15T05:35:37Z","title_canon_sha256":"2d9918c40b1c555b187504d8bfd6495640cb69b83a3a5420613e7b8be62b80c1"},"schema_version":"1.0","source":{"id":"1505.03962","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1505.03962","created_at":"2026-05-18T01:18:25Z"},{"alias_kind":"arxiv_version","alias_value":"1505.03962v3","created_at":"2026-05-18T01:18:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1505.03962","created_at":"2026-05-18T01:18:25Z"},{"alias_kind":"pith_short_12","alias_value":"SUTJLLJZDXTH","created_at":"2026-05-18T12:29:42Z"},{"alias_kind":"pith_short_16","alias_value":"SUTJLLJZDXTHTRKN","created_at":"2026-05-18T12:29:42Z"},{"alias_kind":"pith_short_8","alias_value":"SUTJLLJZ","created_at":"2026-05-18T12:29:42Z"}],"graph_snapshots":[{"event_id":"sha256:640137ef6b5eeb2d8e4f3ba662a34f60d273bdfca37af3a40ae1ab2c249d11a1","target":"graph","created_at":"2026-05-18T01:18:25Z","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 show, without using the Four Color Theorem, that for each planar triangulation, the number of its proper vertex colorings by 4 colors is a determinant and thus can be calculated in a polynomial time. In particular, we can efficiently decide if the number is non-zero.","authors_text":"Martin Loebl","cross_cats":["cs.DM"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-05-15T05:35:37Z","title":"Deciding 4-colorability of planar triangulations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.03962","kind":"arxiv","version":3},"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":"sha256:703318bd41d5cb7283520cd1f48bb52910928115b3037cb6ba695640412142f8","target":"record","created_at":"2026-05-18T01:18:25Z","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":"063a23bf3ffca4770807e01386d346691bdb71926d0d016cffe6db0c73cd6e19","cross_cats_sorted":["cs.DM"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-05-15T05:35:37Z","title_canon_sha256":"2d9918c40b1c555b187504d8bfd6495640cb69b83a3a5420613e7b8be62b80c1"},"schema_version":"1.0","source":{"id":"1505.03962","kind":"arxiv","version":3}},"canonical_sha256":"952695ad391de679c54da624bd78026f45d0c0b608659462f89b57c9033ce1d3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"952695ad391de679c54da624bd78026f45d0c0b608659462f89b57c9033ce1d3","first_computed_at":"2026-05-18T01:18:25.477186Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:18:25.477186Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"4//mKJFvFRIru/eX13TnMPipdu56Ck4RoGCZDOB4hQslQfftX3Y+/mRbkDaVjsmDgxw8YB7xIPJD5PkIBLmFBg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:18:25.477687Z","signed_message":"canonical_sha256_bytes"},"source_id":"1505.03962","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:703318bd41d5cb7283520cd1f48bb52910928115b3037cb6ba695640412142f8","sha256:640137ef6b5eeb2d8e4f3ba662a34f60d273bdfca37af3a40ae1ab2c249d11a1"],"state_sha256":"608b81a6a4b5cade935b185691dab5db72315f0c37e83513af84f89170c2e342"}