{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:YZGJ7EOPWX6Q3XILC7NB6KG2MU","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":"320e132ffd52fe6ed733b1c457d85a2f1d897e0abc01c86e630b5d7e3d0ed4a4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2018-08-27T05:40:01Z","title_canon_sha256":"1ce12a9c95e3f77807354b5fc1be3b22e280d56bd2ed5760f2264d6783cc853d"},"schema_version":"1.0","source":{"id":"1808.08691","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1808.08691","created_at":"2026-05-17T23:51:19Z"},{"alias_kind":"arxiv_version","alias_value":"1808.08691v2","created_at":"2026-05-17T23:51:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1808.08691","created_at":"2026-05-17T23:51:19Z"},{"alias_kind":"pith_short_12","alias_value":"YZGJ7EOPWX6Q","created_at":"2026-05-18T12:33:04Z"},{"alias_kind":"pith_short_16","alias_value":"YZGJ7EOPWX6Q3XIL","created_at":"2026-05-18T12:33:04Z"},{"alias_kind":"pith_short_8","alias_value":"YZGJ7EOP","created_at":"2026-05-18T12:33:04Z"}],"graph_snapshots":[{"event_id":"sha256:69c8208024dcf57e7c469423632e63abb59ade23f2f526155cd1e81f006069e1","target":"graph","created_at":"2026-05-17T23:51:19Z","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":"For a graph $H$ and integer $k \\geq 1$, two functions $f, g$ from $V(H)$ into $\\{1, \\dots, k\\}$ are adjacent if for all edges $uv$ of $H$, $f(u) \\neq g(v)$. The graph of all such functions is the exponential graph $K_k^H$. El-Zahar and Sauer proved that if $\\chi(H) \\geq 4$, then $K_3^H$ is 3-chromatic. Tardif showed that, implicit in their proof, is an algorithm for 3-coloring $K_3^H$ whose time complexity is polynomial in the size of $K_3^H$. Tardif then asked if there is an \"explicit\" algorithm for finding such a coloring: Essentially, given a function $f$ belonging to a 3-chromatic componen","authors_text":"Adrien Argento, Alantha Newman, Pierre Charbit","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2018-08-27T05:40:01Z","title":"Explicit 3-colorings for exponential graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1808.08691","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":"sha256:6f361c85575b2d1a8c62173b2bdc98ebcd64c8e6c58e994d6e782226d9ec0ee2","target":"record","created_at":"2026-05-17T23:51:19Z","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":"320e132ffd52fe6ed733b1c457d85a2f1d897e0abc01c86e630b5d7e3d0ed4a4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2018-08-27T05:40:01Z","title_canon_sha256":"1ce12a9c95e3f77807354b5fc1be3b22e280d56bd2ed5760f2264d6783cc853d"},"schema_version":"1.0","source":{"id":"1808.08691","kind":"arxiv","version":2}},"canonical_sha256":"c64c9f91cfb5fd0ddd0b17da1f28da651179a2aaefb3b81383b4a4ea96182451","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c64c9f91cfb5fd0ddd0b17da1f28da651179a2aaefb3b81383b4a4ea96182451","first_computed_at":"2026-05-17T23:51:19.576098Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:51:19.576098Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"o1RAGsO+Owa53Cl7IBo+bxkqvQnlcYGO4SqDdNv0wkHvLcTMhbcIl9RCFpwu2FoGYhGdcf6Ngx4GcEYMi5/eCg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:51:19.576599Z","signed_message":"canonical_sha256_bytes"},"source_id":"1808.08691","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6f361c85575b2d1a8c62173b2bdc98ebcd64c8e6c58e994d6e782226d9ec0ee2","sha256:69c8208024dcf57e7c469423632e63abb59ade23f2f526155cd1e81f006069e1"],"state_sha256":"22934fd35c2e582934b7f653ec62e65a2a45579b6c304900e279604f975bf528"}