{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:NEZTHTWYHINWGYKLWUNQ5QO6AK","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":"b01cf9d5a80f527745561c45c67d8384ace0c93e433531eedc683dc17958c492","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-02-15T16:03:37Z","title_canon_sha256":"fd3327cb0176a36170d9b4459e05c388e0c52fed044899c2bb244333b8085b23"},"schema_version":"1.0","source":{"id":"1602.04717","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1602.04717","created_at":"2026-05-18T01:20:49Z"},{"alias_kind":"arxiv_version","alias_value":"1602.04717v1","created_at":"2026-05-18T01:20:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1602.04717","created_at":"2026-05-18T01:20:49Z"},{"alias_kind":"pith_short_12","alias_value":"NEZTHTWYHINW","created_at":"2026-05-18T12:30:32Z"},{"alias_kind":"pith_short_16","alias_value":"NEZTHTWYHINWGYKL","created_at":"2026-05-18T12:30:32Z"},{"alias_kind":"pith_short_8","alias_value":"NEZTHTWY","created_at":"2026-05-18T12:30:32Z"}],"graph_snapshots":[{"event_id":"sha256:d2616a7a72b3f5666e81bafd6040f53ec7e4046cfe0af6bb7de2adac599e8ffa","target":"graph","created_at":"2026-05-18T01:20:49Z","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":"Thomassen proved that every planar graph $G$ on $n$ vertices has at least $2^{n/9}$ distinct $L$-colorings if $L$ is a 5-list-assignment for $G$ and at least $2^{n/10000}$ distinct $L$-colorings if $L$ is a 3-list-assignment for $G$ and $G$ has girth at least five. Postle and Thomas proved that if $G$ is a graph on $n$ vertices embedded on a surface $\\Sigma$ of genus $g$, then there exist constants $\\epsilon,c_g > 0$ such that if $G$ has an $L$-coloring, then $G$ has at least $c_g2^{\\epsilon n}$ distinct $L$-colorings if $L$ is a 5-list-assignment for $G$ or if $L$ is a 3-list-assignment for $","authors_text":"Luke Postle, Tom Kelly","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-02-15T16:03:37Z","title":"Exponentially Many 4-List-Colorings of Triangle-Free Graphs on Surfaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.04717","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":"sha256:42418a8f38ef7c10272d7f048ce9d9550e0a2adfa7676a2c059d17c2ab3b17d1","target":"record","created_at":"2026-05-18T01:20:49Z","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":"b01cf9d5a80f527745561c45c67d8384ace0c93e433531eedc683dc17958c492","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-02-15T16:03:37Z","title_canon_sha256":"fd3327cb0176a36170d9b4459e05c388e0c52fed044899c2bb244333b8085b23"},"schema_version":"1.0","source":{"id":"1602.04717","kind":"arxiv","version":1}},"canonical_sha256":"693333ced83a1b63614bb51b0ec1de0298eab7f8e87accddf74d6cdd840c3aac","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"693333ced83a1b63614bb51b0ec1de0298eab7f8e87accddf74d6cdd840c3aac","first_computed_at":"2026-05-18T01:20:49.346396Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:20:49.346396Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"hFO2Lxu5aBVCTx4d9uU9+EDY83XYLOOEfw1w5oFCB6I/SaqvsNJ8k1Ev8bgqWIOlrq49CAYwK/m93tK4X1K+Aw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:20:49.346831Z","signed_message":"canonical_sha256_bytes"},"source_id":"1602.04717","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:42418a8f38ef7c10272d7f048ce9d9550e0a2adfa7676a2c059d17c2ab3b17d1","sha256:d2616a7a72b3f5666e81bafd6040f53ec7e4046cfe0af6bb7de2adac599e8ffa"],"state_sha256":"57194f318838044a56861f92e3f170a20b32508a42ce2ee8721e056c0745d088"}