{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:P7GZAKBK5QIN7LSUUEK4XJ4YPO","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":"89e3232f57bb439f2218b866038a3aa34db1caa070ba78b251daa5a2c967f403","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2022-01-10T20:28:48Z","title_canon_sha256":"1ea5d9e11e6410be42209edaeeec3cfb48794c0f4a87777aa9a071950d4a197f"},"schema_version":"1.0","source":{"id":"2201.03633","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2201.03633","created_at":"2026-07-05T03:47:31Z"},{"alias_kind":"arxiv_version","alias_value":"2201.03633v1","created_at":"2026-07-05T03:47:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2201.03633","created_at":"2026-07-05T03:47:31Z"},{"alias_kind":"pith_short_12","alias_value":"P7GZAKBK5QIN","created_at":"2026-07-05T03:47:31Z"},{"alias_kind":"pith_short_16","alias_value":"P7GZAKBK5QIN7LSU","created_at":"2026-07-05T03:47:31Z"},{"alias_kind":"pith_short_8","alias_value":"P7GZAKBK","created_at":"2026-07-05T03:47:31Z"}],"graph_snapshots":[{"event_id":"sha256:060b5a1c60e5bb2ab819d2e6b9f5b3f5c71ef4b0bc33c17d2ca186066e09beae","target":"graph","created_at":"2026-07-05T03:47:31Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2201.03633/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The vertex-edge marking game is played between two players on a graph, $G=(V,E)$, with one player marking vertices and the other marking edges. The players want to minimize/maximize, respectively, the number of marked edges incident to an unmarked vertex. The vertex-edge coloring number for $G$ is the maximum score achievable with perfect play. Bre\\v{s}ar et al., [4], give an upper bound of $5$ for the vertex-edge coloring number for finite planar graphs. It is not known whether the bound is tight. In this paper, in response to questions in [4], we show that the vertex-edge coloring number for","authors_text":"Adam Kraus, Cordell Hammon, Daniel Herden, Guanjie Huang, Isaac Echols, Jasmin Mohn, Jonathan Meddaugh, Jorge Marchena Menendez, Mark Sepanski, Nina Garcia-Montoya, Rafael Morales Jim\\'enez","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2022-01-10T20:28:48Z","title":"Vertex-edge marking score of certain triangular lattices"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2201.03633","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":"sha256:833e9cf910025679b1a48bacf32ea3d4d00ddb86ddf2e7746441e840cb87fa98","target":"record","created_at":"2026-07-05T03:47:31Z","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":"89e3232f57bb439f2218b866038a3aa34db1caa070ba78b251daa5a2c967f403","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2022-01-10T20:28:48Z","title_canon_sha256":"1ea5d9e11e6410be42209edaeeec3cfb48794c0f4a87777aa9a071950d4a197f"},"schema_version":"1.0","source":{"id":"2201.03633","kind":"arxiv","version":1}},"canonical_sha256":"7fcd90282aec10dfae54a115cba7987b8fbd2d9b2e1d9a2e8369b5e337ab52e4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7fcd90282aec10dfae54a115cba7987b8fbd2d9b2e1d9a2e8369b5e337ab52e4","first_computed_at":"2026-07-05T03:47:31.670982Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T03:47:31.670982Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"VGVaxJoHV1eFNwCaBZJXATccqFlQnIMx42wvCm5rcROv5SK2uUNiHkRlyDT5oVFexly9BwcKvC9o1PFEQikYAw==","signature_status":"signed_v1","signed_at":"2026-07-05T03:47:31.671413Z","signed_message":"canonical_sha256_bytes"},"source_id":"2201.03633","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:833e9cf910025679b1a48bacf32ea3d4d00ddb86ddf2e7746441e840cb87fa98","sha256:060b5a1c60e5bb2ab819d2e6b9f5b3f5c71ef4b0bc33c17d2ca186066e09beae"],"state_sha256":"4002ebabc02687aef80b0a2a5dce83cd6ba087e93cdbff2369340c8ad4ea468a"}