{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:FJI5RJM6UQEL5AXUUNWMV3RQGE","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":"b52eee30c6bb48efcca3a71c5034df21b3c1ad2db819a8be5458a10f5e5fc781","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2023-11-06T14:28:33Z","title_canon_sha256":"82bc20e14dfcb25f00910307495c64e7cb945a07825d565077bb3224a082dc43"},"schema_version":"1.0","source":{"id":"2311.03132","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2311.03132","created_at":"2026-07-05T07:09:36Z"},{"alias_kind":"arxiv_version","alias_value":"2311.03132v1","created_at":"2026-07-05T07:09:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2311.03132","created_at":"2026-07-05T07:09:36Z"},{"alias_kind":"pith_short_12","alias_value":"FJI5RJM6UQEL","created_at":"2026-07-05T07:09:36Z"},{"alias_kind":"pith_short_16","alias_value":"FJI5RJM6UQEL5AXU","created_at":"2026-07-05T07:09:36Z"},{"alias_kind":"pith_short_8","alias_value":"FJI5RJM6","created_at":"2026-07-05T07:09:36Z"}],"graph_snapshots":[{"event_id":"sha256:4a14a8d7a4c45504f13b9da42e7a7a4992f320fbad4f721ae72499c27d8630ab","target":"graph","created_at":"2026-07-05T07:09:36Z","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/2311.03132/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We show that $\\limsup |E(G)|/|V(G)| = 2.5$ over all $4$-critical planar graphs $G$, answering a question of Gr\\\"unbaum from 1988.","authors_text":"Carl Feghali, Zden\\v{e}k Dvo\\v{r}\\'ak","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2023-11-06T14:28:33Z","title":"Solution to a problem of Gr\\\"unbaum on the edge density of $4$-critical planar graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2311.03132","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":"sha256:1b1dd099a2f1926bf5643aa388b8cbd5ced1ba028c487a22cb12729d785bbc79","target":"record","created_at":"2026-07-05T07:09:36Z","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":"b52eee30c6bb48efcca3a71c5034df21b3c1ad2db819a8be5458a10f5e5fc781","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2023-11-06T14:28:33Z","title_canon_sha256":"82bc20e14dfcb25f00910307495c64e7cb945a07825d565077bb3224a082dc43"},"schema_version":"1.0","source":{"id":"2311.03132","kind":"arxiv","version":1}},"canonical_sha256":"2a51d8a59ea408be82f4a36ccaee303120c2944d0fbeb3d20c261a4026fb38cc","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2a51d8a59ea408be82f4a36ccaee303120c2944d0fbeb3d20c261a4026fb38cc","first_computed_at":"2026-07-05T07:09:36.619189Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T07:09:36.619189Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"LwwFi6WnkVJwuKdkn/PLNgxoEDfLRGjHNrHZX9TeJR86QL2XZz3YsrY9GvkLNfOwSwg4pzjWEERYTdVz1x60AA==","signature_status":"signed_v1","signed_at":"2026-07-05T07:09:36.619600Z","signed_message":"canonical_sha256_bytes"},"source_id":"2311.03132","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1b1dd099a2f1926bf5643aa388b8cbd5ced1ba028c487a22cb12729d785bbc79","sha256:4a14a8d7a4c45504f13b9da42e7a7a4992f320fbad4f721ae72499c27d8630ab"],"state_sha256":"9312ca839e63cf83915a9204d358d6a7aae931b3dcc97e29fab0b4a299ecead3"}