{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:KYA3HT4DHHMJ6FBJIJVIN7ZDEE","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":"a38442d3416402d54b44e3ac5585cf2926f4ce2a9bfeb639f159dfd6f8d923ee","cross_cats_sorted":["cs.DM"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2014-09-19T21:01:03Z","title_canon_sha256":"0ceaae1178fb357f58147698decd836ed6b6bcc2a5ad43a4fb965e407223d094"},"schema_version":"1.0","source":{"id":"1409.5816","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1409.5816","created_at":"2026-05-18T02:42:15Z"},{"alias_kind":"arxiv_version","alias_value":"1409.5816v1","created_at":"2026-05-18T02:42:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1409.5816","created_at":"2026-05-18T02:42:15Z"},{"alias_kind":"pith_short_12","alias_value":"KYA3HT4DHHMJ","created_at":"2026-05-18T12:28:35Z"},{"alias_kind":"pith_short_16","alias_value":"KYA3HT4DHHMJ6FBJ","created_at":"2026-05-18T12:28:35Z"},{"alias_kind":"pith_short_8","alias_value":"KYA3HT4D","created_at":"2026-05-18T12:28:35Z"}],"graph_snapshots":[{"event_id":"sha256:6b85a7e72266357a088e14553bf3c2999645e329a4f73db56c598be5ae442663","target":"graph","created_at":"2026-05-18T02:42:15Z","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":"In this paper, we prove that every planar 4-connected graph has a CZ-representation---a string representation using paths in a rectangular grid that contain at most one vertical segment. Furthermore, two paths representing vertices $u,v$ intersect precisely once whenever there is an edge between $u$ and $v$. The required size of the grid is $n \\times 2n$.","authors_text":"Martin Derka, Therese Biedl","cross_cats":["cs.DM"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2014-09-19T21:01:03Z","title":"1-String CZ-Representation of Planar Graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.5816","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:b85b37b692745f1a9f2970f2caf5e53b531e475dd9b00685d053be38d4e22eba","target":"record","created_at":"2026-05-18T02:42:15Z","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":"a38442d3416402d54b44e3ac5585cf2926f4ce2a9bfeb639f159dfd6f8d923ee","cross_cats_sorted":["cs.DM"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2014-09-19T21:01:03Z","title_canon_sha256":"0ceaae1178fb357f58147698decd836ed6b6bcc2a5ad43a4fb965e407223d094"},"schema_version":"1.0","source":{"id":"1409.5816","kind":"arxiv","version":1}},"canonical_sha256":"5601b3cf8339d89f1429426a86ff2321100eb0b76ca86446a185e8e82fc43ccc","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5601b3cf8339d89f1429426a86ff2321100eb0b76ca86446a185e8e82fc43ccc","first_computed_at":"2026-05-18T02:42:15.971718Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:42:15.971718Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"u9QypCkSIShhyyZdsb+a/r+VMul4+MV9zj9LR0dCn9S2SHyTzJtJWR/LYLsAQc/JP/CZ7PeUOLzxUI+ts0CfCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:42:15.972617Z","signed_message":"canonical_sha256_bytes"},"source_id":"1409.5816","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b85b37b692745f1a9f2970f2caf5e53b531e475dd9b00685d053be38d4e22eba","sha256:6b85a7e72266357a088e14553bf3c2999645e329a4f73db56c598be5ae442663"],"state_sha256":"a6efef4598a759ec622d86eeb80344230c4b788b0ae1f2c303a875da925bd53d"}