{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:RHD27LVV4VQYKLAHHC3KDGA35M","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":"3fd2975ae762885d9b5fd483dfb565906a228c723ed600031e7dba98036b0547","cross_cats_sorted":["cs.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2016-08-27T05:29:29Z","title_canon_sha256":"c48bac344563493d83b6ba8b64caf95c221d124450f368b852e007afd2ddcf6f"},"schema_version":"1.0","source":{"id":"1608.07662","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1608.07662","created_at":"2026-05-18T01:06:24Z"},{"alias_kind":"arxiv_version","alias_value":"1608.07662v2","created_at":"2026-05-18T01:06:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1608.07662","created_at":"2026-05-18T01:06:24Z"},{"alias_kind":"pith_short_12","alias_value":"RHD27LVV4VQY","created_at":"2026-05-18T12:30:41Z"},{"alias_kind":"pith_short_16","alias_value":"RHD27LVV4VQYKLAH","created_at":"2026-05-18T12:30:41Z"},{"alias_kind":"pith_short_8","alias_value":"RHD27LVV","created_at":"2026-05-18T12:30:41Z"}],"graph_snapshots":[{"event_id":"sha256:a820b99d2b06a3398622f13ed17ddc5abff6c5fcc6ca93bc23feaa5faf3e6cce","target":"graph","created_at":"2026-05-18T01:06:24Z","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 characterized some 1-plane embedding as the forbidden configuration such that a given 1-plane embedding of a graph is drawable in straight-lines if and only if it does not contain the configuration [C. Thomassen, Rectilinear drawings of graphs, J. Graph Theory, 10(3), 335-341, 1988].\n  In this paper, we characterize some 1-plane embedding as the forbidden configuration such that a given 1-plane embedding of a graph can be re-embedded into a straight-line drawable 1-plane embedding of the same graph if and only if it does not contain the configuration. Re-embedding of a 1-plane embedd","authors_text":"Hiroshi Nagamochi, Seok-Hee Hong","cross_cats":["cs.DS"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2016-08-27T05:29:29Z","title":"Re-embedding a 1-Plane Graph into a Straight-line Drawing in Linear Time"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.07662","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":"sha256:4a01fc22d414a2a4726544071dd9c7e28271509d12cd923fd8f936cd1515205e","target":"record","created_at":"2026-05-18T01:06:24Z","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":"3fd2975ae762885d9b5fd483dfb565906a228c723ed600031e7dba98036b0547","cross_cats_sorted":["cs.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2016-08-27T05:29:29Z","title_canon_sha256":"c48bac344563493d83b6ba8b64caf95c221d124450f368b852e007afd2ddcf6f"},"schema_version":"1.0","source":{"id":"1608.07662","kind":"arxiv","version":2}},"canonical_sha256":"89c7afaeb5e561852c0738b6a1981beb318bad53ffb34b6da185f22c429459b8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"89c7afaeb5e561852c0738b6a1981beb318bad53ffb34b6da185f22c429459b8","first_computed_at":"2026-05-18T01:06:24.031843Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:06:24.031843Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"53RTkhcfYmDWS/T33K3SCbSg8g5b/p8USQA6kUYwRGekyJT877sJD5nLLVyIWZUV9VzCSzrzR7RqSs9IFlIfAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:06:24.032283Z","signed_message":"canonical_sha256_bytes"},"source_id":"1608.07662","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4a01fc22d414a2a4726544071dd9c7e28271509d12cd923fd8f936cd1515205e","sha256:a820b99d2b06a3398622f13ed17ddc5abff6c5fcc6ca93bc23feaa5faf3e6cce"],"state_sha256":"0dfbd68de847d32c75bd3feb6c3ba9a37df3f29982bb5093cf38a606a015e0ec"}