{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:2CHEV5PR3PHK5LJ5PZRI2E34PW","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":"6f743652004dc40bc3cbb0e6f9b808de6bfe5625a6e731649a298d62499d1eaf","cross_cats_sorted":["cs.DM"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-10-18T08:00:55Z","title_canon_sha256":"0a99d516d3b6b9d57508f417527f04618f60d1d2f256f5ae53b391503ec63320"},"schema_version":"1.0","source":{"id":"1610.05466","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1610.05466","created_at":"2026-05-18T00:53:15Z"},{"alias_kind":"arxiv_version","alias_value":"1610.05466v2","created_at":"2026-05-18T00:53:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.05466","created_at":"2026-05-18T00:53:15Z"},{"alias_kind":"pith_short_12","alias_value":"2CHEV5PR3PHK","created_at":"2026-05-18T12:29:52Z"},{"alias_kind":"pith_short_16","alias_value":"2CHEV5PR3PHK5LJ5","created_at":"2026-05-18T12:29:52Z"},{"alias_kind":"pith_short_8","alias_value":"2CHEV5PR","created_at":"2026-05-18T12:29:52Z"}],"graph_snapshots":[{"event_id":"sha256:3dec74fa88551ed92a1ad49a36256fc138ba388a49f70ab96f5696884826747b","target":"graph","created_at":"2026-05-18T00:53:15Z","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 note we determine the set of expansions such that a partial cube is planar if and only if it arises by a sequence of such expansions from a single vertex. This corrects a result of Peterin.","authors_text":"Kolja Knauer, R\\'emi Desgranges","cross_cats":["cs.DM"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-10-18T08:00:55Z","title":"A correction of a characterization of planar partial cubes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.05466","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:a0ff5e6c66fc48d2ba6c2d36c9c6a96f454f3689da3497c87430969e1c84ffbe","target":"record","created_at":"2026-05-18T00:53:15Z","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":"6f743652004dc40bc3cbb0e6f9b808de6bfe5625a6e731649a298d62499d1eaf","cross_cats_sorted":["cs.DM"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-10-18T08:00:55Z","title_canon_sha256":"0a99d516d3b6b9d57508f417527f04618f60d1d2f256f5ae53b391503ec63320"},"schema_version":"1.0","source":{"id":"1610.05466","kind":"arxiv","version":2}},"canonical_sha256":"d08e4af5f1dbceaead3d7e628d137c7d85ea300f9bc9c3ff38c5302959eb34ff","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d08e4af5f1dbceaead3d7e628d137c7d85ea300f9bc9c3ff38c5302959eb34ff","first_computed_at":"2026-05-18T00:53:15.435664Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:53:15.435664Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"RP8xN2MtitkHUpaUPJrg4QuUvkOINOtqDGMYVssJZrkXEZtIEEp+JmgoFBrcSmye9pLTZDgXNaLVshgkw8SsDg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:53:15.436100Z","signed_message":"canonical_sha256_bytes"},"source_id":"1610.05466","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a0ff5e6c66fc48d2ba6c2d36c9c6a96f454f3689da3497c87430969e1c84ffbe","sha256:3dec74fa88551ed92a1ad49a36256fc138ba388a49f70ab96f5696884826747b"],"state_sha256":"e0d6d29fd3a0fe21125cbd227c448328f340a8d43230882d60106d7afb141f1d"}