{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:W3CUPJTNTCQGKANSVDD5EOTO3T","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":"8a2cd0b1c0558140d1bd336f7fd6177a0e7182b32fa69703d77b003be53f107a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2019-08-09T07:08:23Z","title_canon_sha256":"32ffc439ae43f0d756a53675916bd71031fba3c51069af508dcd5f3ba4b7dbc2"},"schema_version":"1.0","source":{"id":"1908.03341","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1908.03341","created_at":"2026-07-05T00:55:45Z"},{"alias_kind":"arxiv_version","alias_value":"1908.03341v2","created_at":"2026-07-05T00:55:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1908.03341","created_at":"2026-07-05T00:55:45Z"},{"alias_kind":"pith_short_12","alias_value":"W3CUPJTNTCQG","created_at":"2026-07-05T00:55:45Z"},{"alias_kind":"pith_short_16","alias_value":"W3CUPJTNTCQGKANS","created_at":"2026-07-05T00:55:45Z"},{"alias_kind":"pith_short_8","alias_value":"W3CUPJTN","created_at":"2026-07-05T00:55:45Z"}],"graph_snapshots":[{"event_id":"sha256:06730df3fa962102b4b887a9794cb6cc4a04960ae9b47a37265ac394b27bf69f","target":"graph","created_at":"2026-07-05T00:55:45Z","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/1908.03341/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"An \\emph{adjacency labeling scheme} for a given class of graphs is  an algorithm that for every graph $G$ from the class, assigns bit  strings (labels) to vertices of $G$ so that for any two vertices  $u,v$, whether $u$ and $v$ are adjacent can be determined by a fixed  procedure that examines only their labels. It is known that planar  graphs with $n$ vertices admit a labeling scheme with labels of bit length  $(2+o(1))\\log{n}$.  In this work we improve this bound by designing a labeling scheme  with labels of bit length $(\\frac{4}{3}+o(1))\\log{n}$.      In graph-theoretical terms, this impli","authors_text":"Cyril Gavoille (LaBRI), Marthe Bonamy (LaBRI), Michal Pilipczuk","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2019-08-09T07:08:23Z","title":"Shorter Labeling Schemes for Planar Graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.03341","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":"sha256:6927f5acbd0ce91772e3b5bb0f658661750ced21d36e4cd7d3ef2d5253296f3f","target":"record","created_at":"2026-07-05T00:55:45Z","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":"8a2cd0b1c0558140d1bd336f7fd6177a0e7182b32fa69703d77b003be53f107a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2019-08-09T07:08:23Z","title_canon_sha256":"32ffc439ae43f0d756a53675916bd71031fba3c51069af508dcd5f3ba4b7dbc2"},"schema_version":"1.0","source":{"id":"1908.03341","kind":"arxiv","version":2}},"canonical_sha256":"b6c547a66d98a06501b2a8c7d23a6edcd3f403b51abd81aea60cc839b3bc23a0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b6c547a66d98a06501b2a8c7d23a6edcd3f403b51abd81aea60cc839b3bc23a0","first_computed_at":"2026-07-05T00:55:45.355457Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T00:55:45.355457Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"D0Fm+CKPuNLmsfYw4TCUQvXBw1alLkEKSn8jbwUAIlrQ33Vvt/lPXs8M7KX7JrLMpU9qCGgl7BgNKP5l/EBtDg==","signature_status":"signed_v1","signed_at":"2026-07-05T00:55:45.355941Z","signed_message":"canonical_sha256_bytes"},"source_id":"1908.03341","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6927f5acbd0ce91772e3b5bb0f658661750ced21d36e4cd7d3ef2d5253296f3f","sha256:06730df3fa962102b4b887a9794cb6cc4a04960ae9b47a37265ac394b27bf69f"],"state_sha256":"b37015c919f1ada204819b98cf872953a4bb3995bd875ffddbbc287d5bcab195"}