{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:IMY4HSF5NQ3WGSKCMCBTEJYNKK","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":"790d2338d1f18eab2f71c2abe4e8c5d174591039a26588b4dba4d89737f886b4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2014-04-03T15:44:54Z","title_canon_sha256":"80c78940cbfc84c41505c15c9d67452357d7363d15c4a18cdd80ce76ace69b0f"},"schema_version":"1.0","source":{"id":"1404.0977","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1404.0977","created_at":"2026-05-18T02:54:54Z"},{"alias_kind":"arxiv_version","alias_value":"1404.0977v1","created_at":"2026-05-18T02:54:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1404.0977","created_at":"2026-05-18T02:54:54Z"},{"alias_kind":"pith_short_12","alias_value":"IMY4HSF5NQ3W","created_at":"2026-05-18T12:28:33Z"},{"alias_kind":"pith_short_16","alias_value":"IMY4HSF5NQ3WGSKC","created_at":"2026-05-18T12:28:33Z"},{"alias_kind":"pith_short_8","alias_value":"IMY4HSF5","created_at":"2026-05-18T12:28:33Z"}],"graph_snapshots":[{"event_id":"sha256:d137cc716c4bff004348b161a26ea59e174f85a0a0d3fc83f2363677f3652c2d","target":"graph","created_at":"2026-05-18T02:54:54Z","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":"We show how to combine two techniques for efficiently computing shortest paths in directed planar graphs. The first is the linear-time shortest-path algorithm of Henzinger, Klein, Subramanian, and Rao [STOC'94]. The second is Fakcharoenphol and Rao's algorithm [FOCS'01] for emulating Dijkstra's algorithm on the dense distance graph (DDG). A DDG is defined for a decomposition of a planar graph $G$ into regions of at most $r$ vertices each, for some parameter $r < n$. The vertex set of the DDG is the set of $\\Theta(n/\\sqrt r)$ vertices of $G$ that belong to more than one region (boundary vertice","authors_text":"Oren Weimann, Shay Mozes, Yahav Nussbaum","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2014-04-03T15:44:54Z","title":"Faster Shortest Paths in Dense Distance Graphs, with Applications"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.0977","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":"sha256:68cfc0b848617fe335b68a68124e93ecbddba0c0da5b98e9320f89dd1bd56abc","target":"record","created_at":"2026-05-18T02:54:54Z","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":"790d2338d1f18eab2f71c2abe4e8c5d174591039a26588b4dba4d89737f886b4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2014-04-03T15:44:54Z","title_canon_sha256":"80c78940cbfc84c41505c15c9d67452357d7363d15c4a18cdd80ce76ace69b0f"},"schema_version":"1.0","source":{"id":"1404.0977","kind":"arxiv","version":1}},"canonical_sha256":"4331c3c8bd6c37634942608332270d52ba0a02860f0f7b8bd4c1b68cdf264616","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4331c3c8bd6c37634942608332270d52ba0a02860f0f7b8bd4c1b68cdf264616","first_computed_at":"2026-05-18T02:54:54.852244Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:54:54.852244Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"fYZ1dVy6vCPGtotpzoBoXUtV7PW5nVKsdUZDvojo4h9PUwnxiEe7EPkLvx7LCob7q5NFaekrB5BdJnLagOlgCw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:54:54.852788Z","signed_message":"canonical_sha256_bytes"},"source_id":"1404.0977","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:68cfc0b848617fe335b68a68124e93ecbddba0c0da5b98e9320f89dd1bd56abc","sha256:d137cc716c4bff004348b161a26ea59e174f85a0a0d3fc83f2363677f3652c2d"],"state_sha256":"e5ec171c916f918211f914b4753c9ba0f7c31d5fc8d46ee2f9f3c2ed1aeac3b5"}