{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:U4ECIUOKPOXV3UGHVZT2ZNXTSW","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":"28e9e00283188e63e0aa889c01e1fc0a7e0d3074efed12729dda2f63eb9f9ef7","cross_cats_sorted":["cs.CC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2011-05-24T14:04:00Z","title_canon_sha256":"cccb5da9953a9a83426e3818b39c4ffae58f233b833bf0419f3e0d2b30e45525"},"schema_version":"1.0","source":{"id":"1105.4770","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1105.4770","created_at":"2026-05-18T04:21:21Z"},{"alias_kind":"arxiv_version","alias_value":"1105.4770v1","created_at":"2026-05-18T04:21:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1105.4770","created_at":"2026-05-18T04:21:21Z"},{"alias_kind":"pith_short_12","alias_value":"U4ECIUOKPOXV","created_at":"2026-05-18T12:26:42Z"},{"alias_kind":"pith_short_16","alias_value":"U4ECIUOKPOXV3UGH","created_at":"2026-05-18T12:26:42Z"},{"alias_kind":"pith_short_8","alias_value":"U4ECIUOK","created_at":"2026-05-18T12:26:42Z"}],"graph_snapshots":[{"event_id":"sha256:fccffb8c989e715d6dff4f4d05349a463393b8b308059f765338d18290fabd7b","target":"graph","created_at":"2026-05-18T04:21:21Z","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":"Let G be an edge weighted undirected graph. For every pair of nodes consider the shortest cycle containing these nodes in G. The cycle diameter of G is the maximum length of a cycle in this set. Let H be a directed graph obtained by directing the edges of G. The cycle diameter of H is similarly defined except for that cycles are replaced by directed closed walks. Is there always an orientation H of G whose cycle diameter is bounded by a constant times the cycle diameter of G? We prove this property for planar graphs. These results have implications on the problem of approximating an orientatio","authors_text":"Nili Guttmann-Beck, Refael Hassin","cross_cats":["cs.CC"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2011-05-24T14:04:00Z","title":"Minimum diameter and cycle-diameter orientations on planar graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1105.4770","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":"sha256:35a9b4bb82ace6bac23457fb546b70fbbc9c832008222984250df0212640b8f7","target":"record","created_at":"2026-05-18T04:21:21Z","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":"28e9e00283188e63e0aa889c01e1fc0a7e0d3074efed12729dda2f63eb9f9ef7","cross_cats_sorted":["cs.CC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2011-05-24T14:04:00Z","title_canon_sha256":"cccb5da9953a9a83426e3818b39c4ffae58f233b833bf0419f3e0d2b30e45525"},"schema_version":"1.0","source":{"id":"1105.4770","kind":"arxiv","version":1}},"canonical_sha256":"a7082451ca7baf5dd0c7ae67acb6f395bb18a9be6730735393837e7539c66066","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a7082451ca7baf5dd0c7ae67acb6f395bb18a9be6730735393837e7539c66066","first_computed_at":"2026-05-18T04:21:21.823666Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:21:21.823666Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"fwjg6M88s7Uq/9wibWnas5CHi2HNfojJ/HYemhevP79RTL0TJ6BIYV4JBeowqspB+OW2GPj0cVZYVrrqquESBA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:21:21.824067Z","signed_message":"canonical_sha256_bytes"},"source_id":"1105.4770","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:35a9b4bb82ace6bac23457fb546b70fbbc9c832008222984250df0212640b8f7","sha256:fccffb8c989e715d6dff4f4d05349a463393b8b308059f765338d18290fabd7b"],"state_sha256":"fa8a3c74508edca258ec383dfdb9ec8fd5e9909432007da2045dea686deb4604"}