{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:IMMWRE6TMWCKK5YYVOCU63HVQG","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":"e7290f18ece5d63573bf45fc8d8d7fbaf2ac61670e2c67fd017829ddfa2d93e4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-06-03T15:59:26Z","title_canon_sha256":"fc78fdce201b2d6151123c1405e9d422aff43e203cc4fba365e5b030683512a8"},"schema_version":"1.0","source":{"id":"1706.00970","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1706.00970","created_at":"2026-05-18T00:43:07Z"},{"alias_kind":"arxiv_version","alias_value":"1706.00970v1","created_at":"2026-05-18T00:43:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1706.00970","created_at":"2026-05-18T00:43:07Z"},{"alias_kind":"pith_short_12","alias_value":"IMMWRE6TMWCK","created_at":"2026-05-18T12:31:21Z"},{"alias_kind":"pith_short_16","alias_value":"IMMWRE6TMWCKK5YY","created_at":"2026-05-18T12:31:21Z"},{"alias_kind":"pith_short_8","alias_value":"IMMWRE6T","created_at":"2026-05-18T12:31:21Z"}],"graph_snapshots":[{"event_id":"sha256:6e904bb4bdba8e7bac29d5930e8edd852dbc5ecb8d4b6da0e1418abc49a9fe7f","target":"graph","created_at":"2026-05-18T00:43:07Z","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":"Felsner introduced a cycle reversal, namely the `flip' reversal, for \\alpha-orientations (i.e., each vertex admits a prescribed out-degree) of a graph G embedded on the plane and further proved that the set of all the \\alpha-orientations of G carries a distributive lattice with respect to the flip reversals. In this paper, we give an explicit formula for the minimum number of flips needed to transform one \\alpha-orientation into another for graphs embedded on the plane or sphere, respectively.","authors_text":"Fuji Zhang, Jianguo Qian, Weijuan Zhang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-06-03T15:59:26Z","title":"Flip-distance between \\alpha-orientations of graphs embedded on plane and sphere"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.00970","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:bf0e00cac881262f7fce3f8837a0d9f7f5024612e9b4c6785c8f3579e9e46123","target":"record","created_at":"2026-05-18T00:43:07Z","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":"e7290f18ece5d63573bf45fc8d8d7fbaf2ac61670e2c67fd017829ddfa2d93e4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-06-03T15:59:26Z","title_canon_sha256":"fc78fdce201b2d6151123c1405e9d422aff43e203cc4fba365e5b030683512a8"},"schema_version":"1.0","source":{"id":"1706.00970","kind":"arxiv","version":1}},"canonical_sha256":"43196893d36584a57718ab854f6cf581907b84063710f6bdb5d60375bee1183e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"43196893d36584a57718ab854f6cf581907b84063710f6bdb5d60375bee1183e","first_computed_at":"2026-05-18T00:43:07.202305Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:43:07.202305Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ANNDan5wI8OZSa4cR9tEXz3cQ6/ImKhI8kxOv/5sRPhtyjUrBVgAqjSLDIlqAWRDGBxssF9tiwkq4B0CgGZBDg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:43:07.203017Z","signed_message":"canonical_sha256_bytes"},"source_id":"1706.00970","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bf0e00cac881262f7fce3f8837a0d9f7f5024612e9b4c6785c8f3579e9e46123","sha256:6e904bb4bdba8e7bac29d5930e8edd852dbc5ecb8d4b6da0e1418abc49a9fe7f"],"state_sha256":"92ad6549ebe1dd893f30d496602754997c78cf7108c4142a07633823f42becd0"}