{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:NNFT7OJJTJWLM57JCGC46M6JVQ","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":"ffc025087c6a66ba9eab090935c9116ea7e23be21012cfe3970e539f9cc636c3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2013-03-24T15:12:27Z","title_canon_sha256":"2be4b0aaebac2a3ae4c2733f2d3fcc4207be14c227f33f4eb9ba13fc75628d8d"},"schema_version":"1.0","source":{"id":"1303.5958","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1303.5958","created_at":"2026-05-18T03:29:52Z"},{"alias_kind":"arxiv_version","alias_value":"1303.5958v1","created_at":"2026-05-18T03:29:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1303.5958","created_at":"2026-05-18T03:29:52Z"},{"alias_kind":"pith_short_12","alias_value":"NNFT7OJJTJWL","created_at":"2026-05-18T12:27:52Z"},{"alias_kind":"pith_short_16","alias_value":"NNFT7OJJTJWLM57J","created_at":"2026-05-18T12:27:52Z"},{"alias_kind":"pith_short_8","alias_value":"NNFT7OJJ","created_at":"2026-05-18T12:27:52Z"}],"graph_snapshots":[{"event_id":"sha256:0466b906c614823818160baf966eb665c6d8ec9ad7cdb39f75ce985a45e345be","target":"graph","created_at":"2026-05-18T03:29:52Z","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 present a new algorithm for computing motorcycle graphs that runs in O(n^(4/3+e)) time for any e>0, improving on all previously known algorithms. The main application of this result is to computing the straight skeleton of a polygon. It allows us to compute the straight skeleton of a non-degenerate polygon with h holes in O(n.sqrt(h+1)log^2(n)+n^(4/3+e)) expected time. If all input coordinates are O(log n)-bit rational numbers, we can compute the straight skeleton of a (possibly degenerate) polygon with h holes in O(n.sqrt(h+1)log^3(n)) expected time.\n  In particular, it means that we can c","authors_text":"Antoine Vigneron, Lie Yan","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2013-03-24T15:12:27Z","title":"A Faster Algorithm for Computing Motorcycle Graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1303.5958","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":"sha256:90e08366f9b63cd5740ab61bab8a247c7d7f1924ef55fa50a3ef75ca156e3e7f","target":"record","created_at":"2026-05-18T03:29:52Z","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":"ffc025087c6a66ba9eab090935c9116ea7e23be21012cfe3970e539f9cc636c3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2013-03-24T15:12:27Z","title_canon_sha256":"2be4b0aaebac2a3ae4c2733f2d3fcc4207be14c227f33f4eb9ba13fc75628d8d"},"schema_version":"1.0","source":{"id":"1303.5958","kind":"arxiv","version":1}},"canonical_sha256":"6b4b3fb9299a6cb677e91185cf33c9ac1326ae4916ecdd0088bc05211a7aa308","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6b4b3fb9299a6cb677e91185cf33c9ac1326ae4916ecdd0088bc05211a7aa308","first_computed_at":"2026-05-18T03:29:52.386080Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:29:52.386080Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"BFW/hU6pKqJ0YPcGZnLauqKL0xjulbcJPAgiax+ruGRqpaz6Gpi+/MqbT6J2FHh1XIOry+ns0VdoP8EuDKFrDA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:29:52.386615Z","signed_message":"canonical_sha256_bytes"},"source_id":"1303.5958","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:90e08366f9b63cd5740ab61bab8a247c7d7f1924ef55fa50a3ef75ca156e3e7f","sha256:0466b906c614823818160baf966eb665c6d8ec9ad7cdb39f75ce985a45e345be"],"state_sha256":"cdb70b514eb015cc49b69a08142032169d745c534d0a0156ca1ca84c85feeb0a"}