{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2007:Z75CAUY6B7ZVDBXHVCZ4VSULDR","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":"5cdb0f1ef6f59759215f15e7281461855efde9b9b3f5e175134c0ec516ca2fe7","cross_cats_sorted":["math.MG"],"license":"","primary_cat":"cs.CG","submitted_at":"2007-02-16T06:00:08Z","title_canon_sha256":"ef070a8557d4876d9e1ceca84b6c1f9be674ddd1d91864126d39b7e7fc332288"},"schema_version":"1.0","source":{"id":"cs/0702090","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"cs/0702090","created_at":"2026-05-18T04:41:53Z"},{"alias_kind":"arxiv_version","alias_value":"cs/0702090v2","created_at":"2026-05-18T04:41:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.cs/0702090","created_at":"2026-05-18T04:41:53Z"},{"alias_kind":"pith_short_12","alias_value":"Z75CAUY6B7ZV","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_16","alias_value":"Z75CAUY6B7ZVDBXH","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_8","alias_value":"Z75CAUY6","created_at":"2026-05-18T12:25:56Z"}],"graph_snapshots":[{"event_id":"sha256:05f1a364fa1207ce0ea840e03b659f84141ceadd5b2803f95edd4ac26076413d","target":"graph","created_at":"2026-05-18T04:41:53Z","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":"The aperture angle alpha(x, Q) of a point x not in Q in the plane with respect to a convex polygon Q is the angle of the smallest cone with apex x that contains Q. The aperture angle approximation error of a compact convex set C in the plane with respect to an inscribed convex polygon Q of C is the minimum aperture angle of any x in C Q with respect to Q. We show that for any compact convex set C in the plane and any k > 2, there is an inscribed convex k-gon Q of C with aperture angle approximation error (1 - 2/(k+1)) pi. This bound is optimal, and settles a conjecture by Fekete from the early","authors_text":"Hee-Kap Ahn, Joachim Gudmundsson, Otfried Cheong, Sang Won Bae","cross_cats":["math.MG"],"headline":"","license":"","primary_cat":"cs.CG","submitted_at":"2007-02-16T06:00:08Z","title":"Aperture-Angle and Hausdorff-Approximation of Convex Figures"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"cs/0702090","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":"sha256:6a406f18e28e5a2d053403ee8296030b45a951d771324b2e91692be83682e0c7","target":"record","created_at":"2026-05-18T04:41:53Z","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":"5cdb0f1ef6f59759215f15e7281461855efde9b9b3f5e175134c0ec516ca2fe7","cross_cats_sorted":["math.MG"],"license":"","primary_cat":"cs.CG","submitted_at":"2007-02-16T06:00:08Z","title_canon_sha256":"ef070a8557d4876d9e1ceca84b6c1f9be674ddd1d91864126d39b7e7fc332288"},"schema_version":"1.0","source":{"id":"cs/0702090","kind":"arxiv","version":2}},"canonical_sha256":"cffa20531e0ff35186e7a8b3caca8b1c445c9981e19c086dfc3b0edfd23ca744","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"cffa20531e0ff35186e7a8b3caca8b1c445c9981e19c086dfc3b0edfd23ca744","first_computed_at":"2026-05-18T04:41:53.072659Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:41:53.072659Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ubR4Yp/sJfxIwbwj6rgpTEYFz4jnrZw7hqXfV71AnGUi6EIJvJItt7TcwmUdE3s734kP1xZc7yxC+SZb/qFEDg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:41:53.073088Z","signed_message":"canonical_sha256_bytes"},"source_id":"cs/0702090","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6a406f18e28e5a2d053403ee8296030b45a951d771324b2e91692be83682e0c7","sha256:05f1a364fa1207ce0ea840e03b659f84141ceadd5b2803f95edd4ac26076413d"],"state_sha256":"e2a75d18ab652c69d2c1a728a16d594ca35269bb2111620db81cd19a1d7a1f97"}