{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:6IJVUGX4F6LPN5I7GRTHMWZB3X","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":"0441200aacd4548d9f18cf3afc74d60f2cf69b0627a0e06c1e5b23453e5bfef5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2018-02-08T11:04:02Z","title_canon_sha256":"d46edc5f52fa48dd7f94d93c38a55b2452ee1048f887523e0cc23f770289f2bf"},"schema_version":"1.0","source":{"id":"1802.02808","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1802.02808","created_at":"2026-05-17T23:41:13Z"},{"alias_kind":"arxiv_version","alias_value":"1802.02808v1","created_at":"2026-05-17T23:41:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1802.02808","created_at":"2026-05-17T23:41:13Z"},{"alias_kind":"pith_short_12","alias_value":"6IJVUGX4F6LP","created_at":"2026-05-18T12:32:08Z"},{"alias_kind":"pith_short_16","alias_value":"6IJVUGX4F6LPN5I7","created_at":"2026-05-18T12:32:08Z"},{"alias_kind":"pith_short_8","alias_value":"6IJVUGX4","created_at":"2026-05-18T12:32:08Z"}],"graph_snapshots":[{"event_id":"sha256:b280c680c6078ce01e8c34cafb5e34a89141609e6f7c8ea21f23cf6cf0563a7b","target":"graph","created_at":"2026-05-17T23:41:13Z","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":"In this paper we prove asymptotic upper bounds on the variance of the number of vertices and missed area of inscribed random disc-polygons in smooth convex discs whose boundary is $C^2_+$. We also consider a circumscribed variant of this probability model in which the convex disc is approximated by the intersection of random circles.","authors_text":"Ferenc Fodor, Viktor V\\'igh","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2018-02-08T11:04:02Z","title":"Variance estimates for random disc-polygons in smooth convex discs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.02808","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:f10545c5a3d0b0363d215708c7253262c923e3522d1b98b06747daa5ff6107f7","target":"record","created_at":"2026-05-17T23:41:13Z","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":"0441200aacd4548d9f18cf3afc74d60f2cf69b0627a0e06c1e5b23453e5bfef5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2018-02-08T11:04:02Z","title_canon_sha256":"d46edc5f52fa48dd7f94d93c38a55b2452ee1048f887523e0cc23f770289f2bf"},"schema_version":"1.0","source":{"id":"1802.02808","kind":"arxiv","version":1}},"canonical_sha256":"f2135a1afc2f96f6f51f3466765b21ddd34b9fa5be4122630c6bccfa97c47f35","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f2135a1afc2f96f6f51f3466765b21ddd34b9fa5be4122630c6bccfa97c47f35","first_computed_at":"2026-05-17T23:41:13.321063Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:41:13.321063Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"mGT2nGk91vjVFzLxvuLVjusKSV5BltPwpkmJj1/yS0xZEX3lcmas4pDUNbkkS2jJNYGY1uTRBbFP4nKg8yOeDw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:41:13.321584Z","signed_message":"canonical_sha256_bytes"},"source_id":"1802.02808","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f10545c5a3d0b0363d215708c7253262c923e3522d1b98b06747daa5ff6107f7","sha256:b280c680c6078ce01e8c34cafb5e34a89141609e6f7c8ea21f23cf6cf0563a7b"],"state_sha256":"0e042281a3ec8993a3679c3e3650d4bbee3b7b0bff04b2a82d66373252592c28"}