{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:T5BKGYESDKYZMTERBSHF3O36WA","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":"aceedeec9e6a82be318c664f17b2650801af5536d0f7f607017c16b9cceaaa0b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2010-03-22T16:29:29Z","title_canon_sha256":"8a43a90739a06bd5e1d0803dfc2c8a4f25657711f02aaac8882944dd129ca019"},"schema_version":"1.0","source":{"id":"1003.4209","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1003.4209","created_at":"2026-05-18T02:24:36Z"},{"alias_kind":"arxiv_version","alias_value":"1003.4209v3","created_at":"2026-05-18T02:24:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1003.4209","created_at":"2026-05-18T02:24:36Z"},{"alias_kind":"pith_short_12","alias_value":"T5BKGYESDKYZ","created_at":"2026-05-18T12:26:13Z"},{"alias_kind":"pith_short_16","alias_value":"T5BKGYESDKYZMTER","created_at":"2026-05-18T12:26:13Z"},{"alias_kind":"pith_short_8","alias_value":"T5BKGYES","created_at":"2026-05-18T12:26:13Z"}],"graph_snapshots":[{"event_id":"sha256:734bcd965aee1e260e5bbf51b3d8accc3c26d250745f1bf029d1f364c990197d","target":"graph","created_at":"2026-05-18T02:24:36Z","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 study the probability distribution of the area and the number of vertices of random polygons in a convex set $K\\subset\\mathbb{R}^2$. The novel aspect of our approach is that it yields uniform estimates for all convex sets $K\\subset\\mathbb{R}^2$ without imposing any regularity conditions on the boundary $\\partial K$. Our main result is a central limit theorem for both the area and the number of vertices, settling a well-known conjecture in the field. We also obtain asymptotic results relating the growth of the expectation and variance of these two functionals.","authors_text":"John Pardon","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2010-03-22T16:29:29Z","title":"Central limit theorems for random polygons in an arbitrary convex set"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1003.4209","kind":"arxiv","version":3},"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":"sha256:2b11bdf49f307f74eee7080455ee7dcf10dc9d3f01abfca3e7c0716385b12221","target":"record","created_at":"2026-05-18T02:24:36Z","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":"aceedeec9e6a82be318c664f17b2650801af5536d0f7f607017c16b9cceaaa0b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2010-03-22T16:29:29Z","title_canon_sha256":"8a43a90739a06bd5e1d0803dfc2c8a4f25657711f02aaac8882944dd129ca019"},"schema_version":"1.0","source":{"id":"1003.4209","kind":"arxiv","version":3}},"canonical_sha256":"9f42a360921ab1964c910c8e5dbb7eb0148ae4eecbeda916017924b9b0c78f14","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9f42a360921ab1964c910c8e5dbb7eb0148ae4eecbeda916017924b9b0c78f14","first_computed_at":"2026-05-18T02:24:36.283722Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:24:36.283722Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Fs35urk+qKnQRhKywcwE7CI8QRE3IwIeFPzRvfKvzbrBj4jGsulpw/9EQ0Yl1F1pmbp95AQAqGQ725y+qFkKDA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:24:36.284362Z","signed_message":"canonical_sha256_bytes"},"source_id":"1003.4209","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2b11bdf49f307f74eee7080455ee7dcf10dc9d3f01abfca3e7c0716385b12221","sha256:734bcd965aee1e260e5bbf51b3d8accc3c26d250745f1bf029d1f364c990197d"],"state_sha256":"c377da6b19b7dc8c8e05ffad6c0d07704c825a64e982a8aa3275a4dc8dc7848f"}