{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:HNGUTD7YCZ7B3ZREGBOP7PE45Z","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":"825fbddadce00596390db6f011549c5e597078cffcbd3d261bc0cc5307d4a305","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2024-10-15T15:44:32Z","title_canon_sha256":"b06f17d2286969c95a55fa8d1ceb1efafea515a9db214a25f2911d4d4dd6b612"},"schema_version":"1.0","source":{"id":"2410.11706","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2410.11706","created_at":"2026-05-20T00:05:25Z"},{"alias_kind":"arxiv_version","alias_value":"2410.11706v2","created_at":"2026-05-20T00:05:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2410.11706","created_at":"2026-05-20T00:05:25Z"},{"alias_kind":"pith_short_12","alias_value":"HNGUTD7YCZ7B","created_at":"2026-05-20T00:05:25Z"},{"alias_kind":"pith_short_16","alias_value":"HNGUTD7YCZ7B3ZRE","created_at":"2026-05-20T00:05:25Z"},{"alias_kind":"pith_short_8","alias_value":"HNGUTD7Y","created_at":"2026-05-20T00:05:25Z"}],"graph_snapshots":[{"event_id":"sha256:ea1c5ec1128251e0e27d8ae68aeb67f768dcd1d57ef7124009a35f1afec06daf","target":"graph","created_at":"2026-05-20T00:05:25Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2410.11706/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Let $\\mathbb{P}_K(n)$ be the probability that $n$ points $z_1,\\ldots,z_n$ picked uniformly and independently in $K$, a non-flat compact convex polygon in $\\mathbb{R}^2$, are in convex position, that is, form the vertex set of a convex polygon. In this paper, we give an equivalent of $\\mathbb{P}_K(n)$ when $n\\to\\infty$. This improves on a famous result of B\\'ar\\'any (yet valid for a general convex domain $K$) and a result we initiated in the case where $K$ is a regular convex polygon.","authors_text":"Ludovic Morin","cross_cats":["math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2024-10-15T15:44:32Z","title":"Probability that $n$ points are in convex position in a general convex polygon: Asymptotic results"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2410.11706","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":"sha256:81143ab95e947c2a1f7790893365c04f9551376e1161fcde51fbcd7311c6a2ef","target":"record","created_at":"2026-05-20T00:05:25Z","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":"825fbddadce00596390db6f011549c5e597078cffcbd3d261bc0cc5307d4a305","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2024-10-15T15:44:32Z","title_canon_sha256":"b06f17d2286969c95a55fa8d1ceb1efafea515a9db214a25f2911d4d4dd6b612"},"schema_version":"1.0","source":{"id":"2410.11706","kind":"arxiv","version":2}},"canonical_sha256":"3b4d498ff8167e1de624305cffbc9cee534e55da2e232a80252992dcf7ba9907","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3b4d498ff8167e1de624305cffbc9cee534e55da2e232a80252992dcf7ba9907","first_computed_at":"2026-05-20T00:05:25.946751Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-20T00:05:25.946751Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Cbw9k1pxf1Ngh37UzVwJMsYb+aVN0HMmrmLYnpvqVKEaWUECgueXarNka173Ru6QjRHtXFMd/oYAtdt1q+bZDw==","signature_status":"signed_v1","signed_at":"2026-05-20T00:05:25.947532Z","signed_message":"canonical_sha256_bytes"},"source_id":"2410.11706","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:81143ab95e947c2a1f7790893365c04f9551376e1161fcde51fbcd7311c6a2ef","sha256:ea1c5ec1128251e0e27d8ae68aeb67f768dcd1d57ef7124009a35f1afec06daf"],"state_sha256":"3a73fabb21defb815e85224f119d79adf3cfc8d35fabc3cab26762230242c1e5"}