{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2008:2VXVDPFKXT36Z36TPSHDJFWSVL","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":"1d9a7cffce108a08a52055066b3cfd5cc780c81cf5d8dda6bfd2767a332e497c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2008-12-16T15:17:25Z","title_canon_sha256":"3b585c0b67f6018f59cac79f3eab98243c8cb13d787eda585ea24be6007b9c1d"},"schema_version":"1.0","source":{"id":"0812.3084","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0812.3084","created_at":"2026-05-18T04:40:09Z"},{"alias_kind":"arxiv_version","alias_value":"0812.3084v3","created_at":"2026-05-18T04:40:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0812.3084","created_at":"2026-05-18T04:40:09Z"},{"alias_kind":"pith_short_12","alias_value":"2VXVDPFKXT36","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_16","alias_value":"2VXVDPFKXT36Z36T","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_8","alias_value":"2VXVDPFK","created_at":"2026-05-18T12:25:56Z"}],"graph_snapshots":[{"event_id":"sha256:653f1ac40903927ca64548230c7981f45269a8e81dc7c3ae7e69dcf319cd31a2","target":"graph","created_at":"2026-05-18T04:40:09Z","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 give error bounds which demonstrate optimal rates of convergence in the CLT for the total covered volume and the number of isolated shapes, for germ-grain models with fixed grain radius over a binomial point process of $n$ points in a toroidal spatial region of volume $n$. The proof is based on Stein's method via size-biased couplings.","authors_text":"Larry Goldstein, Mathew D. Penrose","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2008-12-16T15:17:25Z","title":"Normal approximation for coverage models over binomial point processes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0812.3084","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":"sha256:7e5df9e661c9a2914f27f51cba4edfb9da3e53f500181ce86d6b6510cb8eb36e","target":"record","created_at":"2026-05-18T04:40:09Z","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":"1d9a7cffce108a08a52055066b3cfd5cc780c81cf5d8dda6bfd2767a332e497c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2008-12-16T15:17:25Z","title_canon_sha256":"3b585c0b67f6018f59cac79f3eab98243c8cb13d787eda585ea24be6007b9c1d"},"schema_version":"1.0","source":{"id":"0812.3084","kind":"arxiv","version":3}},"canonical_sha256":"d56f51bcaabcf7ecefd37c8e3496d2aaeb5f1ec4750854f9595cda64795d2f89","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d56f51bcaabcf7ecefd37c8e3496d2aaeb5f1ec4750854f9595cda64795d2f89","first_computed_at":"2026-05-18T04:40:09.580673Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:40:09.580673Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"r0rpT+iT0vmfmBMfA5oyUzp1dtAzczVNREtMgbvOyD4r++NCrKmKQqaasaJD+OoYJvJID+q+U4zhNtRe4MmtCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:40:09.581124Z","signed_message":"canonical_sha256_bytes"},"source_id":"0812.3084","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7e5df9e661c9a2914f27f51cba4edfb9da3e53f500181ce86d6b6510cb8eb36e","sha256:653f1ac40903927ca64548230c7981f45269a8e81dc7c3ae7e69dcf319cd31a2"],"state_sha256":"6a6fd8ef171129dbd1fe68b7c305c94c97692ba6d5e4c65663591ac46afbf608"}