{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:PSFPFLOVUV3OSPRG5WUKFQ4XE2","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":"6880c2bdc21d8821afe8f45bc9afec68c923cb43f011c06d9cbedb3054d8107e","cross_cats_sorted":["math.ST","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-01-08T11:36:30Z","title_canon_sha256":"d41866bb104b178b420dc6a53483ac7a04288fc937fa98dc931b475988620597"},"schema_version":"1.0","source":{"id":"1301.1499","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1301.1499","created_at":"2026-05-18T03:36:57Z"},{"alias_kind":"arxiv_version","alias_value":"1301.1499v1","created_at":"2026-05-18T03:36:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1301.1499","created_at":"2026-05-18T03:36:57Z"},{"alias_kind":"pith_short_12","alias_value":"PSFPFLOVUV3O","created_at":"2026-05-18T12:27:57Z"},{"alias_kind":"pith_short_16","alias_value":"PSFPFLOVUV3OSPRG","created_at":"2026-05-18T12:27:57Z"},{"alias_kind":"pith_short_8","alias_value":"PSFPFLOV","created_at":"2026-05-18T12:27:57Z"}],"graph_snapshots":[{"event_id":"sha256:e46b00f6df5701b2f927d849a5fbb5ce5f6dd255cb6d060f5dcd11ec178b5261","target":"graph","created_at":"2026-05-18T03:36:57Z","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 paper considers the stationary Poisson Boolean model with spherical grains and proposes a family of nonparametric estimators for the radius distribution. These estimators are based on observed distances and radii, weighted in an appropriate way. They are ratio-unbiased and asymptotically consistent for growing observation window. It is shown that the asymptotic variance exists and is given by a fairly explicit integral expression. Asymptotic normality is established under a suitable integrability assumption on the weight function. The paper also provides a short discussion of related estim","authors_text":"Daniel Hug, G\\\"unter Last, Wolfgang Weil, Zbyn\\v{e}k Pawlas","cross_cats":["math.ST","stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-01-08T11:36:30Z","title":"Statistics for Poisson models of overlapping spheres"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.1499","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:adc2f0672609dd503c953c73e468afdfa49acabcd3f961b5d3a5708a09708fcb","target":"record","created_at":"2026-05-18T03:36:57Z","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":"6880c2bdc21d8821afe8f45bc9afec68c923cb43f011c06d9cbedb3054d8107e","cross_cats_sorted":["math.ST","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-01-08T11:36:30Z","title_canon_sha256":"d41866bb104b178b420dc6a53483ac7a04288fc937fa98dc931b475988620597"},"schema_version":"1.0","source":{"id":"1301.1499","kind":"arxiv","version":1}},"canonical_sha256":"7c8af2add5a576e93e26eda8a2c39726b433baf4bf2907f29b6195534b22fe57","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7c8af2add5a576e93e26eda8a2c39726b433baf4bf2907f29b6195534b22fe57","first_computed_at":"2026-05-18T03:36:57.316778Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:36:57.316778Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"FoYLJg1U9XhZDNbIem56GAqqDQiJ8l7kb1Is9OrD+i9cTK9RMe7HFzxG9PXPC3QIsVM4VWPQ98s5PF5XnM8OBw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:36:57.317344Z","signed_message":"canonical_sha256_bytes"},"source_id":"1301.1499","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:adc2f0672609dd503c953c73e468afdfa49acabcd3f961b5d3a5708a09708fcb","sha256:e46b00f6df5701b2f927d849a5fbb5ce5f6dd255cb6d060f5dcd11ec178b5261"],"state_sha256":"b769b0e73c54b733f2b92cb8007a28e692a105dee718bd2015458d47442c9c75"}