{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:BIYWKMGFUMBJAQAZ3PHSHIWB7U","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":"d9b00d2c9f8c870d0a2cbcf7b17dca2b1f5aa731b2a2f3bc7bfc81ace35aad3e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2009-05-29T14:20:33Z","title_canon_sha256":"4ab0b6e925ce05364f6b4d55c4acd70306d7cf8f0c11ff46bd0bc5b32a1bfc00"},"schema_version":"1.0","source":{"id":"0905.4874","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0905.4874","created_at":"2026-05-18T04:32:01Z"},{"alias_kind":"arxiv_version","alias_value":"0905.4874v2","created_at":"2026-05-18T04:32:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0905.4874","created_at":"2026-05-18T04:32:01Z"},{"alias_kind":"pith_short_12","alias_value":"BIYWKMGFUMBJ","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_16","alias_value":"BIYWKMGFUMBJAQAZ","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_8","alias_value":"BIYWKMGF","created_at":"2026-05-18T12:25:58Z"}],"graph_snapshots":[{"event_id":"sha256:704873cc74a843feeb39cd5c08824f2051fbf805470c330b59a18138db7b8677","target":"graph","created_at":"2026-05-18T04:32:01Z","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 aim of this paper is to give a precise estimate on the tail probability of the visibility function in a germ-grain model: this function is defined as the length of the longest ray starting at the origin that does not intersect an obstacle in a Boolean model. We proceed in two or more dimensions using coverage techniques. Moreover, convergence results involving a type I extreme value distribution are shown in the two particular cases of small obstacles or a large obstacle-free region.","authors_text":"Julien Michel (UMPA-ENSL), Pierre Calka (MAP5), Sylvain Porret-Blanc (UMPA-ENSL)","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2009-05-29T14:20:33Z","title":"Asymptotics of the visibility function in the Boolean model"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0905.4874","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:e6e120794dedea9d885d9c7d139b8ccddb71558ec37ce9552db8eadfce7e50fe","target":"record","created_at":"2026-05-18T04:32:01Z","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":"d9b00d2c9f8c870d0a2cbcf7b17dca2b1f5aa731b2a2f3bc7bfc81ace35aad3e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2009-05-29T14:20:33Z","title_canon_sha256":"4ab0b6e925ce05364f6b4d55c4acd70306d7cf8f0c11ff46bd0bc5b32a1bfc00"},"schema_version":"1.0","source":{"id":"0905.4874","kind":"arxiv","version":2}},"canonical_sha256":"0a316530c5a302904019dbcf23a2c1fd2285a47f04b129a82bb39b38e4b6b8a8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0a316530c5a302904019dbcf23a2c1fd2285a47f04b129a82bb39b38e4b6b8a8","first_computed_at":"2026-05-18T04:32:01.859343Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:32:01.859343Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"qNLQ7+ULT2iyfO5CaqbbP8rpweLKHgzfFVWfAJWFDNC3dq9+4zmgVnZ/fZfGpkSOBkFao209fd3kf67Wd0dnDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:32:01.859763Z","signed_message":"canonical_sha256_bytes"},"source_id":"0905.4874","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e6e120794dedea9d885d9c7d139b8ccddb71558ec37ce9552db8eadfce7e50fe","sha256:704873cc74a843feeb39cd5c08824f2051fbf805470c330b59a18138db7b8677"],"state_sha256":"8d18b2414459a188e2b4b76e87677eccfd21dbd3c49c18d2ff6f199adbd9fe5d"}