{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:PHOQHYST5GDNJUCJPMPUZVAMG4","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":"0f719adbf338e897db177caeb3ae008fa02a598e9dea6367343742357c2c0cd8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-01-25T14:35:19Z","title_canon_sha256":"ce58fc9bb7c2e1bd978236ba8dc015fa870b91ccdfeb5c8ab63eede3d80b3e05"},"schema_version":"1.0","source":{"id":"1201.5282","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1201.5282","created_at":"2026-05-18T03:38:56Z"},{"alias_kind":"arxiv_version","alias_value":"1201.5282v1","created_at":"2026-05-18T03:38:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1201.5282","created_at":"2026-05-18T03:38:56Z"},{"alias_kind":"pith_short_12","alias_value":"PHOQHYST5GDN","created_at":"2026-05-18T12:27:18Z"},{"alias_kind":"pith_short_16","alias_value":"PHOQHYST5GDNJUCJ","created_at":"2026-05-18T12:27:18Z"},{"alias_kind":"pith_short_8","alias_value":"PHOQHYST","created_at":"2026-05-18T12:27:18Z"}],"graph_snapshots":[{"event_id":"sha256:221cc32820c348778f27dc230a34daf2f860f03da5c0dd3bd89da3d64b9561d5","target":"graph","created_at":"2026-05-18T03:38:56Z","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":"Let $\\eta_t$ be a Poisson point process of intensity $t\\geq 1$ on some state space $\\Y$ and $f$ be a non-negative symmetric function on $\\Y^k$ for some $k\\geq 1$. Applying $f$ to all $k$-tuples of distinct points of $\\eta_t$ generates a point process $\\xi_t$ on the positive real-half axis. The scaling limit of $\\xi_t$ as $t$ tends to infinity is shown to be a Poisson point process with explicitly known intensity measure. From this, a limit theorem for the the $m$-th smallest point of $\\xi_t$ is concluded. This is strengthened by providing a rate of convergence. The technical background include","authors_text":"Christoph Thaele, Matthias Schulte","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-01-25T14:35:19Z","title":"The scaling limit of Poisson-driven order statistics with applications in geometric probability"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1201.5282","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":"sha256:81d04f1a072bd9be828b4a6910cc166f9057126cd59644dfe65886aa85652a0a","target":"record","created_at":"2026-05-18T03:38:56Z","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":"0f719adbf338e897db177caeb3ae008fa02a598e9dea6367343742357c2c0cd8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-01-25T14:35:19Z","title_canon_sha256":"ce58fc9bb7c2e1bd978236ba8dc015fa870b91ccdfeb5c8ab63eede3d80b3e05"},"schema_version":"1.0","source":{"id":"1201.5282","kind":"arxiv","version":1}},"canonical_sha256":"79dd03e253e986d4d0497b1f4cd40c37115823eb141c60ccf2bd8fbceebc3f53","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"79dd03e253e986d4d0497b1f4cd40c37115823eb141c60ccf2bd8fbceebc3f53","first_computed_at":"2026-05-18T03:38:56.162351Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:38:56.162351Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ypA6CwcXP+WNJNtEb+qweMur8+SH2zALJG5Ru+1FcrkRgm3+KLTg189v2R/Hr+opB10qdRii9DS/07NoXLGAAw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:38:56.163251Z","signed_message":"canonical_sha256_bytes"},"source_id":"1201.5282","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:81d04f1a072bd9be828b4a6910cc166f9057126cd59644dfe65886aa85652a0a","sha256:221cc32820c348778f27dc230a34daf2f860f03da5c0dd3bd89da3d64b9561d5"],"state_sha256":"27365d8817be0211fbb347753c0f3d2e67fecb3e3f8942152411b82955cb6cf8"}