{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:X5GPZVHUQLMCWZZZKI5ZQE2GPB","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":"aa13eda540bbf88b2304f094c9ff8927d224c4291f0df5c46226de2a8f5ad250","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-06-20T18:42:18Z","title_canon_sha256":"43982668ddc0e654e515ca9acafae105d6add67d66319114bd1e621e3e09404b"},"schema_version":"1.0","source":{"id":"1406.5484","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1406.5484","created_at":"2026-05-18T01:12:58Z"},{"alias_kind":"arxiv_version","alias_value":"1406.5484v3","created_at":"2026-05-18T01:12:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1406.5484","created_at":"2026-05-18T01:12:58Z"},{"alias_kind":"pith_short_12","alias_value":"X5GPZVHUQLMC","created_at":"2026-05-18T12:28:57Z"},{"alias_kind":"pith_short_16","alias_value":"X5GPZVHUQLMCWZZZ","created_at":"2026-05-18T12:28:57Z"},{"alias_kind":"pith_short_8","alias_value":"X5GPZVHU","created_at":"2026-05-18T12:28:57Z"}],"graph_snapshots":[{"event_id":"sha256:e99e837dcc600fe499f0767d55678abbd4e79ad80ba9243ba3eb216a051dc4bd","target":"graph","created_at":"2026-05-18T01:12:58Z","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":"A Poisson or a binomial process on an abstract state space and a symmetric function $f$ acting on $k$-tuples of its points are considered. They induce a point process on the target space of $f$. The main result is a functional limit theorem which provides an upper bound for an optimal transportation distance between the image process and a Poisson process on the target space. The technical background are a version of Stein's method for Poisson process approximation, a Glauber dynamics representation for the Poisson process and the Malliavin formalism. As applications of the main result, error ","authors_text":"Christoph Th\\\"ale, Laurent Decreusefond, Matthias Schulte","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-06-20T18:42:18Z","title":"Functional Poisson approximation in Kantorovich-Rubinstein distance with applications to U-statistics and stochastic geometry"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.5484","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:bfeb8e57d6c08b11fe96daf58545ead3c2b555e350be9201bee6bcd4a45efc04","target":"record","created_at":"2026-05-18T01:12:58Z","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":"aa13eda540bbf88b2304f094c9ff8927d224c4291f0df5c46226de2a8f5ad250","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-06-20T18:42:18Z","title_canon_sha256":"43982668ddc0e654e515ca9acafae105d6add67d66319114bd1e621e3e09404b"},"schema_version":"1.0","source":{"id":"1406.5484","kind":"arxiv","version":3}},"canonical_sha256":"bf4cfcd4f482d82b6739523b98134678645dd1d42fdf6ee7f8141d791a8499b9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"bf4cfcd4f482d82b6739523b98134678645dd1d42fdf6ee7f8141d791a8499b9","first_computed_at":"2026-05-18T01:12:58.782869Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:12:58.782869Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"lBNZBjf0ZYwkQKL/W0rHFRZVOh89khlfC7dlxoeWou3wRiKOZ6N7eXLdT6x3swD2hJ9ggrcS4jaZJyHzmjtjCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:12:58.783206Z","signed_message":"canonical_sha256_bytes"},"source_id":"1406.5484","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bfeb8e57d6c08b11fe96daf58545ead3c2b555e350be9201bee6bcd4a45efc04","sha256:e99e837dcc600fe499f0767d55678abbd4e79ad80ba9243ba3eb216a051dc4bd"],"state_sha256":"bc77b98c8a6f6104c56093e4f2b273f898d8bbae7d37cea606bb09e16889b719"}