{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:E7J4UJSUHF33PRCUUHUWDIUILP","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":"a3aee813061df03483435c2a85e774b9e3e5f8ebe230d6f7050bf0c92ad48e38","cross_cats_sorted":["stat.ML","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2025-09-04T13:55:01Z","title_canon_sha256":"e00b19f5abe92845d8036d7104b4ea37b84bc9f159b71908c90bb1910cdd27a3"},"schema_version":"1.0","source":{"id":"2509.04225","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2509.04225","created_at":"2026-07-05T12:04:55Z"},{"alias_kind":"arxiv_version","alias_value":"2509.04225v1","created_at":"2026-07-05T12:04:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2509.04225","created_at":"2026-07-05T12:04:55Z"},{"alias_kind":"pith_short_12","alias_value":"E7J4UJSUHF33","created_at":"2026-07-05T12:04:55Z"},{"alias_kind":"pith_short_16","alias_value":"E7J4UJSUHF33PRCU","created_at":"2026-07-05T12:04:55Z"},{"alias_kind":"pith_short_8","alias_value":"E7J4UJSU","created_at":"2026-07-05T12:04:55Z"}],"graph_snapshots":[{"event_id":"sha256:dd2ec2f4f44fc93692eb193e8c6558667b2158d18a2260fa4353d04b42426b06","target":"graph","created_at":"2026-07-05T12:04:55Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2509.04225/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We statistically analyze empirical plug-in estimators for unbalanced optimal transport (UOT) formalisms, focusing on the Kantorovich-Rubinstein distance, between general intensity measures based on observations from spatio-temporal point processes. Specifically, we model the observations by two weakly time-stationary point processes with spatial intensity measures $\\mu$ and $\\nu$ over the expanding window $(0,t]$ as $t$ increases to infinity, and establish sharp convergence rates of the empirical UOT in terms of the intrinsic dimensions of the measures. We assume a sub-quadratic temporal growt","authors_text":"Axel Munk, Dominic Schuhmacher, Marina Struleva, Shayan Hundrieser","cross_cats":["stat.ML","stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2025-09-04T13:55:01Z","title":"Sharp Convergence Rates of Empirical Unbalanced Optimal Transport for Spatio-Temporal Point Processes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2509.04225","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":"sha256:3847222f3096f111129626b62fc6aa52c1bd15bdefc5bce1c76b524f3e2a6c38","target":"record","created_at":"2026-07-05T12:04:55Z","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":"a3aee813061df03483435c2a85e774b9e3e5f8ebe230d6f7050bf0c92ad48e38","cross_cats_sorted":["stat.ML","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2025-09-04T13:55:01Z","title_canon_sha256":"e00b19f5abe92845d8036d7104b4ea37b84bc9f159b71908c90bb1910cdd27a3"},"schema_version":"1.0","source":{"id":"2509.04225","kind":"arxiv","version":1}},"canonical_sha256":"27d3ca26543977b7c454a1e961a2885bc1af7d274572fc72b64868ae7307b0b3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"27d3ca26543977b7c454a1e961a2885bc1af7d274572fc72b64868ae7307b0b3","first_computed_at":"2026-07-05T12:04:55.833254Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T12:04:55.833254Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"+KGyMNirRWxRLudr4C/mBKEYKhSzz8oob/WgGidvHHTHYe5Jq7yEaZ4t0HKdIuLqSRDBhnRAEq1n0OB359tbAA==","signature_status":"signed_v1","signed_at":"2026-07-05T12:04:55.833747Z","signed_message":"canonical_sha256_bytes"},"source_id":"2509.04225","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3847222f3096f111129626b62fc6aa52c1bd15bdefc5bce1c76b524f3e2a6c38","sha256:dd2ec2f4f44fc93692eb193e8c6558667b2158d18a2260fa4353d04b42426b06"],"state_sha256":"c75aa1e866616fa13917b718f32f03a587c13d58f5a8ed9c3f5c5358b4f6c687"}