{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:GGIZUADC4EHFUJ6W3U63NTKQLE","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":"e7c52bfd77621ce79e6f3b455a07a2f2f050cb9fa8ee034fe7d984d7f9912000","cross_cats_sorted":["math.ST","stat.TH"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"stat.ME","submitted_at":"2023-07-12T12:40:16Z","title_canon_sha256":"4c079ce0d58f6b90ceb3422296550420076d962158d9527cf5743aa3952cb173"},"schema_version":"1.0","source":{"id":"2307.06137","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2307.06137","created_at":"2026-07-05T07:42:40Z"},{"alias_kind":"arxiv_version","alias_value":"2307.06137v3","created_at":"2026-07-05T07:42:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2307.06137","created_at":"2026-07-05T07:42:40Z"},{"alias_kind":"pith_short_12","alias_value":"GGIZUADC4EHF","created_at":"2026-07-05T07:42:40Z"},{"alias_kind":"pith_short_16","alias_value":"GGIZUADC4EHFUJ6W","created_at":"2026-07-05T07:42:40Z"},{"alias_kind":"pith_short_8","alias_value":"GGIZUADC","created_at":"2026-07-05T07:42:40Z"}],"graph_snapshots":[{"event_id":"sha256:05e513fefc4c63bdeebff182c1ec3b6bd5cb9498bb97eb621055420319211a3b","target":"graph","created_at":"2026-07-05T07:42:40Z","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/2307.06137/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Distribution data refers to a data set where each sample is represented as a probability distribution, a subject area receiving burgeoning interest in the field of statistics. Although several studies have developed distribution-to-distribution regression models for univariate variables, the multivariate scenario remains under-explored due to technical complexities. In this study, we introduce models for regression from one Gaussian distribution to another, utilizing the Wasserstein metric. These models are constructed using the geometry of the Wasserstein space, which enables the transformati","authors_text":"Masaaki Imaizumi, Ryo Okano","cross_cats":["math.ST","stat.TH"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"stat.ME","submitted_at":"2023-07-12T12:40:16Z","title":"Distribution-on-Distribution Regression with Wasserstein Metric: Multivariate Gaussian Case"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2307.06137","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":"sha256:1a4bb0ac3d7d15a762725638fc83d9e8014df75c7f3100b47ad28b50e46b174b","target":"record","created_at":"2026-07-05T07:42:40Z","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":"e7c52bfd77621ce79e6f3b455a07a2f2f050cb9fa8ee034fe7d984d7f9912000","cross_cats_sorted":["math.ST","stat.TH"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"stat.ME","submitted_at":"2023-07-12T12:40:16Z","title_canon_sha256":"4c079ce0d58f6b90ceb3422296550420076d962158d9527cf5743aa3952cb173"},"schema_version":"1.0","source":{"id":"2307.06137","kind":"arxiv","version":3}},"canonical_sha256":"31919a0062e10e5a27d6dd3db6cd50592663039601a53649a4db7f4a14179593","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"31919a0062e10e5a27d6dd3db6cd50592663039601a53649a4db7f4a14179593","first_computed_at":"2026-07-05T07:42:40.838672Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T07:42:40.838672Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"9z+w+XGMiS2ozn0fkkCGnm+BqviS9HcAWNtOPdFxOU+hIetaWXNN8WoFbbQZHq2Z3LbGI0AaiL/l1VJ0jowvAQ==","signature_status":"signed_v1","signed_at":"2026-07-05T07:42:40.839088Z","signed_message":"canonical_sha256_bytes"},"source_id":"2307.06137","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1a4bb0ac3d7d15a762725638fc83d9e8014df75c7f3100b47ad28b50e46b174b","sha256:05e513fefc4c63bdeebff182c1ec3b6bd5cb9498bb97eb621055420319211a3b"],"state_sha256":"9ba519e606b0be0c94b4f6f89f779b6dbccceb1eaaae8a6136d1671a0cbb4efd"}