{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:UYFGBQWMQGSRYHPM347QTQX3KX","short_pith_number":"pith:UYFGBQWM","schema_version":"1.0","canonical_sha256":"a60a60c2cc81a51c1decdf3f09c2fb55d90653ec568680e744c33971877d777f","source":{"kind":"arxiv","id":"1707.07163","version":1},"attestation_state":"computed","paper":{"title":"Warped Riemannian metrics for location-scale models","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"Lionel Bombrun, Salem Said, Yannick Berthoumieu","submitted_at":"2017-07-22T13:39:06Z","abstract_excerpt":"The present paper shows that warped Riemannian metrics, a class of Riemannian metrics which play a prominent role in Riemannian geometry, are also of fundamental importance in information geometry. Precisely, the paper features a new theorem, which states that the Rao-Fisher information metric of any location-scale model, defined on a Riemannian manifold, is a warped Riemannian metric, whenever this model is invariant under the action of some Lie group. This theorem is a valuable tool in finding the expression of the Rao-Fisher information metric of location-scale models defined on high-dimens"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1707.07163","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2017-07-22T13:39:06Z","cross_cats_sorted":["stat.TH"],"title_canon_sha256":"28fad24f433ff6e124c2ee29f2034fd4e4aa4ec689570026b371dd2fd88b7374","abstract_canon_sha256":"d721eaca1f3f1d0808def1a0bdeb4939aa302239c69934e382c5b352c79e0663"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:39:45.157938Z","signature_b64":"QAN8gtvA9giRsfkeGBa+4j6g13NMEw6ZoPCY2g9meh+63yPNEnMKV2x571eBsMeZSwDD4OGBLv8UzuYBgnQKDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a60a60c2cc81a51c1decdf3f09c2fb55d90653ec568680e744c33971877d777f","last_reissued_at":"2026-05-18T00:39:45.157205Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:39:45.157205Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Warped Riemannian metrics for location-scale models","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"Lionel Bombrun, Salem Said, Yannick Berthoumieu","submitted_at":"2017-07-22T13:39:06Z","abstract_excerpt":"The present paper shows that warped Riemannian metrics, a class of Riemannian metrics which play a prominent role in Riemannian geometry, are also of fundamental importance in information geometry. Precisely, the paper features a new theorem, which states that the Rao-Fisher information metric of any location-scale model, defined on a Riemannian manifold, is a warped Riemannian metric, whenever this model is invariant under the action of some Lie group. This theorem is a valuable tool in finding the expression of the Rao-Fisher information metric of location-scale models defined on high-dimens"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.07163","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1707.07163","created_at":"2026-05-18T00:39:45.157345+00:00"},{"alias_kind":"arxiv_version","alias_value":"1707.07163v1","created_at":"2026-05-18T00:39:45.157345+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1707.07163","created_at":"2026-05-18T00:39:45.157345+00:00"},{"alias_kind":"pith_short_12","alias_value":"UYFGBQWMQGSR","created_at":"2026-05-18T12:31:49.984773+00:00"},{"alias_kind":"pith_short_16","alias_value":"UYFGBQWMQGSRYHPM","created_at":"2026-05-18T12:31:49.984773+00:00"},{"alias_kind":"pith_short_8","alias_value":"UYFGBQWM","created_at":"2026-05-18T12:31:49.984773+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/UYFGBQWMQGSRYHPM347QTQX3KX","json":"https://pith.science/pith/UYFGBQWMQGSRYHPM347QTQX3KX.json","graph_json":"https://pith.science/api/pith-number/UYFGBQWMQGSRYHPM347QTQX3KX/graph.json","events_json":"https://pith.science/api/pith-number/UYFGBQWMQGSRYHPM347QTQX3KX/events.json","paper":"https://pith.science/paper/UYFGBQWM"},"agent_actions":{"view_html":"https://pith.science/pith/UYFGBQWMQGSRYHPM347QTQX3KX","download_json":"https://pith.science/pith/UYFGBQWMQGSRYHPM347QTQX3KX.json","view_paper":"https://pith.science/paper/UYFGBQWM","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1707.07163&json=true","fetch_graph":"https://pith.science/api/pith-number/UYFGBQWMQGSRYHPM347QTQX3KX/graph.json","fetch_events":"https://pith.science/api/pith-number/UYFGBQWMQGSRYHPM347QTQX3KX/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/UYFGBQWMQGSRYHPM347QTQX3KX/action/timestamp_anchor","attest_storage":"https://pith.science/pith/UYFGBQWMQGSRYHPM347QTQX3KX/action/storage_attestation","attest_author":"https://pith.science/pith/UYFGBQWMQGSRYHPM347QTQX3KX/action/author_attestation","sign_citation":"https://pith.science/pith/UYFGBQWMQGSRYHPM347QTQX3KX/action/citation_signature","submit_replication":"https://pith.science/pith/UYFGBQWMQGSRYHPM347QTQX3KX/action/replication_record"}},"created_at":"2026-05-18T00:39:45.157345+00:00","updated_at":"2026-05-18T00:39:45.157345+00:00"}