{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:BAD4UBQILZHFPTOAD255646QAY","short_pith_number":"pith:BAD4UBQI","schema_version":"1.0","canonical_sha256":"0807ca06085e4e57cdc01ebbdf73d006364cba4bb4cc210a5ed3279b0138fb63","source":{"kind":"arxiv","id":"1602.04457","version":3},"attestation_state":"computed","paper":{"title":"A JKO splitting scheme for Kantorovich-Fisher-Rao gradient flows","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"L\\'eonard Monsaingeon, Thomas Gallou\\\"et","submitted_at":"2016-02-14T14:04:53Z","abstract_excerpt":"In this article we set up a splitting variant of the JKO scheme in order to handle gradient flows with respect to the Kantorovich-Fisher-Rao metric, recently introduced and defined on the space of positive Radon measure with varying masses. We perform successively a time step for the quadratic Wasserstein/Monge-Kantorovich distance, and then for the Hellinger/Fisher-Rao distance. Exploiting some inf-convolution structure of the metric we show convergence of the whole process for the standard class of energy functionals under suitable compactness assumptions, and investigate in details the case"},"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":"1602.04457","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-02-14T14:04:53Z","cross_cats_sorted":[],"title_canon_sha256":"18f3eec7c0355f7072fb6a960e70eb1409facc9cc634e5bb1aa7ed2e1a1cbb0c","abstract_canon_sha256":"513cf1cbed8aea03cedc58f31a7e91cca56b85de180549d98d2aaec3f8f43b8f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:16:45.900375Z","signature_b64":"pjQcuoJW5rxDUtlGfB49KgjA2W5BV6PCk27V21L944fMjPbHvrzSitSzcnkoAolN3cYB4XJgnPgDDsEtQakwCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0807ca06085e4e57cdc01ebbdf73d006364cba4bb4cc210a5ed3279b0138fb63","last_reissued_at":"2026-05-18T00:16:45.899717Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:16:45.899717Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A JKO splitting scheme for Kantorovich-Fisher-Rao gradient flows","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"L\\'eonard Monsaingeon, Thomas Gallou\\\"et","submitted_at":"2016-02-14T14:04:53Z","abstract_excerpt":"In this article we set up a splitting variant of the JKO scheme in order to handle gradient flows with respect to the Kantorovich-Fisher-Rao metric, recently introduced and defined on the space of positive Radon measure with varying masses. We perform successively a time step for the quadratic Wasserstein/Monge-Kantorovich distance, and then for the Hellinger/Fisher-Rao distance. Exploiting some inf-convolution structure of the metric we show convergence of the whole process for the standard class of energy functionals under suitable compactness assumptions, and investigate in details the case"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.04457","kind":"arxiv","version":3},"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":"1602.04457","created_at":"2026-05-18T00:16:45.899824+00:00"},{"alias_kind":"arxiv_version","alias_value":"1602.04457v3","created_at":"2026-05-18T00:16:45.899824+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1602.04457","created_at":"2026-05-18T00:16:45.899824+00:00"},{"alias_kind":"pith_short_12","alias_value":"BAD4UBQILZHF","created_at":"2026-05-18T12:30:07.202191+00:00"},{"alias_kind":"pith_short_16","alias_value":"BAD4UBQILZHFPTOA","created_at":"2026-05-18T12:30:07.202191+00:00"},{"alias_kind":"pith_short_8","alias_value":"BAD4UBQI","created_at":"2026-05-18T12:30:07.202191+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2502.10600","citing_title":"Weighted quantization using MMD: From mean field to mean shift via gradient flows","ref_index":37,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/BAD4UBQILZHFPTOAD255646QAY","json":"https://pith.science/pith/BAD4UBQILZHFPTOAD255646QAY.json","graph_json":"https://pith.science/api/pith-number/BAD4UBQILZHFPTOAD255646QAY/graph.json","events_json":"https://pith.science/api/pith-number/BAD4UBQILZHFPTOAD255646QAY/events.json","paper":"https://pith.science/paper/BAD4UBQI"},"agent_actions":{"view_html":"https://pith.science/pith/BAD4UBQILZHFPTOAD255646QAY","download_json":"https://pith.science/pith/BAD4UBQILZHFPTOAD255646QAY.json","view_paper":"https://pith.science/paper/BAD4UBQI","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1602.04457&json=true","fetch_graph":"https://pith.science/api/pith-number/BAD4UBQILZHFPTOAD255646QAY/graph.json","fetch_events":"https://pith.science/api/pith-number/BAD4UBQILZHFPTOAD255646QAY/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/BAD4UBQILZHFPTOAD255646QAY/action/timestamp_anchor","attest_storage":"https://pith.science/pith/BAD4UBQILZHFPTOAD255646QAY/action/storage_attestation","attest_author":"https://pith.science/pith/BAD4UBQILZHFPTOAD255646QAY/action/author_attestation","sign_citation":"https://pith.science/pith/BAD4UBQILZHFPTOAD255646QAY/action/citation_signature","submit_replication":"https://pith.science/pith/BAD4UBQILZHFPTOAD255646QAY/action/replication_record"}},"created_at":"2026-05-18T00:16:45.899824+00:00","updated_at":"2026-05-18T00:16:45.899824+00:00"}