{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:BAD4UBQILZHFPTOAD255646QAY","short_pith_number":"pith:BAD4UBQI","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"},"canonical_sha256":"0807ca06085e4e57cdc01ebbdf73d006364cba4bb4cc210a5ed3279b0138fb63","source":{"kind":"arxiv","id":"1602.04457","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1602.04457","created_at":"2026-05-18T00:16:45Z"},{"alias_kind":"arxiv_version","alias_value":"1602.04457v3","created_at":"2026-05-18T00:16:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1602.04457","created_at":"2026-05-18T00:16:45Z"},{"alias_kind":"pith_short_12","alias_value":"BAD4UBQILZHF","created_at":"2026-05-18T12:30:07Z"},{"alias_kind":"pith_short_16","alias_value":"BAD4UBQILZHFPTOA","created_at":"2026-05-18T12:30:07Z"},{"alias_kind":"pith_short_8","alias_value":"BAD4UBQI","created_at":"2026-05-18T12:30:07Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:BAD4UBQILZHFPTOAD255646QAY","target":"record","payload":{"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"},"canonical_sha256":"0807ca06085e4e57cdc01ebbdf73d006364cba4bb4cc210a5ed3279b0138fb63","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"},"source_kind":"arxiv","source_id":"1602.04457","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:16:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lgNrf7NPYGgOtrZA+F44dMAcX+mOG8In7z9gfUgdHJgoyxvnwWIixE4jp7AZJtHR7yit3EkTDOcnwkkaJGk/CQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T07:30:37.642803Z"},"content_sha256":"e9d0a0431b29f55b4d71b3ecf3488c46835500180a21d7d25e949296bdc2d941","schema_version":"1.0","event_id":"sha256:e9d0a0431b29f55b4d71b3ecf3488c46835500180a21d7d25e949296bdc2d941"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:BAD4UBQILZHFPTOAD255646QAY","target":"graph","payload":{"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:16:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"og20DHzzaoCQ3lkao72ii8/rPTGwg4MrtApVBhMC9Ci8RkHJu3QYdIAwedtwYRNqD76AbXKPUierZTlWvn49CQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T07:30:37.643463Z"},"content_sha256":"e6528535a6475e2c5cc51de467f26ee6cfed6df3e7e4cc5e2d076e7717e244bc","schema_version":"1.0","event_id":"sha256:e6528535a6475e2c5cc51de467f26ee6cfed6df3e7e4cc5e2d076e7717e244bc"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/BAD4UBQILZHFPTOAD255646QAY/bundle.json","state_url":"https://pith.science/pith/BAD4UBQILZHFPTOAD255646QAY/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/BAD4UBQILZHFPTOAD255646QAY/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-05-25T07:30:37Z","links":{"resolver":"https://pith.science/pith/BAD4UBQILZHFPTOAD255646QAY","bundle":"https://pith.science/pith/BAD4UBQILZHFPTOAD255646QAY/bundle.json","state":"https://pith.science/pith/BAD4UBQILZHFPTOAD255646QAY/state.json","well_known_bundle":"https://pith.science/.well-known/pith/BAD4UBQILZHFPTOAD255646QAY/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:BAD4UBQILZHFPTOAD255646QAY","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":"513cf1cbed8aea03cedc58f31a7e91cca56b85de180549d98d2aaec3f8f43b8f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-02-14T14:04:53Z","title_canon_sha256":"18f3eec7c0355f7072fb6a960e70eb1409facc9cc634e5bb1aa7ed2e1a1cbb0c"},"schema_version":"1.0","source":{"id":"1602.04457","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1602.04457","created_at":"2026-05-18T00:16:45Z"},{"alias_kind":"arxiv_version","alias_value":"1602.04457v3","created_at":"2026-05-18T00:16:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1602.04457","created_at":"2026-05-18T00:16:45Z"},{"alias_kind":"pith_short_12","alias_value":"BAD4UBQILZHF","created_at":"2026-05-18T12:30:07Z"},{"alias_kind":"pith_short_16","alias_value":"BAD4UBQILZHFPTOA","created_at":"2026-05-18T12:30:07Z"},{"alias_kind":"pith_short_8","alias_value":"BAD4UBQI","created_at":"2026-05-18T12:30:07Z"}],"graph_snapshots":[{"event_id":"sha256:e6528535a6475e2c5cc51de467f26ee6cfed6df3e7e4cc5e2d076e7717e244bc","target":"graph","created_at":"2026-05-18T00:16:45Z","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":"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","authors_text":"L\\'eonard Monsaingeon, Thomas Gallou\\\"et","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-02-14T14:04:53Z","title":"A JKO splitting scheme for Kantorovich-Fisher-Rao gradient flows"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.04457","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:e9d0a0431b29f55b4d71b3ecf3488c46835500180a21d7d25e949296bdc2d941","target":"record","created_at":"2026-05-18T00:16:45Z","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":"513cf1cbed8aea03cedc58f31a7e91cca56b85de180549d98d2aaec3f8f43b8f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-02-14T14:04:53Z","title_canon_sha256":"18f3eec7c0355f7072fb6a960e70eb1409facc9cc634e5bb1aa7ed2e1a1cbb0c"},"schema_version":"1.0","source":{"id":"1602.04457","kind":"arxiv","version":3}},"canonical_sha256":"0807ca06085e4e57cdc01ebbdf73d006364cba4bb4cc210a5ed3279b0138fb63","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0807ca06085e4e57cdc01ebbdf73d006364cba4bb4cc210a5ed3279b0138fb63","first_computed_at":"2026-05-18T00:16:45.899717Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:16:45.899717Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"pjQcuoJW5rxDUtlGfB49KgjA2W5BV6PCk27V21L944fMjPbHvrzSitSzcnkoAolN3cYB4XJgnPgDDsEtQakwCw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:16:45.900375Z","signed_message":"canonical_sha256_bytes"},"source_id":"1602.04457","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e9d0a0431b29f55b4d71b3ecf3488c46835500180a21d7d25e949296bdc2d941","sha256:e6528535a6475e2c5cc51de467f26ee6cfed6df3e7e4cc5e2d076e7717e244bc"],"state_sha256":"be0817976b06446d87147925cd2e3957c9066f74b0ac8e64bf5386267d8aa526"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Tx1dI24ySq9yWxLw6WZ9ho7rJ+nWzqGpfj0WQec2QQvEJsIo1SK4p4g2yKpC5xhK+pt1wKMAG6vYovz6Q2cDBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-25T07:30:37.647025Z","bundle_sha256":"3a84d6f5200ef971390b7b3657df03307cb3b3acf236d09746449f1f7fbbec56"}}