{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:5Z2NQRS5AHYAYYZ67BA6WLNGT5","short_pith_number":"pith:5Z2NQRS5","canonical_record":{"source":{"id":"1811.09387","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-11-23T08:33:11Z","cross_cats_sorted":["math.OC"],"title_canon_sha256":"f22cd57294e76ae7ac0ffe09f697e8cd254340dbe0c132798c190a7147adfbfa","abstract_canon_sha256":"b5328cc2cf85c8f5a6be4d0811f66ba79d3ea41e37044d390e57f54d3ad8754f"},"schema_version":"1.0"},"canonical_sha256":"ee74d8465d01f00c633ef841eb2da69f5778dd4544e5ee5d45f47a3db82b670c","source":{"kind":"arxiv","id":"1811.09387","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1811.09387","created_at":"2026-05-17T23:50:58Z"},{"alias_kind":"arxiv_version","alias_value":"1811.09387v2","created_at":"2026-05-17T23:50:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1811.09387","created_at":"2026-05-17T23:50:58Z"},{"alias_kind":"pith_short_12","alias_value":"5Z2NQRS5AHYA","created_at":"2026-05-18T12:32:08Z"},{"alias_kind":"pith_short_16","alias_value":"5Z2NQRS5AHYAYYZ6","created_at":"2026-05-18T12:32:08Z"},{"alias_kind":"pith_short_8","alias_value":"5Z2NQRS5","created_at":"2026-05-18T12:32:08Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:5Z2NQRS5AHYAYYZ67BA6WLNGT5","target":"record","payload":{"canonical_record":{"source":{"id":"1811.09387","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-11-23T08:33:11Z","cross_cats_sorted":["math.OC"],"title_canon_sha256":"f22cd57294e76ae7ac0ffe09f697e8cd254340dbe0c132798c190a7147adfbfa","abstract_canon_sha256":"b5328cc2cf85c8f5a6be4d0811f66ba79d3ea41e37044d390e57f54d3ad8754f"},"schema_version":"1.0"},"canonical_sha256":"ee74d8465d01f00c633ef841eb2da69f5778dd4544e5ee5d45f47a3db82b670c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:50:58.856159Z","signature_b64":"Q8qXA3Qrj5sf0lGO0gOGjVbrrfmpI3BEXiRNkpitd3Ubzu2Nj/y1x8JKNPgbUtxaoffYpIuBL6cES/TOFM4JBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ee74d8465d01f00c633ef841eb2da69f5778dd4544e5ee5d45f47a3db82b670c","last_reissued_at":"2026-05-17T23:50:58.854129Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:50:58.854129Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1811.09387","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:50:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+wAxZOt7qNH/tXfvtASA/BwstgMEa5fEelUegyiIaXL9/gM6H+vALlPpwzUoQBIdRfuJ4+rD7q9b6MLjiDTbBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-21T06:02:44.903572Z"},"content_sha256":"a613dbd97c8e6454e57a7c465bb571596180037500d76fd0e17bcf6bb46d9ea1","schema_version":"1.0","event_id":"sha256:a613dbd97c8e6454e57a7c465bb571596180037500d76fd0e17bcf6bb46d9ea1"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:5Z2NQRS5AHYAYYZ67BA6WLNGT5","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Kinetic Methods for Inverse Problems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OC"],"primary_cat":"math.NA","authors_text":"Giuseppe Visconti, Michael Herty","submitted_at":"2018-11-23T08:33:11Z","abstract_excerpt":"The Ensemble Kalman Filter method can be used as an iterative numerical scheme for parameter identification or nonlinear filtering problems. We study the limit of infinitely large ensemble size and derive the corresponding mean-field limit of the ensemble method. The solution of the inverse problem is provided by the expected value of the distribution of the ensembles and the kinetic equation allows, in simple cases, to analyze stability of these solutions. Further, we present a slight but stable modification of the method which leads to a Fokker-Planck-type kinetic equation. The kinetic metho"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.09387","kind":"arxiv","version":2},"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":"2026-05-17T23:50:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KZ8FLOlEfvWJh4cfQMAe54BKzlGsvSVcXsSFu01kbhBQZB5I8xCzyKFL/UQrAPV0KoT3pc6Z0TIRM3nyFOFOCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-21T06:02:44.903923Z"},"content_sha256":"504bd57030db48f39a9de3fded0f59ed66eace7793e7b7530f46c4946f7a57ab","schema_version":"1.0","event_id":"sha256:504bd57030db48f39a9de3fded0f59ed66eace7793e7b7530f46c4946f7a57ab"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/5Z2NQRS5AHYAYYZ67BA6WLNGT5/bundle.json","state_url":"https://pith.science/pith/5Z2NQRS5AHYAYYZ67BA6WLNGT5/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/5Z2NQRS5AHYAYYZ67BA6WLNGT5/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":"2026-06-21T06:02:44Z","links":{"resolver":"https://pith.science/pith/5Z2NQRS5AHYAYYZ67BA6WLNGT5","bundle":"https://pith.science/pith/5Z2NQRS5AHYAYYZ67BA6WLNGT5/bundle.json","state":"https://pith.science/pith/5Z2NQRS5AHYAYYZ67BA6WLNGT5/state.json","well_known_bundle":"https://pith.science/.well-known/pith/5Z2NQRS5AHYAYYZ67BA6WLNGT5/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:5Z2NQRS5AHYAYYZ67BA6WLNGT5","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":"b5328cc2cf85c8f5a6be4d0811f66ba79d3ea41e37044d390e57f54d3ad8754f","cross_cats_sorted":["math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-11-23T08:33:11Z","title_canon_sha256":"f22cd57294e76ae7ac0ffe09f697e8cd254340dbe0c132798c190a7147adfbfa"},"schema_version":"1.0","source":{"id":"1811.09387","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1811.09387","created_at":"2026-05-17T23:50:58Z"},{"alias_kind":"arxiv_version","alias_value":"1811.09387v2","created_at":"2026-05-17T23:50:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1811.09387","created_at":"2026-05-17T23:50:58Z"},{"alias_kind":"pith_short_12","alias_value":"5Z2NQRS5AHYA","created_at":"2026-05-18T12:32:08Z"},{"alias_kind":"pith_short_16","alias_value":"5Z2NQRS5AHYAYYZ6","created_at":"2026-05-18T12:32:08Z"},{"alias_kind":"pith_short_8","alias_value":"5Z2NQRS5","created_at":"2026-05-18T12:32:08Z"}],"graph_snapshots":[{"event_id":"sha256:504bd57030db48f39a9de3fded0f59ed66eace7793e7b7530f46c4946f7a57ab","target":"graph","created_at":"2026-05-17T23:50:58Z","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":"The Ensemble Kalman Filter method can be used as an iterative numerical scheme for parameter identification or nonlinear filtering problems. We study the limit of infinitely large ensemble size and derive the corresponding mean-field limit of the ensemble method. The solution of the inverse problem is provided by the expected value of the distribution of the ensembles and the kinetic equation allows, in simple cases, to analyze stability of these solutions. Further, we present a slight but stable modification of the method which leads to a Fokker-Planck-type kinetic equation. The kinetic metho","authors_text":"Giuseppe Visconti, Michael Herty","cross_cats":["math.OC"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-11-23T08:33:11Z","title":"Kinetic Methods for Inverse Problems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.09387","kind":"arxiv","version":2},"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:a613dbd97c8e6454e57a7c465bb571596180037500d76fd0e17bcf6bb46d9ea1","target":"record","created_at":"2026-05-17T23:50:58Z","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":"b5328cc2cf85c8f5a6be4d0811f66ba79d3ea41e37044d390e57f54d3ad8754f","cross_cats_sorted":["math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-11-23T08:33:11Z","title_canon_sha256":"f22cd57294e76ae7ac0ffe09f697e8cd254340dbe0c132798c190a7147adfbfa"},"schema_version":"1.0","source":{"id":"1811.09387","kind":"arxiv","version":2}},"canonical_sha256":"ee74d8465d01f00c633ef841eb2da69f5778dd4544e5ee5d45f47a3db82b670c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ee74d8465d01f00c633ef841eb2da69f5778dd4544e5ee5d45f47a3db82b670c","first_computed_at":"2026-05-17T23:50:58.854129Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:50:58.854129Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Q8qXA3Qrj5sf0lGO0gOGjVbrrfmpI3BEXiRNkpitd3Ubzu2Nj/y1x8JKNPgbUtxaoffYpIuBL6cES/TOFM4JBg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:50:58.856159Z","signed_message":"canonical_sha256_bytes"},"source_id":"1811.09387","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a613dbd97c8e6454e57a7c465bb571596180037500d76fd0e17bcf6bb46d9ea1","sha256:504bd57030db48f39a9de3fded0f59ed66eace7793e7b7530f46c4946f7a57ab"],"state_sha256":"353c2bf0a49b0e9a031e5d64e1085c2f661bb57210e3968bb9e5fe26f19b6504"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"W3TST8afXPBqbpfxvB+g5Y5B+56hSfsg2Tg3wa0GCf41W0XtJRZqb6bDEtOyKFvaFnsrLVI8deODBDexT9B/Cg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-21T06:02:44.905895Z","bundle_sha256":"b1f7d688aac999bb61c8c3d0bfe9737329c7be0a0bc69856f6b4f0851e8a3764"}}