{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:PSGWX5JKSYXG3JH4NUMQCA3UJ6","short_pith_number":"pith:PSGWX5JK","canonical_record":{"source":{"id":"1704.00102","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2017-04-01T02:11:56Z","cross_cats_sorted":["cs.SY"],"title_canon_sha256":"86dd20455ee1c5a06f5d5296251f94f372707cf9d40106b35e4e66aa084c4154","abstract_canon_sha256":"999ce7f2349a67302c29a4c7bdb74145125979fe9ad65c66999033dc527501b2"},"schema_version":"1.0"},"canonical_sha256":"7c8d6bf52a962e6da4fc6d190103744fa071ee5b2a8ef2b338093eb62f1e061e","source":{"kind":"arxiv","id":"1704.00102","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1704.00102","created_at":"2026-05-18T00:33:59Z"},{"alias_kind":"arxiv_version","alias_value":"1704.00102v4","created_at":"2026-05-18T00:33:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1704.00102","created_at":"2026-05-18T00:33:59Z"},{"alias_kind":"pith_short_12","alias_value":"PSGWX5JKSYXG","created_at":"2026-05-18T12:31:37Z"},{"alias_kind":"pith_short_16","alias_value":"PSGWX5JKSYXG3JH4","created_at":"2026-05-18T12:31:37Z"},{"alias_kind":"pith_short_8","alias_value":"PSGWX5JK","created_at":"2026-05-18T12:31:37Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:PSGWX5JKSYXG3JH4NUMQCA3UJ6","target":"record","payload":{"canonical_record":{"source":{"id":"1704.00102","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2017-04-01T02:11:56Z","cross_cats_sorted":["cs.SY"],"title_canon_sha256":"86dd20455ee1c5a06f5d5296251f94f372707cf9d40106b35e4e66aa084c4154","abstract_canon_sha256":"999ce7f2349a67302c29a4c7bdb74145125979fe9ad65c66999033dc527501b2"},"schema_version":"1.0"},"canonical_sha256":"7c8d6bf52a962e6da4fc6d190103744fa071ee5b2a8ef2b338093eb62f1e061e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:33:59.235534Z","signature_b64":"oZeEx5Iqe5ZjJbt0izICA4uJIONkkU6DfocpfuSsSIV4tbrVaPo7VwWLDoWJ4A3NniZ94e/yl5mCItCrycVWBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7c8d6bf52a962e6da4fc6d190103744fa071ee5b2a8ef2b338093eb62f1e061e","last_reissued_at":"2026-05-18T00:33:59.234928Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:33:59.234928Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1704.00102","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:33:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"EuYXVz3gy/FKvW0TiBFzHlc2izdaOmegGA4ilgxjNGnfrnaLTf4mSnsN50mnfF8SMezCAG2PAc6CyXyMREltCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T00:24:40.163674Z"},"content_sha256":"ae41c3761fddaea748b31b51dd4c87a4970af48201ddf0265041a056b0c0971c","schema_version":"1.0","event_id":"sha256:ae41c3761fddaea748b31b51dd4c87a4970af48201ddf0265041a056b0c0971c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:PSGWX5JKSYXG3JH4NUMQCA3UJ6","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Gradient Flows in Uncertainty Propagation and Filtering of Linear Gaussian Systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.SY"],"primary_cat":"math.OC","authors_text":"Abhishek Halder, Tryphon T. Georgiou","submitted_at":"2017-04-01T02:11:56Z","abstract_excerpt":"The purpose of this work is mostly expository and aims to elucidate the Jordan-Kinderlehrer-Otto (JKO) scheme for uncertainty propagation, and a variant, the Laugesen-Mehta-Meyn-Raginsky (LMMR) scheme for filtering. We point out that these variational schemes can be understood as proximal operators in the space of density functions, realizing gradient flows. These schemes hold the promise of leading to efficient ways for solving the Fokker-Planck equation as well as the equations of non-linear filtering. Our aim in this paper is to develop in detail the underlying ideas in the setting of linea"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.00102","kind":"arxiv","version":4},"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":"2026-05-18T00:33:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"AVqWqp1oJmxzVCes4Vy4VU+BxhU0hk/5lZgIosvPltw8Vz+iFQX3lEQ9hORlCBCXezDZTnDqZL20XnqZ6kXkBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T00:24:40.164443Z"},"content_sha256":"73cda44133bd0dd092fc6c0cb722de4005c23029ddc627f0d937fb268a35ecd2","schema_version":"1.0","event_id":"sha256:73cda44133bd0dd092fc6c0cb722de4005c23029ddc627f0d937fb268a35ecd2"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/PSGWX5JKSYXG3JH4NUMQCA3UJ6/bundle.json","state_url":"https://pith.science/pith/PSGWX5JKSYXG3JH4NUMQCA3UJ6/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/PSGWX5JKSYXG3JH4NUMQCA3UJ6/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":"2026-06-11T00:24:40Z","links":{"resolver":"https://pith.science/pith/PSGWX5JKSYXG3JH4NUMQCA3UJ6","bundle":"https://pith.science/pith/PSGWX5JKSYXG3JH4NUMQCA3UJ6/bundle.json","state":"https://pith.science/pith/PSGWX5JKSYXG3JH4NUMQCA3UJ6/state.json","well_known_bundle":"https://pith.science/.well-known/pith/PSGWX5JKSYXG3JH4NUMQCA3UJ6/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:PSGWX5JKSYXG3JH4NUMQCA3UJ6","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":"999ce7f2349a67302c29a4c7bdb74145125979fe9ad65c66999033dc527501b2","cross_cats_sorted":["cs.SY"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2017-04-01T02:11:56Z","title_canon_sha256":"86dd20455ee1c5a06f5d5296251f94f372707cf9d40106b35e4e66aa084c4154"},"schema_version":"1.0","source":{"id":"1704.00102","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1704.00102","created_at":"2026-05-18T00:33:59Z"},{"alias_kind":"arxiv_version","alias_value":"1704.00102v4","created_at":"2026-05-18T00:33:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1704.00102","created_at":"2026-05-18T00:33:59Z"},{"alias_kind":"pith_short_12","alias_value":"PSGWX5JKSYXG","created_at":"2026-05-18T12:31:37Z"},{"alias_kind":"pith_short_16","alias_value":"PSGWX5JKSYXG3JH4","created_at":"2026-05-18T12:31:37Z"},{"alias_kind":"pith_short_8","alias_value":"PSGWX5JK","created_at":"2026-05-18T12:31:37Z"}],"graph_snapshots":[{"event_id":"sha256:73cda44133bd0dd092fc6c0cb722de4005c23029ddc627f0d937fb268a35ecd2","target":"graph","created_at":"2026-05-18T00:33:59Z","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 purpose of this work is mostly expository and aims to elucidate the Jordan-Kinderlehrer-Otto (JKO) scheme for uncertainty propagation, and a variant, the Laugesen-Mehta-Meyn-Raginsky (LMMR) scheme for filtering. We point out that these variational schemes can be understood as proximal operators in the space of density functions, realizing gradient flows. These schemes hold the promise of leading to efficient ways for solving the Fokker-Planck equation as well as the equations of non-linear filtering. Our aim in this paper is to develop in detail the underlying ideas in the setting of linea","authors_text":"Abhishek Halder, Tryphon T. Georgiou","cross_cats":["cs.SY"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2017-04-01T02:11:56Z","title":"Gradient Flows in Uncertainty Propagation and Filtering of Linear Gaussian Systems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.00102","kind":"arxiv","version":4},"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:ae41c3761fddaea748b31b51dd4c87a4970af48201ddf0265041a056b0c0971c","target":"record","created_at":"2026-05-18T00:33:59Z","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":"999ce7f2349a67302c29a4c7bdb74145125979fe9ad65c66999033dc527501b2","cross_cats_sorted":["cs.SY"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2017-04-01T02:11:56Z","title_canon_sha256":"86dd20455ee1c5a06f5d5296251f94f372707cf9d40106b35e4e66aa084c4154"},"schema_version":"1.0","source":{"id":"1704.00102","kind":"arxiv","version":4}},"canonical_sha256":"7c8d6bf52a962e6da4fc6d190103744fa071ee5b2a8ef2b338093eb62f1e061e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7c8d6bf52a962e6da4fc6d190103744fa071ee5b2a8ef2b338093eb62f1e061e","first_computed_at":"2026-05-18T00:33:59.234928Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:33:59.234928Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"oZeEx5Iqe5ZjJbt0izICA4uJIONkkU6DfocpfuSsSIV4tbrVaPo7VwWLDoWJ4A3NniZ94e/yl5mCItCrycVWBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:33:59.235534Z","signed_message":"canonical_sha256_bytes"},"source_id":"1704.00102","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ae41c3761fddaea748b31b51dd4c87a4970af48201ddf0265041a056b0c0971c","sha256:73cda44133bd0dd092fc6c0cb722de4005c23029ddc627f0d937fb268a35ecd2"],"state_sha256":"c963a8c0683e4599c384026306bd4e31c0bc27169be924f8ae831613efecc356"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ANlbj/2dwPQhQbQXSvtfYg8/1NSIzfesY4nJv8pleoP63smLfgRD6kxZN27yx66vq56XtMgB13yLjz3Iy4scBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-11T00:24:40.168957Z","bundle_sha256":"cecb6df1f6a2991e78a57c1c3c9a026484da5a05c58659c1e5d0e56dd44c4bf9"}}