{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:7VXRUSAUZ343JWI5UIGN2R6Y27","short_pith_number":"pith:7VXRUSAU","canonical_record":{"source":{"id":"2509.07474","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.OC","submitted_at":"2025-09-09T07:52:28Z","cross_cats_sorted":[],"title_canon_sha256":"98144835d82fdb25707ce8521dd8885b4c1d03e8c659f05761ca3ec3ec993146","abstract_canon_sha256":"72ff10437101e28aa89e5aa730311f77072c2c6086b8b5730e66662d0179f8d3"},"schema_version":"1.0"},"canonical_sha256":"fd6f1a4814cef9b4d91da20cdd47d8d7ca6e254a40fa0d12b2d6a0b9273619c9","source":{"kind":"arxiv","id":"2509.07474","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2509.07474","created_at":"2026-07-05T12:07:22Z"},{"alias_kind":"arxiv_version","alias_value":"2509.07474v1","created_at":"2026-07-05T12:07:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2509.07474","created_at":"2026-07-05T12:07:22Z"},{"alias_kind":"pith_short_12","alias_value":"7VXRUSAUZ343","created_at":"2026-07-05T12:07:22Z"},{"alias_kind":"pith_short_16","alias_value":"7VXRUSAUZ343JWI5","created_at":"2026-07-05T12:07:22Z"},{"alias_kind":"pith_short_8","alias_value":"7VXRUSAU","created_at":"2026-07-05T12:07:22Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:7VXRUSAUZ343JWI5UIGN2R6Y27","target":"record","payload":{"canonical_record":{"source":{"id":"2509.07474","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.OC","submitted_at":"2025-09-09T07:52:28Z","cross_cats_sorted":[],"title_canon_sha256":"98144835d82fdb25707ce8521dd8885b4c1d03e8c659f05761ca3ec3ec993146","abstract_canon_sha256":"72ff10437101e28aa89e5aa730311f77072c2c6086b8b5730e66662d0179f8d3"},"schema_version":"1.0"},"canonical_sha256":"fd6f1a4814cef9b4d91da20cdd47d8d7ca6e254a40fa0d12b2d6a0b9273619c9","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T12:07:22.042210Z","signature_b64":"PZD2PE0I/D7rMJT0tDA9wiy3XbI3HMMUPPGAfQe0tMPU/tUL78qK8rJCYuuJBclIe1GMXZrUvBaXTlRXutqLBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fd6f1a4814cef9b4d91da20cdd47d8d7ca6e254a40fa0d12b2d6a0b9273619c9","last_reissued_at":"2026-07-05T12:07:22.041726Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T12:07:22.041726Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2509.07474","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T12:07:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Q/5jorZ1MywDPM8Jby0WtgL8lNdAW27UBPWz2cckRQWj8/z1eO0EO5ulzn4sQQNhdBdb2W74DFbyCOcHfpYZBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-10T19:34:52.350238Z"},"content_sha256":"f445722172d8231ac718ed6d92d1e11690973ecdf313a76b9831c7d0663d98c3","schema_version":"1.0","event_id":"sha256:f445722172d8231ac718ed6d92d1e11690973ecdf313a76b9831c7d0663d98c3"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:7VXRUSAUZ343JWI5UIGN2R6Y27","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"DKFNet: Differentiable Kalman Filter for Field Inversion and Machine Learning","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Sicheng He, Yuan Wu","submitted_at":"2025-09-09T07:52:28Z","abstract_excerpt":"The Kalman filter is a fundamental tool for state estimation in dynamical systems. While originally developed for linear Gaussian settings, it has been extended to nonlinear problems through approaches such as the extended and unscented Kalman filters. Despite its broad use, a persistent limitation is that the underlying approximate model is fixed, which can lead to significant deviations from the true system dynamics. To address this limitation, we introduce the differentiable Kalman filter (DKF), an adjoint-based two-level optimization framework designed to reduce the mismatch between approx"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2509.07474","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2509.07474/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T12:07:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7YsK8TQhvSCzsz11KzBWbhfbpfeoY8i5Lb2wd0JYDYa9iLdIbm1oID8ewPnwtFsCN+EjxXHpqVTCqDGkNJZzBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-10T19:34:52.350756Z"},"content_sha256":"14602875843c9e043866e22e541fcbcbcfc8bc5f73ea522c460df828a70ac575","schema_version":"1.0","event_id":"sha256:14602875843c9e043866e22e541fcbcbcfc8bc5f73ea522c460df828a70ac575"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/7VXRUSAUZ343JWI5UIGN2R6Y27/bundle.json","state_url":"https://pith.science/pith/7VXRUSAUZ343JWI5UIGN2R6Y27/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/7VXRUSAUZ343JWI5UIGN2R6Y27/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":"2026-08-10T19:34:52Z","links":{"resolver":"https://pith.science/pith/7VXRUSAUZ343JWI5UIGN2R6Y27","bundle":"https://pith.science/pith/7VXRUSAUZ343JWI5UIGN2R6Y27/bundle.json","state":"https://pith.science/pith/7VXRUSAUZ343JWI5UIGN2R6Y27/state.json","well_known_bundle":"https://pith.science/.well-known/pith/7VXRUSAUZ343JWI5UIGN2R6Y27/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:7VXRUSAUZ343JWI5UIGN2R6Y27","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":"72ff10437101e28aa89e5aa730311f77072c2c6086b8b5730e66662d0179f8d3","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.OC","submitted_at":"2025-09-09T07:52:28Z","title_canon_sha256":"98144835d82fdb25707ce8521dd8885b4c1d03e8c659f05761ca3ec3ec993146"},"schema_version":"1.0","source":{"id":"2509.07474","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2509.07474","created_at":"2026-07-05T12:07:22Z"},{"alias_kind":"arxiv_version","alias_value":"2509.07474v1","created_at":"2026-07-05T12:07:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2509.07474","created_at":"2026-07-05T12:07:22Z"},{"alias_kind":"pith_short_12","alias_value":"7VXRUSAUZ343","created_at":"2026-07-05T12:07:22Z"},{"alias_kind":"pith_short_16","alias_value":"7VXRUSAUZ343JWI5","created_at":"2026-07-05T12:07:22Z"},{"alias_kind":"pith_short_8","alias_value":"7VXRUSAU","created_at":"2026-07-05T12:07:22Z"}],"graph_snapshots":[{"event_id":"sha256:14602875843c9e043866e22e541fcbcbcfc8bc5f73ea522c460df828a70ac575","target":"graph","created_at":"2026-07-05T12:07:22Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2509.07474/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The Kalman filter is a fundamental tool for state estimation in dynamical systems. While originally developed for linear Gaussian settings, it has been extended to nonlinear problems through approaches such as the extended and unscented Kalman filters. Despite its broad use, a persistent limitation is that the underlying approximate model is fixed, which can lead to significant deviations from the true system dynamics. To address this limitation, we introduce the differentiable Kalman filter (DKF), an adjoint-based two-level optimization framework designed to reduce the mismatch between approx","authors_text":"Sicheng He, Yuan Wu","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.OC","submitted_at":"2025-09-09T07:52:28Z","title":"DKFNet: Differentiable Kalman Filter for Field Inversion and Machine Learning"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2509.07474","kind":"arxiv","version":1},"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:f445722172d8231ac718ed6d92d1e11690973ecdf313a76b9831c7d0663d98c3","target":"record","created_at":"2026-07-05T12:07:22Z","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":"72ff10437101e28aa89e5aa730311f77072c2c6086b8b5730e66662d0179f8d3","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.OC","submitted_at":"2025-09-09T07:52:28Z","title_canon_sha256":"98144835d82fdb25707ce8521dd8885b4c1d03e8c659f05761ca3ec3ec993146"},"schema_version":"1.0","source":{"id":"2509.07474","kind":"arxiv","version":1}},"canonical_sha256":"fd6f1a4814cef9b4d91da20cdd47d8d7ca6e254a40fa0d12b2d6a0b9273619c9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fd6f1a4814cef9b4d91da20cdd47d8d7ca6e254a40fa0d12b2d6a0b9273619c9","first_computed_at":"2026-07-05T12:07:22.041726Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T12:07:22.041726Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"PZD2PE0I/D7rMJT0tDA9wiy3XbI3HMMUPPGAfQe0tMPU/tUL78qK8rJCYuuJBclIe1GMXZrUvBaXTlRXutqLBQ==","signature_status":"signed_v1","signed_at":"2026-07-05T12:07:22.042210Z","signed_message":"canonical_sha256_bytes"},"source_id":"2509.07474","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f445722172d8231ac718ed6d92d1e11690973ecdf313a76b9831c7d0663d98c3","sha256:14602875843c9e043866e22e541fcbcbcfc8bc5f73ea522c460df828a70ac575"],"state_sha256":"81cca588f2cd6ceb558cca63a68d2138d41d6bd7f5a85613bdf9b4861986117e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PUrxbudSKIWF9xAOH5wWhjhbZMVLiOszXuNvQ3j3vsmK4vfBxq8vDqRECiqkTbgWAPmwTUfCpIi5KQ8zfizvCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-10T19:34:52.356244Z","bundle_sha256":"9df6a807d1f7ee3450121b77a898361bec47b59d44a4f56d60289b8fa265fada"}}