{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:W2HQHOWGMYHGNP6VJESZOLW5KW","short_pith_number":"pith:W2HQHOWG","canonical_record":{"source":{"id":"1908.04010","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2019-08-12T05:51:44Z","cross_cats_sorted":["cs.CE","cs.NA","cs.SY","eess.SY","math.OC"],"title_canon_sha256":"8bbb92d7b20ed03a71527b4408199dfc2635821cad4b3c8d9b41e30cac2a2d21","abstract_canon_sha256":"af237a32ff390c5a4d347789109d4e8ae6e0effae3182c81cf2f37afd5933d51"},"schema_version":"1.0"},"canonical_sha256":"b68f03bac6660e66bfd54925972edd55b7f6d01c0fadf2203dae8bb9361b3625","source":{"kind":"arxiv","id":"1908.04010","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1908.04010","created_at":"2026-07-04T23:53:19Z"},{"alias_kind":"arxiv_version","alias_value":"1908.04010v1","created_at":"2026-07-04T23:53:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1908.04010","created_at":"2026-07-04T23:53:19Z"},{"alias_kind":"pith_short_12","alias_value":"W2HQHOWGMYHG","created_at":"2026-07-04T23:53:19Z"},{"alias_kind":"pith_short_16","alias_value":"W2HQHOWGMYHGNP6V","created_at":"2026-07-04T23:53:19Z"},{"alias_kind":"pith_short_8","alias_value":"W2HQHOWG","created_at":"2026-07-04T23:53:19Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:W2HQHOWGMYHGNP6VJESZOLW5KW","target":"record","payload":{"canonical_record":{"source":{"id":"1908.04010","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2019-08-12T05:51:44Z","cross_cats_sorted":["cs.CE","cs.NA","cs.SY","eess.SY","math.OC"],"title_canon_sha256":"8bbb92d7b20ed03a71527b4408199dfc2635821cad4b3c8d9b41e30cac2a2d21","abstract_canon_sha256":"af237a32ff390c5a4d347789109d4e8ae6e0effae3182c81cf2f37afd5933d51"},"schema_version":"1.0"},"canonical_sha256":"b68f03bac6660e66bfd54925972edd55b7f6d01c0fadf2203dae8bb9361b3625","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T23:53:19.945465Z","signature_b64":"8d7GDNNIfMKpLZXe+9MpCo2KxUU6N572ugN3GVb6ioO01O+RNZXSkF8H1XkvvaAsmcxnnIpDpPmUL+kObpwiDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b68f03bac6660e66bfd54925972edd55b7f6d01c0fadf2203dae8bb9361b3625","last_reissued_at":"2026-07-04T23:53:19.945065Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T23:53:19.945065Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1908.04010","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":"2026-07-04T23:53:19Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"U49RIsvBdZzStSCSoa2h/1QlVO1h4D+EGxEkrm7ryPJ5fEhDsTjlZtM/zd7utrXnMjGi+GXGizmCrQQWg557Aw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-16T13:22:00.774679Z"},"content_sha256":"3295b4804d22b568ef094c512c4d68af81d0572f13ce7607526bfb42a9622f39","schema_version":"1.0","event_id":"sha256:3295b4804d22b568ef094c512c4d68af81d0572f13ce7607526bfb42a9622f39"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:W2HQHOWGMYHGNP6VJESZOLW5KW","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Solving high-dimensional nonlinear filtering problems using a tensor train decomposition method","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CE","cs.NA","cs.SY","eess.SY","math.OC"],"primary_cat":"math.NA","authors_text":"Sijing Li, Stephen S.T. Yau, Zhiwen Zhang, Zhongjian Wang","submitted_at":"2019-08-12T05:51:44Z","abstract_excerpt":"In this paper, we propose an efficient numerical method to solve high-dimensional nonlinear filtering (NLF) problems. Specifically, we use the tensor train decomposition method to solve the forward Kolmogorov equation (FKE) arising from the NLF problem. Our method consists of offline and online stages. In the offline stage, we use the finite difference method to discretize the partial differential operators involved in the FKE and extract low-dimensional structures in the solution space using the tensor train decomposition method. In addition, we approximate the evolution of the FKE operator u"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.04010","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/1908.04010/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":"2026-07-04T23:53:19Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"80gcMmI8iS6EaVcaXRZehmpJdeJ0TxaT1OP0KL+FYvZ7KpTwBdVUDahpF/AxepQNviKEaKD61Fv23c5HNBkBBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-16T13:22:00.775200Z"},"content_sha256":"527899fa6bb2c744aa3ec09bd11d2fa76bd63330c3ef4477ff4920607fc0f99c","schema_version":"1.0","event_id":"sha256:527899fa6bb2c744aa3ec09bd11d2fa76bd63330c3ef4477ff4920607fc0f99c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/W2HQHOWGMYHGNP6VJESZOLW5KW/bundle.json","state_url":"https://pith.science/pith/W2HQHOWGMYHGNP6VJESZOLW5KW/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/W2HQHOWGMYHGNP6VJESZOLW5KW/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":"2026-08-16T13:22:00Z","links":{"resolver":"https://pith.science/pith/W2HQHOWGMYHGNP6VJESZOLW5KW","bundle":"https://pith.science/pith/W2HQHOWGMYHGNP6VJESZOLW5KW/bundle.json","state":"https://pith.science/pith/W2HQHOWGMYHGNP6VJESZOLW5KW/state.json","well_known_bundle":"https://pith.science/.well-known/pith/W2HQHOWGMYHGNP6VJESZOLW5KW/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:W2HQHOWGMYHGNP6VJESZOLW5KW","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":"af237a32ff390c5a4d347789109d4e8ae6e0effae3182c81cf2f37afd5933d51","cross_cats_sorted":["cs.CE","cs.NA","cs.SY","eess.SY","math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2019-08-12T05:51:44Z","title_canon_sha256":"8bbb92d7b20ed03a71527b4408199dfc2635821cad4b3c8d9b41e30cac2a2d21"},"schema_version":"1.0","source":{"id":"1908.04010","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1908.04010","created_at":"2026-07-04T23:53:19Z"},{"alias_kind":"arxiv_version","alias_value":"1908.04010v1","created_at":"2026-07-04T23:53:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1908.04010","created_at":"2026-07-04T23:53:19Z"},{"alias_kind":"pith_short_12","alias_value":"W2HQHOWGMYHG","created_at":"2026-07-04T23:53:19Z"},{"alias_kind":"pith_short_16","alias_value":"W2HQHOWGMYHGNP6V","created_at":"2026-07-04T23:53:19Z"},{"alias_kind":"pith_short_8","alias_value":"W2HQHOWG","created_at":"2026-07-04T23:53:19Z"}],"graph_snapshots":[{"event_id":"sha256:527899fa6bb2c744aa3ec09bd11d2fa76bd63330c3ef4477ff4920607fc0f99c","target":"graph","created_at":"2026-07-04T23:53:19Z","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/1908.04010/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper, we propose an efficient numerical method to solve high-dimensional nonlinear filtering (NLF) problems. Specifically, we use the tensor train decomposition method to solve the forward Kolmogorov equation (FKE) arising from the NLF problem. Our method consists of offline and online stages. In the offline stage, we use the finite difference method to discretize the partial differential operators involved in the FKE and extract low-dimensional structures in the solution space using the tensor train decomposition method. In addition, we approximate the evolution of the FKE operator u","authors_text":"Sijing Li, Stephen S.T. Yau, Zhiwen Zhang, Zhongjian Wang","cross_cats":["cs.CE","cs.NA","cs.SY","eess.SY","math.OC"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2019-08-12T05:51:44Z","title":"Solving high-dimensional nonlinear filtering problems using a tensor train decomposition method"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.04010","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":"sha256:3295b4804d22b568ef094c512c4d68af81d0572f13ce7607526bfb42a9622f39","target":"record","created_at":"2026-07-04T23:53:19Z","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":"af237a32ff390c5a4d347789109d4e8ae6e0effae3182c81cf2f37afd5933d51","cross_cats_sorted":["cs.CE","cs.NA","cs.SY","eess.SY","math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2019-08-12T05:51:44Z","title_canon_sha256":"8bbb92d7b20ed03a71527b4408199dfc2635821cad4b3c8d9b41e30cac2a2d21"},"schema_version":"1.0","source":{"id":"1908.04010","kind":"arxiv","version":1}},"canonical_sha256":"b68f03bac6660e66bfd54925972edd55b7f6d01c0fadf2203dae8bb9361b3625","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b68f03bac6660e66bfd54925972edd55b7f6d01c0fadf2203dae8bb9361b3625","first_computed_at":"2026-07-04T23:53:19.945065Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T23:53:19.945065Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"8d7GDNNIfMKpLZXe+9MpCo2KxUU6N572ugN3GVb6ioO01O+RNZXSkF8H1XkvvaAsmcxnnIpDpPmUL+kObpwiDQ==","signature_status":"signed_v1","signed_at":"2026-07-04T23:53:19.945465Z","signed_message":"canonical_sha256_bytes"},"source_id":"1908.04010","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3295b4804d22b568ef094c512c4d68af81d0572f13ce7607526bfb42a9622f39","sha256:527899fa6bb2c744aa3ec09bd11d2fa76bd63330c3ef4477ff4920607fc0f99c"],"state_sha256":"526582134db33c182b32ae628f02ac337d42f2f04014e9eb9408bc75e4521473"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"z+RpxjQZueaPVcL/hikIoeptnn281DrnCdJNzT6iQq6Ma9RJYDDZaAeKDIESMm/AXavMaEzFtCZtMDCMe1NbDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-16T13:22:00.779997Z","bundle_sha256":"ee50c73c7b37de58d1cca3ab4d888dcea36876089aebf0e4488ebddd61e39822"}}