{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:JZU3JOEKVA7VRJ6FRDW4KFQ4MB","short_pith_number":"pith:JZU3JOEK","canonical_record":{"source":{"id":"2404.09323","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.OC","submitted_at":"2024-04-14T18:46:54Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"ea1411ad1269fab558d3cda42290cc4022cefc23b07dd84ca36c93878f858f54","abstract_canon_sha256":"d6f1436b383d45270577bfb793c489a81ee37d6dc956fee375bd7b8a57c17880"},"schema_version":"1.0"},"canonical_sha256":"4e69b4b88aa83f58a7c588edc5161c604425d9b0303750b0f0c90dd866b6c03a","source":{"kind":"arxiv","id":"2404.09323","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2404.09323","created_at":"2026-07-05T08:50:55Z"},{"alias_kind":"arxiv_version","alias_value":"2404.09323v3","created_at":"2026-07-05T08:50:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2404.09323","created_at":"2026-07-05T08:50:55Z"},{"alias_kind":"pith_short_12","alias_value":"JZU3JOEKVA7V","created_at":"2026-07-05T08:50:55Z"},{"alias_kind":"pith_short_16","alias_value":"JZU3JOEKVA7VRJ6F","created_at":"2026-07-05T08:50:55Z"},{"alias_kind":"pith_short_8","alias_value":"JZU3JOEK","created_at":"2026-07-05T08:50:55Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:JZU3JOEKVA7VRJ6FRDW4KFQ4MB","target":"record","payload":{"canonical_record":{"source":{"id":"2404.09323","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.OC","submitted_at":"2024-04-14T18:46:54Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"ea1411ad1269fab558d3cda42290cc4022cefc23b07dd84ca36c93878f858f54","abstract_canon_sha256":"d6f1436b383d45270577bfb793c489a81ee37d6dc956fee375bd7b8a57c17880"},"schema_version":"1.0"},"canonical_sha256":"4e69b4b88aa83f58a7c588edc5161c604425d9b0303750b0f0c90dd866b6c03a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T08:50:55.615379Z","signature_b64":"1GzZiSwT7hA93C67zqZcSVCAnNKXdeaVq7WUeE2ZWjesjLhF7MvSLkDGG4Av/RkqECOMXL4ZOQqJrEamvJBUAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4e69b4b88aa83f58a7c588edc5161c604425d9b0303750b0f0c90dd866b6c03a","last_reissued_at":"2026-07-05T08:50:55.614882Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T08:50:55.614882Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2404.09323","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":"2026-07-05T08:50:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LwGhMq2FrKG+BaXNOXc23vh0e/r55CqYdGWdAresHfg9vyBmbfwD4GjZrzjcX6LYbj1sBZhRjveqV9TE2Q8qBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-22T15:46:06.039596Z"},"content_sha256":"b7f591bec6bd9325855180bac4cba9c0945d4dfec6a122a01ee06afb94bed35b","schema_version":"1.0","event_id":"sha256:b7f591bec6bd9325855180bac4cba9c0945d4dfec6a122a01ee06afb94bed35b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:JZU3JOEKVA7VRJ6FRDW4KFQ4MB","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Incremental data compression for PDE-constrained optimization with a data assimilation application","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.OC","authors_text":"John R. Singler, Xiaoming He, Xuejian Li","submitted_at":"2024-04-14T18:46:54Z","abstract_excerpt":"We propose and analyze an inexact gradient method based on incremental proper orthogonal decomposition (iPOD) to address the data storage difficulty in time-dependent PDE-constrained optimization, particularly for a data assimilation problem as a detailed demonstration for the key ideas. The proposed method is proved robust by rigorous analysis. We first derive a sharp data compression error estimate of the iPOD with the help of Hilbert-Schmidt operators. Then we demonstrate a numerical PDE analysis to show how to properly choose the Hilbert space for the iPOD data compression so that the grad"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2404.09323","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2404.09323/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":"2026-07-05T08:50:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"UkWl9AwdZ0KUVRCgtnGKM8ujPohxO+3GZsJFynl5czRNoNtJNixQmcEU0FF7dHPxqALS7IRAsz6H9V2XQXpBDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-22T15:46:06.039971Z"},"content_sha256":"1c6a6c8319959dbf5e8a44e9f06164e753e8d750d7b6fd4015edbc961aa0c6d0","schema_version":"1.0","event_id":"sha256:1c6a6c8319959dbf5e8a44e9f06164e753e8d750d7b6fd4015edbc961aa0c6d0"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/JZU3JOEKVA7VRJ6FRDW4KFQ4MB/bundle.json","state_url":"https://pith.science/pith/JZU3JOEKVA7VRJ6FRDW4KFQ4MB/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/JZU3JOEKVA7VRJ6FRDW4KFQ4MB/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":"2026-08-22T15:46:06Z","links":{"resolver":"https://pith.science/pith/JZU3JOEKVA7VRJ6FRDW4KFQ4MB","bundle":"https://pith.science/pith/JZU3JOEKVA7VRJ6FRDW4KFQ4MB/bundle.json","state":"https://pith.science/pith/JZU3JOEKVA7VRJ6FRDW4KFQ4MB/state.json","well_known_bundle":"https://pith.science/.well-known/pith/JZU3JOEKVA7VRJ6FRDW4KFQ4MB/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:JZU3JOEKVA7VRJ6FRDW4KFQ4MB","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":"d6f1436b383d45270577bfb793c489a81ee37d6dc956fee375bd7b8a57c17880","cross_cats_sorted":["math.AP"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.OC","submitted_at":"2024-04-14T18:46:54Z","title_canon_sha256":"ea1411ad1269fab558d3cda42290cc4022cefc23b07dd84ca36c93878f858f54"},"schema_version":"1.0","source":{"id":"2404.09323","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2404.09323","created_at":"2026-07-05T08:50:55Z"},{"alias_kind":"arxiv_version","alias_value":"2404.09323v3","created_at":"2026-07-05T08:50:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2404.09323","created_at":"2026-07-05T08:50:55Z"},{"alias_kind":"pith_short_12","alias_value":"JZU3JOEKVA7V","created_at":"2026-07-05T08:50:55Z"},{"alias_kind":"pith_short_16","alias_value":"JZU3JOEKVA7VRJ6F","created_at":"2026-07-05T08:50:55Z"},{"alias_kind":"pith_short_8","alias_value":"JZU3JOEK","created_at":"2026-07-05T08:50:55Z"}],"graph_snapshots":[{"event_id":"sha256:1c6a6c8319959dbf5e8a44e9f06164e753e8d750d7b6fd4015edbc961aa0c6d0","target":"graph","created_at":"2026-07-05T08:50:55Z","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/2404.09323/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We propose and analyze an inexact gradient method based on incremental proper orthogonal decomposition (iPOD) to address the data storage difficulty in time-dependent PDE-constrained optimization, particularly for a data assimilation problem as a detailed demonstration for the key ideas. The proposed method is proved robust by rigorous analysis. We first derive a sharp data compression error estimate of the iPOD with the help of Hilbert-Schmidt operators. Then we demonstrate a numerical PDE analysis to show how to properly choose the Hilbert space for the iPOD data compression so that the grad","authors_text":"John R. Singler, Xiaoming He, Xuejian Li","cross_cats":["math.AP"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.OC","submitted_at":"2024-04-14T18:46:54Z","title":"Incremental data compression for PDE-constrained optimization with a data assimilation application"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2404.09323","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:b7f591bec6bd9325855180bac4cba9c0945d4dfec6a122a01ee06afb94bed35b","target":"record","created_at":"2026-07-05T08:50:55Z","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":"d6f1436b383d45270577bfb793c489a81ee37d6dc956fee375bd7b8a57c17880","cross_cats_sorted":["math.AP"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.OC","submitted_at":"2024-04-14T18:46:54Z","title_canon_sha256":"ea1411ad1269fab558d3cda42290cc4022cefc23b07dd84ca36c93878f858f54"},"schema_version":"1.0","source":{"id":"2404.09323","kind":"arxiv","version":3}},"canonical_sha256":"4e69b4b88aa83f58a7c588edc5161c604425d9b0303750b0f0c90dd866b6c03a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4e69b4b88aa83f58a7c588edc5161c604425d9b0303750b0f0c90dd866b6c03a","first_computed_at":"2026-07-05T08:50:55.614882Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T08:50:55.614882Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"1GzZiSwT7hA93C67zqZcSVCAnNKXdeaVq7WUeE2ZWjesjLhF7MvSLkDGG4Av/RkqECOMXL4ZOQqJrEamvJBUAw==","signature_status":"signed_v1","signed_at":"2026-07-05T08:50:55.615379Z","signed_message":"canonical_sha256_bytes"},"source_id":"2404.09323","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b7f591bec6bd9325855180bac4cba9c0945d4dfec6a122a01ee06afb94bed35b","sha256:1c6a6c8319959dbf5e8a44e9f06164e753e8d750d7b6fd4015edbc961aa0c6d0"],"state_sha256":"75a62ebc7bf2a7c15333b9b407871a413363b7c06e715d1b08794c9307e83bb0"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pF/WbTYHuZIORRSjoeXmYxmzTnhWuLvOc1p5Q149IaeZU48KcvXo+zbSZ/UolDykdnfGlGJADPBD/4o4JoovDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-22T15:46:06.042742Z","bundle_sha256":"11ec81026f97abf435de5260d8f96d5cd79f0d5758db37808d6994a799578f4c"}}