{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2021:EUV6WFBXNCG7QDVO7BGNBKQHIL","short_pith_number":"pith:EUV6WFBX","canonical_record":{"source":{"id":"2110.07676","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NA","submitted_at":"2021-10-14T19:18:09Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"8fa6cfb1047080f29aacd7bd16f3305b59d9a60a973da30faceb1cc520a69d86","abstract_canon_sha256":"4bfacc3fdd5c1584b7128003421ce95bac27232ac4c04cdb78e4d9575ea9563a"},"schema_version":"1.0"},"canonical_sha256":"252beb1437688df80eaef84cd0aa0742f089f40c7123430d17904cc8df5e58c0","source":{"kind":"arxiv","id":"2110.07676","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2110.07676","created_at":"2026-07-05T03:22:48Z"},{"alias_kind":"arxiv_version","alias_value":"2110.07676v1","created_at":"2026-07-05T03:22:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2110.07676","created_at":"2026-07-05T03:22:48Z"},{"alias_kind":"pith_short_12","alias_value":"EUV6WFBXNCG7","created_at":"2026-07-05T03:22:48Z"},{"alias_kind":"pith_short_16","alias_value":"EUV6WFBXNCG7QDVO","created_at":"2026-07-05T03:22:48Z"},{"alias_kind":"pith_short_8","alias_value":"EUV6WFBX","created_at":"2026-07-05T03:22:48Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2021:EUV6WFBXNCG7QDVO7BGNBKQHIL","target":"record","payload":{"canonical_record":{"source":{"id":"2110.07676","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NA","submitted_at":"2021-10-14T19:18:09Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"8fa6cfb1047080f29aacd7bd16f3305b59d9a60a973da30faceb1cc520a69d86","abstract_canon_sha256":"4bfacc3fdd5c1584b7128003421ce95bac27232ac4c04cdb78e4d9575ea9563a"},"schema_version":"1.0"},"canonical_sha256":"252beb1437688df80eaef84cd0aa0742f089f40c7123430d17904cc8df5e58c0","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T03:22:48.662358Z","signature_b64":"mlVqKiHNwNlzxk+K7AIMZV1VO2x+wb2+eXv7sYfGam8dDpxji8f1zGowJZK1jdzjE+vuXXAmpYxtIy8lHbkGCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"252beb1437688df80eaef84cd0aa0742f089f40c7123430d17904cc8df5e58c0","last_reissued_at":"2026-07-05T03:22:48.661877Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T03:22:48.661877Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2110.07676","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":"2026-07-05T03:22:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZEoZJWP9xYrinlbHS024YsJVJseiQ7zJOuSTWwd8sqP7ZeVQbSYzd8GsfwixIuJ7Yp6f/gdo2WMiL7gYUCALDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-14T06:54:13.633267Z"},"content_sha256":"df8d209f0107c807ea710979338de269cbf4cd6f9a7891bf588a5f47ce82fae5","schema_version":"1.0","event_id":"sha256:df8d209f0107c807ea710979338de269cbf4cd6f9a7891bf588a5f47ce82fae5"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2021:EUV6WFBXNCG7QDVO7BGNBKQHIL","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A data-driven model reduction method for parabolic inverse source problems and its convergence analysis","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"Wenlong Zhang, Zhiwen Zhang, Zhongjian Wang","submitted_at":"2021-10-14T19:18:09Z","abstract_excerpt":"In this paper, we propose a data-driven model reduction method to solve parabolic inverse source problems efficiently. Our method consists of offline and online stages. In the off-line stage, we explore the low-dimensional structures in the solution space of the parabolic partial differential equations (PDEs) in the forward problem with a given class of source functions and construct a small number of proper orthogonal decomposition (POD) basis functions to achieve significant dimension reduction. Equipped with the POD basis functions, we can solve the forward problem extremely fast in the onl"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2110.07676","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/2110.07676/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":"2026-07-05T03:22:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"EAHD+79t9IcyieV1y8coMXwZumOKcFhzdtJaXi7mIX4dT7f8DOrt0kqW/CK2GLeNWjC7HusIqcEAAutsY3+dAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-14T06:54:13.633777Z"},"content_sha256":"70483e6fa5857ef4b6f5a514b7fbb0d80ccb3aee5dd0c9d445ca298d7555acf3","schema_version":"1.0","event_id":"sha256:70483e6fa5857ef4b6f5a514b7fbb0d80ccb3aee5dd0c9d445ca298d7555acf3"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/EUV6WFBXNCG7QDVO7BGNBKQHIL/bundle.json","state_url":"https://pith.science/pith/EUV6WFBXNCG7QDVO7BGNBKQHIL/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/EUV6WFBXNCG7QDVO7BGNBKQHIL/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":"2026-08-14T06:54:13Z","links":{"resolver":"https://pith.science/pith/EUV6WFBXNCG7QDVO7BGNBKQHIL","bundle":"https://pith.science/pith/EUV6WFBXNCG7QDVO7BGNBKQHIL/bundle.json","state":"https://pith.science/pith/EUV6WFBXNCG7QDVO7BGNBKQHIL/state.json","well_known_bundle":"https://pith.science/.well-known/pith/EUV6WFBXNCG7QDVO7BGNBKQHIL/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:EUV6WFBXNCG7QDVO7BGNBKQHIL","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":"4bfacc3fdd5c1584b7128003421ce95bac27232ac4c04cdb78e4d9575ea9563a","cross_cats_sorted":["cs.NA"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NA","submitted_at":"2021-10-14T19:18:09Z","title_canon_sha256":"8fa6cfb1047080f29aacd7bd16f3305b59d9a60a973da30faceb1cc520a69d86"},"schema_version":"1.0","source":{"id":"2110.07676","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2110.07676","created_at":"2026-07-05T03:22:48Z"},{"alias_kind":"arxiv_version","alias_value":"2110.07676v1","created_at":"2026-07-05T03:22:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2110.07676","created_at":"2026-07-05T03:22:48Z"},{"alias_kind":"pith_short_12","alias_value":"EUV6WFBXNCG7","created_at":"2026-07-05T03:22:48Z"},{"alias_kind":"pith_short_16","alias_value":"EUV6WFBXNCG7QDVO","created_at":"2026-07-05T03:22:48Z"},{"alias_kind":"pith_short_8","alias_value":"EUV6WFBX","created_at":"2026-07-05T03:22:48Z"}],"graph_snapshots":[{"event_id":"sha256:70483e6fa5857ef4b6f5a514b7fbb0d80ccb3aee5dd0c9d445ca298d7555acf3","target":"graph","created_at":"2026-07-05T03:22:48Z","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/2110.07676/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper, we propose a data-driven model reduction method to solve parabolic inverse source problems efficiently. Our method consists of offline and online stages. In the off-line stage, we explore the low-dimensional structures in the solution space of the parabolic partial differential equations (PDEs) in the forward problem with a given class of source functions and construct a small number of proper orthogonal decomposition (POD) basis functions to achieve significant dimension reduction. Equipped with the POD basis functions, we can solve the forward problem extremely fast in the onl","authors_text":"Wenlong Zhang, Zhiwen Zhang, Zhongjian Wang","cross_cats":["cs.NA"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NA","submitted_at":"2021-10-14T19:18:09Z","title":"A data-driven model reduction method for parabolic inverse source problems and its convergence analysis"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2110.07676","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:df8d209f0107c807ea710979338de269cbf4cd6f9a7891bf588a5f47ce82fae5","target":"record","created_at":"2026-07-05T03:22:48Z","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":"4bfacc3fdd5c1584b7128003421ce95bac27232ac4c04cdb78e4d9575ea9563a","cross_cats_sorted":["cs.NA"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NA","submitted_at":"2021-10-14T19:18:09Z","title_canon_sha256":"8fa6cfb1047080f29aacd7bd16f3305b59d9a60a973da30faceb1cc520a69d86"},"schema_version":"1.0","source":{"id":"2110.07676","kind":"arxiv","version":1}},"canonical_sha256":"252beb1437688df80eaef84cd0aa0742f089f40c7123430d17904cc8df5e58c0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"252beb1437688df80eaef84cd0aa0742f089f40c7123430d17904cc8df5e58c0","first_computed_at":"2026-07-05T03:22:48.661877Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T03:22:48.661877Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"mlVqKiHNwNlzxk+K7AIMZV1VO2x+wb2+eXv7sYfGam8dDpxji8f1zGowJZK1jdzjE+vuXXAmpYxtIy8lHbkGCw==","signature_status":"signed_v1","signed_at":"2026-07-05T03:22:48.662358Z","signed_message":"canonical_sha256_bytes"},"source_id":"2110.07676","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:df8d209f0107c807ea710979338de269cbf4cd6f9a7891bf588a5f47ce82fae5","sha256:70483e6fa5857ef4b6f5a514b7fbb0d80ccb3aee5dd0c9d445ca298d7555acf3"],"state_sha256":"09d5358fbce327ff883dd1b5cfec7e957005233a542d5a613941b2e10731ecb7"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gZM1MS8PxGY29zpRMWIjyKayLEfuUCYFZs37tTdhitFcK3oRAxGw6/ThquehSSrQYvjLIP3FN/ed0sNeTyheBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-14T06:54:13.639531Z","bundle_sha256":"2e8420958c758fb117eb23f8ea37e4059b28301c93740ec3ee79fb1bf8e6fc1d"}}