{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2022:7GWV4UVQX24FX2B7CMWMA6NXVN","short_pith_number":"pith:7GWV4UVQ","canonical_record":{"source":{"id":"2202.09872","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.NA","submitted_at":"2022-02-20T17:39:46Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"011e06d7d123e10d1dbd747d2713eb57d94cb979184248c3ee568a50b2870fd9","abstract_canon_sha256":"1db707d3d6656bf03e7f3e9030f0fe35883e26ba0766dd9a05e1c065bc92cb45"},"schema_version":"1.0"},"canonical_sha256":"f9ad5e52b0beb85be83f132cc079b7ab6bbee268aaf2ec95c24ece2b704a71c4","source":{"kind":"arxiv","id":"2202.09872","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2202.09872","created_at":"2026-07-05T03:58:26Z"},{"alias_kind":"arxiv_version","alias_value":"2202.09872v1","created_at":"2026-07-05T03:58:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2202.09872","created_at":"2026-07-05T03:58:26Z"},{"alias_kind":"pith_short_12","alias_value":"7GWV4UVQX24F","created_at":"2026-07-05T03:58:26Z"},{"alias_kind":"pith_short_16","alias_value":"7GWV4UVQX24FX2B7","created_at":"2026-07-05T03:58:26Z"},{"alias_kind":"pith_short_8","alias_value":"7GWV4UVQ","created_at":"2026-07-05T03:58:26Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2022:7GWV4UVQX24FX2B7CMWMA6NXVN","target":"record","payload":{"canonical_record":{"source":{"id":"2202.09872","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.NA","submitted_at":"2022-02-20T17:39:46Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"011e06d7d123e10d1dbd747d2713eb57d94cb979184248c3ee568a50b2870fd9","abstract_canon_sha256":"1db707d3d6656bf03e7f3e9030f0fe35883e26ba0766dd9a05e1c065bc92cb45"},"schema_version":"1.0"},"canonical_sha256":"f9ad5e52b0beb85be83f132cc079b7ab6bbee268aaf2ec95c24ece2b704a71c4","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T03:58:26.920154Z","signature_b64":"UbfRwZ61Lw3cLhi5UOZbYRksZ4tJZ4RfrHlUihB5Lrjo+eyhguqJwYWNdu6UUEL6L2Vy7pqS9cM+zgFSdXgZCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f9ad5e52b0beb85be83f132cc079b7ab6bbee268aaf2ec95c24ece2b704a71c4","last_reissued_at":"2026-07-05T03:58:26.919765Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T03:58:26.919765Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2202.09872","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":"2026-07-05T03:58:26Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"F0ezYheksp6PXTa0IhzEEupoZ/+qhBpAGYYKVJIr5E79Cm3YDtSzFgvvbbVRCvmSL501+xenTiFYVgosQirBCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-19T05:27:31.680977Z"},"content_sha256":"836165c29458fa3ef5bb3936afdf1f9dc87f8631cf2d0d8335af86380b01d0b3","schema_version":"1.0","event_id":"sha256:836165c29458fa3ef5bb3936afdf1f9dc87f8631cf2d0d8335af86380b01d0b3"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2022:7GWV4UVQX24FX2B7CMWMA6NXVN","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Localized model reduction for nonlinear elliptic partial differential equations: localized training, partition of unity, and adaptive enrichment","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"Kathrin Smetana, Tommaso Taddei","submitted_at":"2022-02-20T17:39:46Z","abstract_excerpt":"We propose a component-based (CB) parametric model order reduction (pMOR) formulation for parameterized {nonlinear} elliptic partial differential equations (PDEs). CB-pMOR is designed to deal with large-scale problems for which full-order solves are not affordable in a reasonable time frame or parameters' variations induce topology changes that prevent the application of monolithic pMOR techniques. We rely on the partition-of-unity method (PUM) to devise global approximation spaces from local reduced spaces, and on Galerkin projection to compute the global state estimate. We propose a randomiz"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2202.09872","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/2202.09872/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":"2026-07-05T03:58:26Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6ZwWqQGfR3llZ552t4UaXkQe6Qys7D1yHAiaHFEveKUCkwu9pivVImpPbira2LjChqyLzIJ/VXO7YInV85/tCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-19T05:27:31.681504Z"},"content_sha256":"fe6c6daaf8ff64326bf9dbfb06e66f01fdf5bc851cc05e1b46ca09e9a388c0f6","schema_version":"1.0","event_id":"sha256:fe6c6daaf8ff64326bf9dbfb06e66f01fdf5bc851cc05e1b46ca09e9a388c0f6"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/7GWV4UVQX24FX2B7CMWMA6NXVN/bundle.json","state_url":"https://pith.science/pith/7GWV4UVQX24FX2B7CMWMA6NXVN/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/7GWV4UVQX24FX2B7CMWMA6NXVN/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":"2026-08-19T05:27:31Z","links":{"resolver":"https://pith.science/pith/7GWV4UVQX24FX2B7CMWMA6NXVN","bundle":"https://pith.science/pith/7GWV4UVQX24FX2B7CMWMA6NXVN/bundle.json","state":"https://pith.science/pith/7GWV4UVQX24FX2B7CMWMA6NXVN/state.json","well_known_bundle":"https://pith.science/.well-known/pith/7GWV4UVQX24FX2B7CMWMA6NXVN/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:7GWV4UVQX24FX2B7CMWMA6NXVN","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":"1db707d3d6656bf03e7f3e9030f0fe35883e26ba0766dd9a05e1c065bc92cb45","cross_cats_sorted":["cs.NA"],"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.NA","submitted_at":"2022-02-20T17:39:46Z","title_canon_sha256":"011e06d7d123e10d1dbd747d2713eb57d94cb979184248c3ee568a50b2870fd9"},"schema_version":"1.0","source":{"id":"2202.09872","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2202.09872","created_at":"2026-07-05T03:58:26Z"},{"alias_kind":"arxiv_version","alias_value":"2202.09872v1","created_at":"2026-07-05T03:58:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2202.09872","created_at":"2026-07-05T03:58:26Z"},{"alias_kind":"pith_short_12","alias_value":"7GWV4UVQX24F","created_at":"2026-07-05T03:58:26Z"},{"alias_kind":"pith_short_16","alias_value":"7GWV4UVQX24FX2B7","created_at":"2026-07-05T03:58:26Z"},{"alias_kind":"pith_short_8","alias_value":"7GWV4UVQ","created_at":"2026-07-05T03:58:26Z"}],"graph_snapshots":[{"event_id":"sha256:fe6c6daaf8ff64326bf9dbfb06e66f01fdf5bc851cc05e1b46ca09e9a388c0f6","target":"graph","created_at":"2026-07-05T03:58:26Z","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/2202.09872/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We propose a component-based (CB) parametric model order reduction (pMOR) formulation for parameterized {nonlinear} elliptic partial differential equations (PDEs). CB-pMOR is designed to deal with large-scale problems for which full-order solves are not affordable in a reasonable time frame or parameters' variations induce topology changes that prevent the application of monolithic pMOR techniques. We rely on the partition-of-unity method (PUM) to devise global approximation spaces from local reduced spaces, and on Galerkin projection to compute the global state estimate. We propose a randomiz","authors_text":"Kathrin Smetana, Tommaso Taddei","cross_cats":["cs.NA"],"headline":"","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.NA","submitted_at":"2022-02-20T17:39:46Z","title":"Localized model reduction for nonlinear elliptic partial differential equations: localized training, partition of unity, and adaptive enrichment"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2202.09872","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":"sha256:836165c29458fa3ef5bb3936afdf1f9dc87f8631cf2d0d8335af86380b01d0b3","target":"record","created_at":"2026-07-05T03:58:26Z","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":"1db707d3d6656bf03e7f3e9030f0fe35883e26ba0766dd9a05e1c065bc92cb45","cross_cats_sorted":["cs.NA"],"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.NA","submitted_at":"2022-02-20T17:39:46Z","title_canon_sha256":"011e06d7d123e10d1dbd747d2713eb57d94cb979184248c3ee568a50b2870fd9"},"schema_version":"1.0","source":{"id":"2202.09872","kind":"arxiv","version":1}},"canonical_sha256":"f9ad5e52b0beb85be83f132cc079b7ab6bbee268aaf2ec95c24ece2b704a71c4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f9ad5e52b0beb85be83f132cc079b7ab6bbee268aaf2ec95c24ece2b704a71c4","first_computed_at":"2026-07-05T03:58:26.919765Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T03:58:26.919765Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"UbfRwZ61Lw3cLhi5UOZbYRksZ4tJZ4RfrHlUihB5Lrjo+eyhguqJwYWNdu6UUEL6L2Vy7pqS9cM+zgFSdXgZCw==","signature_status":"signed_v1","signed_at":"2026-07-05T03:58:26.920154Z","signed_message":"canonical_sha256_bytes"},"source_id":"2202.09872","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:836165c29458fa3ef5bb3936afdf1f9dc87f8631cf2d0d8335af86380b01d0b3","sha256:fe6c6daaf8ff64326bf9dbfb06e66f01fdf5bc851cc05e1b46ca09e9a388c0f6"],"state_sha256":"4e34b9cbef4c0c01c335f5f1169674e2afff234ab3593139f8ae56f604fedda5"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NwkkzSG0IzUEWxV+zUWQrJHhx9HhU+ErbH5F18Ys4+2qFLIq8Bdu55QmG+J9pCBGzkEJHs4CkGwD6jkLLrS2Cw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-19T05:27:31.687392Z","bundle_sha256":"11badf38529efd068f9a82fb70100821e2105a6af18cbf8df922da07c4ec25b2"}}