{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:E4ERPJN7725RFASZ4WUI5B6GHC","short_pith_number":"pith:E4ERPJN7","canonical_record":{"source":{"id":"2409.08401","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2024-09-12T21:14:01Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"1d07fc11ee312c8b4b6be14dae52c9c29c93e0f615fdfa5115f0a70501341d69","abstract_canon_sha256":"70983d37cb7534429c09d7dcc8eb62660164207cde3ecd4eddd584b13cf0deed"},"schema_version":"1.0"},"canonical_sha256":"270917a5bffebb128259e5a88e87c6388ec6cdd49213daf462c31d2b98164ae5","source":{"kind":"arxiv","id":"2409.08401","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2409.08401","created_at":"2026-07-05T09:06:30Z"},{"alias_kind":"arxiv_version","alias_value":"2409.08401v1","created_at":"2026-07-05T09:06:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2409.08401","created_at":"2026-07-05T09:06:30Z"},{"alias_kind":"pith_short_12","alias_value":"E4ERPJN7725R","created_at":"2026-07-05T09:06:30Z"},{"alias_kind":"pith_short_16","alias_value":"E4ERPJN7725RFASZ","created_at":"2026-07-05T09:06:30Z"},{"alias_kind":"pith_short_8","alias_value":"E4ERPJN7","created_at":"2026-07-05T09:06:30Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:E4ERPJN7725RFASZ4WUI5B6GHC","target":"record","payload":{"canonical_record":{"source":{"id":"2409.08401","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2024-09-12T21:14:01Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"1d07fc11ee312c8b4b6be14dae52c9c29c93e0f615fdfa5115f0a70501341d69","abstract_canon_sha256":"70983d37cb7534429c09d7dcc8eb62660164207cde3ecd4eddd584b13cf0deed"},"schema_version":"1.0"},"canonical_sha256":"270917a5bffebb128259e5a88e87c6388ec6cdd49213daf462c31d2b98164ae5","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T09:06:30.596856Z","signature_b64":"HDK7x5gXP/cW7vjeg19+UiNReBCCG/1rXe02ikKOU6PtiLBa+Jk49xxrpPGnw/J+aKGB6b3q2kdhkrhzILO6BQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"270917a5bffebb128259e5a88e87c6388ec6cdd49213daf462c31d2b98164ae5","last_reissued_at":"2026-07-05T09:06:30.596378Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T09:06:30.596378Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2409.08401","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":"2026-07-05T09:06:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ud0+o4h4X5dp61IhagN6NASoyNka6jzrh4DCHMz+I8zIqG2haVJl4kgX/E139/mwhQEQDUVvX2sOeTCa6IWYBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-07T02:45:35.133749Z"},"content_sha256":"dc4e913ff5e32298a10db3385d0792374264f9bc5ad6c9288b820a481ba88d55","schema_version":"1.0","event_id":"sha256:dc4e913ff5e32298a10db3385d0792374264f9bc5ad6c9288b820a481ba88d55"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:E4ERPJN7725RFASZ4WUI5B6GHC","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Local surrogate models with reduced dimensionality via overlapping domain decomposition and proper generalized decomposition","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"Ben J. Evans, Marco Discacciati, Matteo Giacomini","submitted_at":"2024-09-12T21:14:01Z","abstract_excerpt":"We propose an efficient algorithm that combines overlapping domain decomposition and proper generalized decomposition (PGD) to construct surrogate models of linear elliptic parametric problems. The technique is composed of an offline and an online phase that can be implemented in a fully non-intrusive way. The online phase relies on a substructured algebraic formulation of the alternating Schwarz method, while the offline phase exploits the linearity of the boundary value problem to characterize a PGD basis and generate local surrogate models, with minimal parametric dimensionality, in each su"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2409.08401","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/2409.08401/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":"2026-07-05T09:06:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nW+5AepHjHlu70nIkFB7d6PgRDM6CcVuU6tQIgA4kpZHI6PfxmjfB5JwKoPXHasmhRLz+N+9RKFRtY82GZGqAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-07T02:45:35.134126Z"},"content_sha256":"2b4da223ad8f353bd6c81b38c96ef2669ffbaa0059ef87c763b3f90a1135a752","schema_version":"1.0","event_id":"sha256:2b4da223ad8f353bd6c81b38c96ef2669ffbaa0059ef87c763b3f90a1135a752"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/E4ERPJN7725RFASZ4WUI5B6GHC/bundle.json","state_url":"https://pith.science/pith/E4ERPJN7725RFASZ4WUI5B6GHC/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/E4ERPJN7725RFASZ4WUI5B6GHC/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":"2026-07-07T02:45:35Z","links":{"resolver":"https://pith.science/pith/E4ERPJN7725RFASZ4WUI5B6GHC","bundle":"https://pith.science/pith/E4ERPJN7725RFASZ4WUI5B6GHC/bundle.json","state":"https://pith.science/pith/E4ERPJN7725RFASZ4WUI5B6GHC/state.json","well_known_bundle":"https://pith.science/.well-known/pith/E4ERPJN7725RFASZ4WUI5B6GHC/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:E4ERPJN7725RFASZ4WUI5B6GHC","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":"70983d37cb7534429c09d7dcc8eb62660164207cde3ecd4eddd584b13cf0deed","cross_cats_sorted":["cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2024-09-12T21:14:01Z","title_canon_sha256":"1d07fc11ee312c8b4b6be14dae52c9c29c93e0f615fdfa5115f0a70501341d69"},"schema_version":"1.0","source":{"id":"2409.08401","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2409.08401","created_at":"2026-07-05T09:06:30Z"},{"alias_kind":"arxiv_version","alias_value":"2409.08401v1","created_at":"2026-07-05T09:06:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2409.08401","created_at":"2026-07-05T09:06:30Z"},{"alias_kind":"pith_short_12","alias_value":"E4ERPJN7725R","created_at":"2026-07-05T09:06:30Z"},{"alias_kind":"pith_short_16","alias_value":"E4ERPJN7725RFASZ","created_at":"2026-07-05T09:06:30Z"},{"alias_kind":"pith_short_8","alias_value":"E4ERPJN7","created_at":"2026-07-05T09:06:30Z"}],"graph_snapshots":[{"event_id":"sha256:2b4da223ad8f353bd6c81b38c96ef2669ffbaa0059ef87c763b3f90a1135a752","target":"graph","created_at":"2026-07-05T09:06:30Z","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/2409.08401/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We propose an efficient algorithm that combines overlapping domain decomposition and proper generalized decomposition (PGD) to construct surrogate models of linear elliptic parametric problems. The technique is composed of an offline and an online phase that can be implemented in a fully non-intrusive way. The online phase relies on a substructured algebraic formulation of the alternating Schwarz method, while the offline phase exploits the linearity of the boundary value problem to characterize a PGD basis and generate local surrogate models, with minimal parametric dimensionality, in each su","authors_text":"Ben J. Evans, Marco Discacciati, Matteo Giacomini","cross_cats":["cs.NA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2024-09-12T21:14:01Z","title":"Local surrogate models with reduced dimensionality via overlapping domain decomposition and proper generalized decomposition"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2409.08401","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:dc4e913ff5e32298a10db3385d0792374264f9bc5ad6c9288b820a481ba88d55","target":"record","created_at":"2026-07-05T09:06:30Z","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":"70983d37cb7534429c09d7dcc8eb62660164207cde3ecd4eddd584b13cf0deed","cross_cats_sorted":["cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2024-09-12T21:14:01Z","title_canon_sha256":"1d07fc11ee312c8b4b6be14dae52c9c29c93e0f615fdfa5115f0a70501341d69"},"schema_version":"1.0","source":{"id":"2409.08401","kind":"arxiv","version":1}},"canonical_sha256":"270917a5bffebb128259e5a88e87c6388ec6cdd49213daf462c31d2b98164ae5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"270917a5bffebb128259e5a88e87c6388ec6cdd49213daf462c31d2b98164ae5","first_computed_at":"2026-07-05T09:06:30.596378Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T09:06:30.596378Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"HDK7x5gXP/cW7vjeg19+UiNReBCCG/1rXe02ikKOU6PtiLBa+Jk49xxrpPGnw/J+aKGB6b3q2kdhkrhzILO6BQ==","signature_status":"signed_v1","signed_at":"2026-07-05T09:06:30.596856Z","signed_message":"canonical_sha256_bytes"},"source_id":"2409.08401","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:dc4e913ff5e32298a10db3385d0792374264f9bc5ad6c9288b820a481ba88d55","sha256:2b4da223ad8f353bd6c81b38c96ef2669ffbaa0059ef87c763b3f90a1135a752"],"state_sha256":"a0335b3bcd8304e5c1812847cc61695faa549cae074c0d222c8e3d1ff5194723"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7BFZXUtgaq3K428N6h9QIRxugqyl49B+pXa7TcfVDDIwBsNmRO717edscT8YtEouRAhIGzQPJ2raOpkefvNrDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-07T02:45:35.136120Z","bundle_sha256":"1174685f11d7be7e05a38bafd732fbe1e7a6f4c7ae71e065ce554c3c938bf2d4"}}