{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:P2UCQYMRM3U4XD6SYZWT4FA44Q","short_pith_number":"pith:P2UCQYMR","canonical_record":{"source":{"id":"1511.02021","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2015-11-06T10:21:32Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"ac81132f0ad8e27b648e084db2304703fb95fd594ff09bc48297ab77d287ad6a","abstract_canon_sha256":"390d68b425d0a6e134924318d7c02f94cef947a2cee2738275e54d7e769040cc"},"schema_version":"1.0"},"canonical_sha256":"7ea828619166e9cb8fd2c66d3e141ce41ad830cae659fd03687822ede157efaa","source":{"kind":"arxiv","id":"1511.02021","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1511.02021","created_at":"2026-06-04T17:09:44Z"},{"alias_kind":"arxiv_version","alias_value":"1511.02021v2","created_at":"2026-06-04T17:09:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1511.02021","created_at":"2026-06-04T17:09:44Z"},{"alias_kind":"pith_short_12","alias_value":"P2UCQYMRM3U4","created_at":"2026-06-04T17:09:44Z"},{"alias_kind":"pith_short_16","alias_value":"P2UCQYMRM3U4XD6S","created_at":"2026-06-04T17:09:44Z"},{"alias_kind":"pith_short_8","alias_value":"P2UCQYMR","created_at":"2026-06-04T17:09:44Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:P2UCQYMRM3U4XD6SYZWT4FA44Q","target":"record","payload":{"canonical_record":{"source":{"id":"1511.02021","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2015-11-06T10:21:32Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"ac81132f0ad8e27b648e084db2304703fb95fd594ff09bc48297ab77d287ad6a","abstract_canon_sha256":"390d68b425d0a6e134924318d7c02f94cef947a2cee2738275e54d7e769040cc"},"schema_version":"1.0"},"canonical_sha256":"7ea828619166e9cb8fd2c66d3e141ce41ad830cae659fd03687822ede157efaa","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-04T17:09:44.272889Z","signature_b64":"uycpANUafAYFqv2vYt4vWs4HXhSoZ1Nsy0xiT4KOEYyQJyaFnGe0kKtSOLnzSeZNLzQl0rK/sgHpF3O3xwLsDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7ea828619166e9cb8fd2c66d3e141ce41ad830cae659fd03687822ede157efaa","last_reissued_at":"2026-06-04T17:09:44.272382Z","signature_status":"signed_v1","first_computed_at":"2026-06-04T17:09:44.272382Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1511.02021","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-06-04T17:09:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"km5O0yDmdlIB657uu96Xp/6Oq9uq7yR9qQdgfEAZKlOnqjiUKg3raq78LKSjucGchz778hFmCfVe90zjcgGsBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T10:12:23.517330Z"},"content_sha256":"00d0aa2e54d93d5cb28304484e296337691be04a14a7f50a520882003f606a99","schema_version":"1.0","event_id":"sha256:00d0aa2e54d93d5cb28304484e296337691be04a14a7f50a520882003f606a99"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:P2UCQYMRM3U4XD6SYZWT4FA44Q","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Reduced Basis Methods: Success, Limitations and Future Challenges","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"Mario Ohlberger, Stephan Rave","submitted_at":"2015-11-06T10:21:32Z","abstract_excerpt":"Parametric model order reduction using reduced basis methods can be an effective tool for obtaining quickly solvable reduced order models of parametrized partial differential equation problems. With speedups that can reach several orders of magnitude, reduced basis methods enable high fidelity real-time simulations of complex systems and dramatically reduce the computational costs in many-query applications. In this contribution we analyze the methodology, mainly focussing on the theoretical aspects of the approach. In particular we discuss what is known about the convergence properties of the"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.02021","kind":"arxiv","version":2},"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/1511.02021/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":"2026-06-04T17:09:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"d3wWzTN3B3/QgZfpOjlwt2/7NmTR7ujXna9paTKCJL0vr4zLPRd8nStMHXnljpOq8Z1/u2C7W2c44ZF9BZNVCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T10:12:23.518086Z"},"content_sha256":"6be089c76019b8b15c1ce5a4408210c5fb540ea3c7104e79fc7d879271070ece","schema_version":"1.0","event_id":"sha256:6be089c76019b8b15c1ce5a4408210c5fb540ea3c7104e79fc7d879271070ece"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/P2UCQYMRM3U4XD6SYZWT4FA44Q/bundle.json","state_url":"https://pith.science/pith/P2UCQYMRM3U4XD6SYZWT4FA44Q/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/P2UCQYMRM3U4XD6SYZWT4FA44Q/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":"2026-06-10T10:12:23Z","links":{"resolver":"https://pith.science/pith/P2UCQYMRM3U4XD6SYZWT4FA44Q","bundle":"https://pith.science/pith/P2UCQYMRM3U4XD6SYZWT4FA44Q/bundle.json","state":"https://pith.science/pith/P2UCQYMRM3U4XD6SYZWT4FA44Q/state.json","well_known_bundle":"https://pith.science/.well-known/pith/P2UCQYMRM3U4XD6SYZWT4FA44Q/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:P2UCQYMRM3U4XD6SYZWT4FA44Q","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":"390d68b425d0a6e134924318d7c02f94cef947a2cee2738275e54d7e769040cc","cross_cats_sorted":["cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2015-11-06T10:21:32Z","title_canon_sha256":"ac81132f0ad8e27b648e084db2304703fb95fd594ff09bc48297ab77d287ad6a"},"schema_version":"1.0","source":{"id":"1511.02021","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1511.02021","created_at":"2026-06-04T17:09:44Z"},{"alias_kind":"arxiv_version","alias_value":"1511.02021v2","created_at":"2026-06-04T17:09:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1511.02021","created_at":"2026-06-04T17:09:44Z"},{"alias_kind":"pith_short_12","alias_value":"P2UCQYMRM3U4","created_at":"2026-06-04T17:09:44Z"},{"alias_kind":"pith_short_16","alias_value":"P2UCQYMRM3U4XD6S","created_at":"2026-06-04T17:09:44Z"},{"alias_kind":"pith_short_8","alias_value":"P2UCQYMR","created_at":"2026-06-04T17:09:44Z"}],"graph_snapshots":[{"event_id":"sha256:6be089c76019b8b15c1ce5a4408210c5fb540ea3c7104e79fc7d879271070ece","target":"graph","created_at":"2026-06-04T17:09:44Z","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/1511.02021/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Parametric model order reduction using reduced basis methods can be an effective tool for obtaining quickly solvable reduced order models of parametrized partial differential equation problems. With speedups that can reach several orders of magnitude, reduced basis methods enable high fidelity real-time simulations of complex systems and dramatically reduce the computational costs in many-query applications. In this contribution we analyze the methodology, mainly focussing on the theoretical aspects of the approach. In particular we discuss what is known about the convergence properties of the","authors_text":"Mario Ohlberger, Stephan Rave","cross_cats":["cs.NA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2015-11-06T10:21:32Z","title":"Reduced Basis Methods: Success, Limitations and Future Challenges"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.02021","kind":"arxiv","version":2},"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":"sha256:00d0aa2e54d93d5cb28304484e296337691be04a14a7f50a520882003f606a99","target":"record","created_at":"2026-06-04T17:09:44Z","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":"390d68b425d0a6e134924318d7c02f94cef947a2cee2738275e54d7e769040cc","cross_cats_sorted":["cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2015-11-06T10:21:32Z","title_canon_sha256":"ac81132f0ad8e27b648e084db2304703fb95fd594ff09bc48297ab77d287ad6a"},"schema_version":"1.0","source":{"id":"1511.02021","kind":"arxiv","version":2}},"canonical_sha256":"7ea828619166e9cb8fd2c66d3e141ce41ad830cae659fd03687822ede157efaa","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7ea828619166e9cb8fd2c66d3e141ce41ad830cae659fd03687822ede157efaa","first_computed_at":"2026-06-04T17:09:44.272382Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-04T17:09:44.272382Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"uycpANUafAYFqv2vYt4vWs4HXhSoZ1Nsy0xiT4KOEYyQJyaFnGe0kKtSOLnzSeZNLzQl0rK/sgHpF3O3xwLsDA==","signature_status":"signed_v1","signed_at":"2026-06-04T17:09:44.272889Z","signed_message":"canonical_sha256_bytes"},"source_id":"1511.02021","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:00d0aa2e54d93d5cb28304484e296337691be04a14a7f50a520882003f606a99","sha256:6be089c76019b8b15c1ce5a4408210c5fb540ea3c7104e79fc7d879271070ece"],"state_sha256":"f2806447214a497aa5becbe3a573e557a0e84fd39a1a82e36b682673a40b43db"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"r5V3QDUVI5OuYUPeb5OH6ZD4TQWcveHo/AKQHOWkLykhrxmVbaXpdF/O3UPhZmwHkm2HpgsUmmL0W4Jrog2HCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-10T10:12:23.522264Z","bundle_sha256":"725ce8c7cdf71549b1485fd9c551e0c88390c37906a8341f3f980f58fa2c83fc"}}