{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:5E3JHTB3O7XHI6GWWQOIPSOFTQ","short_pith_number":"pith:5E3JHTB3","canonical_record":{"source":{"id":"1303.6618","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-03-26T19:37:12Z","cross_cats_sorted":["math.NA","stat.CO"],"title_canon_sha256":"a3713ea43e529a58d27b7a70d5130c50b195fc0c497f1da7ccd71d355120a2a0","abstract_canon_sha256":"4502f74bf5998dab01fc39e6444c08bcefdd32979e4c7c735e7aa1f91606f119"},"schema_version":"1.0"},"canonical_sha256":"e93693cc3b77ee7478d6b41c87c9c59c069f039982e1cbbd609916cac8732432","source":{"kind":"arxiv","id":"1303.6618","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1303.6618","created_at":"2026-05-18T02:48:01Z"},{"alias_kind":"arxiv_version","alias_value":"1303.6618v2","created_at":"2026-05-18T02:48:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1303.6618","created_at":"2026-05-18T02:48:01Z"},{"alias_kind":"pith_short_12","alias_value":"5E3JHTB3O7XH","created_at":"2026-05-18T12:27:34Z"},{"alias_kind":"pith_short_16","alias_value":"5E3JHTB3O7XHI6GW","created_at":"2026-05-18T12:27:34Z"},{"alias_kind":"pith_short_8","alias_value":"5E3JHTB3","created_at":"2026-05-18T12:27:34Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:5E3JHTB3O7XHI6GWWQOIPSOFTQ","target":"record","payload":{"canonical_record":{"source":{"id":"1303.6618","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-03-26T19:37:12Z","cross_cats_sorted":["math.NA","stat.CO"],"title_canon_sha256":"a3713ea43e529a58d27b7a70d5130c50b195fc0c497f1da7ccd71d355120a2a0","abstract_canon_sha256":"4502f74bf5998dab01fc39e6444c08bcefdd32979e4c7c735e7aa1f91606f119"},"schema_version":"1.0"},"canonical_sha256":"e93693cc3b77ee7478d6b41c87c9c59c069f039982e1cbbd609916cac8732432","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:48:01.136175Z","signature_b64":"nGym1QQgL/xKsDtBSYRrv6Jpw2vK/I1BLBP+9fu3J7HUaPSlkGAaS0P/faTHPeE6xQ0Wib/gx7AqnTRLSLEgCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e93693cc3b77ee7478d6b41c87c9c59c069f039982e1cbbd609916cac8732432","last_reissued_at":"2026-05-18T02:48:01.135670Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:48:01.135670Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1303.6618","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":"2026-05-18T02:48:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Zn+ezzDafYCQHRe3dBKrwRAlZ7YxjS1Q4guBAYFuPrvdInimEMSe8X7UcRNz4XYbAFpEjlfUB9V9brcTITKoCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T14:41:38.906451Z"},"content_sha256":"1bb7992640d0ac193dd1176f1f4cafca28f4c606e7953622ebbdf5d9994c7cf0","schema_version":"1.0","event_id":"sha256:1bb7992640d0ac193dd1176f1f4cafca28f4c606e7953622ebbdf5d9994c7cf0"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:5E3JHTB3O7XHI6GWWQOIPSOFTQ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Goal-oriented error estimation for the reduced basis method, with application to sensitivity analysis","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NA","stat.CO"],"primary_cat":"math.AP","authors_text":"Alexandre Janon (- M\\'ethodes d'Analyse Stochastique des Codes et Traitements Num\\'eriques, Cl\\'ementine Prieur (- M\\'ethodes d'Analyse Stochastique des Codes et Traitements Num\\'eriques, INRIA Grenoble Rh\\^one-Alpes / LJK Laboratoire Jean Kuntzmann), LM-Orsay), Ma\\\"elle Nodet (- M\\'ethodes d'Analyse Stochastique des Codes et Traitements Num\\'eriques","submitted_at":"2013-03-26T19:37:12Z","abstract_excerpt":"The reduced basis method is a powerful model reduction technique designed to speed up the computation of multiple numerical solutions of parametrized partial differential equations. We consider a quantity of interest, which is a linear functional of the PDE solution. A new probabilistic error bound for the reduced model is proposed. It is efficiently and explicitly computable, and we show on different examples that this error bound is sharper than existing ones. We include application of our work to sensitivity analysis studies."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1303.6618","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":""},"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":"2026-05-18T02:48:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"M2dXsdDXtMF5KX6uBSkskLeuGvi0uW8V4M/Jpp2gz8s+a/F1FTmJ6fXy8joFIkj5uj1miJtQGkLqQvJVo1SICA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T14:41:38.907060Z"},"content_sha256":"beb6d5ab524efce4941f5cc49cc8a98f4e8938ed49c923be80a9d0050f64b9b7","schema_version":"1.0","event_id":"sha256:beb6d5ab524efce4941f5cc49cc8a98f4e8938ed49c923be80a9d0050f64b9b7"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/5E3JHTB3O7XHI6GWWQOIPSOFTQ/bundle.json","state_url":"https://pith.science/pith/5E3JHTB3O7XHI6GWWQOIPSOFTQ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/5E3JHTB3O7XHI6GWWQOIPSOFTQ/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":"2026-05-31T14:41:38Z","links":{"resolver":"https://pith.science/pith/5E3JHTB3O7XHI6GWWQOIPSOFTQ","bundle":"https://pith.science/pith/5E3JHTB3O7XHI6GWWQOIPSOFTQ/bundle.json","state":"https://pith.science/pith/5E3JHTB3O7XHI6GWWQOIPSOFTQ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/5E3JHTB3O7XHI6GWWQOIPSOFTQ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:5E3JHTB3O7XHI6GWWQOIPSOFTQ","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":"4502f74bf5998dab01fc39e6444c08bcefdd32979e4c7c735e7aa1f91606f119","cross_cats_sorted":["math.NA","stat.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-03-26T19:37:12Z","title_canon_sha256":"a3713ea43e529a58d27b7a70d5130c50b195fc0c497f1da7ccd71d355120a2a0"},"schema_version":"1.0","source":{"id":"1303.6618","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1303.6618","created_at":"2026-05-18T02:48:01Z"},{"alias_kind":"arxiv_version","alias_value":"1303.6618v2","created_at":"2026-05-18T02:48:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1303.6618","created_at":"2026-05-18T02:48:01Z"},{"alias_kind":"pith_short_12","alias_value":"5E3JHTB3O7XH","created_at":"2026-05-18T12:27:34Z"},{"alias_kind":"pith_short_16","alias_value":"5E3JHTB3O7XHI6GW","created_at":"2026-05-18T12:27:34Z"},{"alias_kind":"pith_short_8","alias_value":"5E3JHTB3","created_at":"2026-05-18T12:27:34Z"}],"graph_snapshots":[{"event_id":"sha256:beb6d5ab524efce4941f5cc49cc8a98f4e8938ed49c923be80a9d0050f64b9b7","target":"graph","created_at":"2026-05-18T02:48:01Z","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"},"paper":{"abstract_excerpt":"The reduced basis method is a powerful model reduction technique designed to speed up the computation of multiple numerical solutions of parametrized partial differential equations. We consider a quantity of interest, which is a linear functional of the PDE solution. A new probabilistic error bound for the reduced model is proposed. It is efficiently and explicitly computable, and we show on different examples that this error bound is sharper than existing ones. We include application of our work to sensitivity analysis studies.","authors_text":"Alexandre Janon (- M\\'ethodes d'Analyse Stochastique des Codes et Traitements Num\\'eriques, Cl\\'ementine Prieur (- M\\'ethodes d'Analyse Stochastique des Codes et Traitements Num\\'eriques, INRIA Grenoble Rh\\^one-Alpes / LJK Laboratoire Jean Kuntzmann), LM-Orsay), Ma\\\"elle Nodet (- M\\'ethodes d'Analyse Stochastique des Codes et Traitements Num\\'eriques","cross_cats":["math.NA","stat.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-03-26T19:37:12Z","title":"Goal-oriented error estimation for the reduced basis method, with application to sensitivity analysis"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1303.6618","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":"sha256:1bb7992640d0ac193dd1176f1f4cafca28f4c606e7953622ebbdf5d9994c7cf0","target":"record","created_at":"2026-05-18T02:48:01Z","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":"4502f74bf5998dab01fc39e6444c08bcefdd32979e4c7c735e7aa1f91606f119","cross_cats_sorted":["math.NA","stat.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-03-26T19:37:12Z","title_canon_sha256":"a3713ea43e529a58d27b7a70d5130c50b195fc0c497f1da7ccd71d355120a2a0"},"schema_version":"1.0","source":{"id":"1303.6618","kind":"arxiv","version":2}},"canonical_sha256":"e93693cc3b77ee7478d6b41c87c9c59c069f039982e1cbbd609916cac8732432","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e93693cc3b77ee7478d6b41c87c9c59c069f039982e1cbbd609916cac8732432","first_computed_at":"2026-05-18T02:48:01.135670Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:48:01.135670Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"nGym1QQgL/xKsDtBSYRrv6Jpw2vK/I1BLBP+9fu3J7HUaPSlkGAaS0P/faTHPeE6xQ0Wib/gx7AqnTRLSLEgCg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:48:01.136175Z","signed_message":"canonical_sha256_bytes"},"source_id":"1303.6618","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1bb7992640d0ac193dd1176f1f4cafca28f4c606e7953622ebbdf5d9994c7cf0","sha256:beb6d5ab524efce4941f5cc49cc8a98f4e8938ed49c923be80a9d0050f64b9b7"],"state_sha256":"3ad16d999f4d33357a54fa769a1ce2b5fefb66fbff4810cf09b407ef97556a29"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Kaymtvr9k1liEiw6PcBJpnxSfGEqvX2TW2I74nQa4PsDa12uqhnbDWfdt4HiNviAHuny9kZnkYK0m/qPHsklAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T14:41:38.910737Z","bundle_sha256":"757af7eae08335e76141bb31ea01ee997409de8ff8f8bea613afed872fb55cce"}}