{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:BJZZVVKL4LDOUBNWPMY2A43MLC","short_pith_number":"pith:BJZZVVKL","canonical_record":{"source":{"id":"1805.00828","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-05-02T14:08:18Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"4e3e681bd81c119ef4e89fe4a1f9871c5de472055954b69ad841ebb3c9033228","abstract_canon_sha256":"9e9622cfbaf6a4f4353483aa476cf8d83456550ba44aac189b876109946999a2"},"schema_version":"1.0"},"canonical_sha256":"0a739ad54be2c6ea05b67b31a0736c58a1dc29306b86737c276af697747fc088","source":{"kind":"arxiv","id":"1805.00828","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1805.00828","created_at":"2026-06-04T19:11:51Z"},{"alias_kind":"arxiv_version","alias_value":"1805.00828v1","created_at":"2026-06-04T19:11:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1805.00828","created_at":"2026-06-04T19:11:51Z"},{"alias_kind":"pith_short_12","alias_value":"BJZZVVKL4LDO","created_at":"2026-06-04T19:11:51Z"},{"alias_kind":"pith_short_16","alias_value":"BJZZVVKL4LDOUBNW","created_at":"2026-06-04T19:11:51Z"},{"alias_kind":"pith_short_8","alias_value":"BJZZVVKL","created_at":"2026-06-04T19:11:51Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:BJZZVVKL4LDOUBNWPMY2A43MLC","target":"record","payload":{"canonical_record":{"source":{"id":"1805.00828","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-05-02T14:08:18Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"4e3e681bd81c119ef4e89fe4a1f9871c5de472055954b69ad841ebb3c9033228","abstract_canon_sha256":"9e9622cfbaf6a4f4353483aa476cf8d83456550ba44aac189b876109946999a2"},"schema_version":"1.0"},"canonical_sha256":"0a739ad54be2c6ea05b67b31a0736c58a1dc29306b86737c276af697747fc088","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-04T19:11:51.181414Z","signature_b64":"UGn4+cU7P8JzAfO1/FiSb3a7nDrAVlbwQ5eBRTRG0p9COk/PSrnTMHXxPp3s+x/+xCX+FExd4PTTErCJsQjpAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0a739ad54be2c6ea05b67b31a0736c58a1dc29306b86737c276af697747fc088","last_reissued_at":"2026-06-04T19:11:51.180950Z","signature_status":"signed_v1","first_computed_at":"2026-06-04T19:11:51.180950Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1805.00828","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":"2026-06-04T19:11:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tG2nrqdDnmhTKoHj8Xjvb7/Kv/es3PMKQQ3mnRjdLFb2/AOqKIHmoIFFNcYCJGZW6FyQev15loSUY8nYe3d6CA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T17:06:34.763479Z"},"content_sha256":"22d8debd5df0869bf239fd4b561dbe5950dd4684fe06c22c6dcc3773e70a4f4a","schema_version":"1.0","event_id":"sha256:22d8debd5df0869bf239fd4b561dbe5950dd4684fe06c22c6dcc3773e70a4f4a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:BJZZVVKL4LDOUBNWPMY2A43MLC","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Weighted reduced order methods for parametrized partial differential equations with random inputs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"Davide Torlo, Francesco Ballarin, Gianluigi Rozza, Luca Venturi","submitted_at":"2018-05-02T14:08:18Z","abstract_excerpt":"In this manuscript we discuss weighted reduced order methods for stochastic partial differential equations. Random inputs (such as forcing terms, equation coefficients, boundary conditions) are considered as parameters of the equations. We take advantage of the resulting parametrized formulation to propose an efficient reduced order model; we also profit by the underlying stochastic assumption in the definition of suitable weights to drive to reduction process. Two viable strategies are discussed, namely the weighted reduced basis method and the weighted proper orthogonal decomposition method."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.00828","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/1805.00828/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":"2026-06-04T19:11:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"BifyKiONomprEABNmEo61NbIfzzvnSW5YRjxO9MGIOgsktlMSS99kHWPTPlHBnCLUALd+vbLoJXP69eFlViqAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T17:06:34.763851Z"},"content_sha256":"ebfddcae73935082ed4f7243ae420749ba9e23f99d97a6c40d08c87af45ec3e2","schema_version":"1.0","event_id":"sha256:ebfddcae73935082ed4f7243ae420749ba9e23f99d97a6c40d08c87af45ec3e2"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/BJZZVVKL4LDOUBNWPMY2A43MLC/bundle.json","state_url":"https://pith.science/pith/BJZZVVKL4LDOUBNWPMY2A43MLC/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/BJZZVVKL4LDOUBNWPMY2A43MLC/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":"2026-06-20T17:06:34Z","links":{"resolver":"https://pith.science/pith/BJZZVVKL4LDOUBNWPMY2A43MLC","bundle":"https://pith.science/pith/BJZZVVKL4LDOUBNWPMY2A43MLC/bundle.json","state":"https://pith.science/pith/BJZZVVKL4LDOUBNWPMY2A43MLC/state.json","well_known_bundle":"https://pith.science/.well-known/pith/BJZZVVKL4LDOUBNWPMY2A43MLC/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:BJZZVVKL4LDOUBNWPMY2A43MLC","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":"9e9622cfbaf6a4f4353483aa476cf8d83456550ba44aac189b876109946999a2","cross_cats_sorted":["cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-05-02T14:08:18Z","title_canon_sha256":"4e3e681bd81c119ef4e89fe4a1f9871c5de472055954b69ad841ebb3c9033228"},"schema_version":"1.0","source":{"id":"1805.00828","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1805.00828","created_at":"2026-06-04T19:11:51Z"},{"alias_kind":"arxiv_version","alias_value":"1805.00828v1","created_at":"2026-06-04T19:11:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1805.00828","created_at":"2026-06-04T19:11:51Z"},{"alias_kind":"pith_short_12","alias_value":"BJZZVVKL4LDO","created_at":"2026-06-04T19:11:51Z"},{"alias_kind":"pith_short_16","alias_value":"BJZZVVKL4LDOUBNW","created_at":"2026-06-04T19:11:51Z"},{"alias_kind":"pith_short_8","alias_value":"BJZZVVKL","created_at":"2026-06-04T19:11:51Z"}],"graph_snapshots":[{"event_id":"sha256:ebfddcae73935082ed4f7243ae420749ba9e23f99d97a6c40d08c87af45ec3e2","target":"graph","created_at":"2026-06-04T19:11:51Z","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/1805.00828/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this manuscript we discuss weighted reduced order methods for stochastic partial differential equations. Random inputs (such as forcing terms, equation coefficients, boundary conditions) are considered as parameters of the equations. We take advantage of the resulting parametrized formulation to propose an efficient reduced order model; we also profit by the underlying stochastic assumption in the definition of suitable weights to drive to reduction process. Two viable strategies are discussed, namely the weighted reduced basis method and the weighted proper orthogonal decomposition method.","authors_text":"Davide Torlo, Francesco Ballarin, Gianluigi Rozza, Luca Venturi","cross_cats":["cs.NA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-05-02T14:08:18Z","title":"Weighted reduced order methods for parametrized partial differential equations with random inputs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.00828","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":"sha256:22d8debd5df0869bf239fd4b561dbe5950dd4684fe06c22c6dcc3773e70a4f4a","target":"record","created_at":"2026-06-04T19:11:51Z","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":"9e9622cfbaf6a4f4353483aa476cf8d83456550ba44aac189b876109946999a2","cross_cats_sorted":["cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-05-02T14:08:18Z","title_canon_sha256":"4e3e681bd81c119ef4e89fe4a1f9871c5de472055954b69ad841ebb3c9033228"},"schema_version":"1.0","source":{"id":"1805.00828","kind":"arxiv","version":1}},"canonical_sha256":"0a739ad54be2c6ea05b67b31a0736c58a1dc29306b86737c276af697747fc088","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0a739ad54be2c6ea05b67b31a0736c58a1dc29306b86737c276af697747fc088","first_computed_at":"2026-06-04T19:11:51.180950Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-04T19:11:51.180950Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"UGn4+cU7P8JzAfO1/FiSb3a7nDrAVlbwQ5eBRTRG0p9COk/PSrnTMHXxPp3s+x/+xCX+FExd4PTTErCJsQjpAQ==","signature_status":"signed_v1","signed_at":"2026-06-04T19:11:51.181414Z","signed_message":"canonical_sha256_bytes"},"source_id":"1805.00828","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:22d8debd5df0869bf239fd4b561dbe5950dd4684fe06c22c6dcc3773e70a4f4a","sha256:ebfddcae73935082ed4f7243ae420749ba9e23f99d97a6c40d08c87af45ec3e2"],"state_sha256":"9b0813a69022e27f42dd75eb5d2968d6c35bccc26a095b13b6533c4a7791a19d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hyNVtwVV4uE772P8uugkDZD+DUEVkWO8iQReviOAtMy3YRqkT6fP3T42XaAqSPJafZNrO5IGSBarQ8XhJaL3Ag==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-20T17:06:34.765786Z","bundle_sha256":"adde6abd59262fb4a55f6b41d142a60e745c9b282dbc900bd72e59dc66e4bf63"}}