{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:WN4MGAFWSXSO45ZHOWL7NQPLJA","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":"f6579b152af590f006ab8b5ff72d05f8d138bb70ec9e2f69381076c3fe93ea52","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2015-03-16T18:32:00Z","title_canon_sha256":"64d7e8b471f8cdd3f5c8377d4bb5162b9ded592232f51d9f305bf6668c002f26"},"schema_version":"1.0","source":{"id":"1503.04760","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1503.04760","created_at":"2026-05-18T02:23:24Z"},{"alias_kind":"arxiv_version","alias_value":"1503.04760v1","created_at":"2026-05-18T02:23:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.04760","created_at":"2026-05-18T02:23:24Z"},{"alias_kind":"pith_short_12","alias_value":"WN4MGAFWSXSO","created_at":"2026-05-18T12:29:47Z"},{"alias_kind":"pith_short_16","alias_value":"WN4MGAFWSXSO45ZH","created_at":"2026-05-18T12:29:47Z"},{"alias_kind":"pith_short_8","alias_value":"WN4MGAFW","created_at":"2026-05-18T12:29:47Z"}],"graph_snapshots":[{"event_id":"sha256:12ec8af162d6717ea339a9f1a4cebabe84a8edf8246e939282ba026b2b206256","target":"graph","created_at":"2026-05-18T02:23:24Z","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":"We present a certified version of the Natural-Norm Successive Constraint Method (cNNSCM) for fast and accurate Inf-Sup lower bound evaluation of parametric operators. Successive Constraint Methods (SCM) are essential tools for the construction of a lower bound for the inf-sup stability constants which are required in {\\it a posteriori} error analysis of reduced basis approximations. They utilize a Linear Program (LP) relaxation scheme incorporating continuity and stability constraints. The natural-norm approach {\\em linearizes} inf-sup constant as a function of the parameter. The Natural-Norm ","authors_text":"Yanlai Chen","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2015-03-16T18:32:00Z","title":"A Certified Natural-Norm Successive Constraint Method for Parametric Inf-Sup Lower Bounds"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.04760","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":"sha256:184d5e39f8f83ce1da6a1d8d06b8ff376c55035342a2230d533f3607b2dc4386","target":"record","created_at":"2026-05-18T02:23:24Z","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":"f6579b152af590f006ab8b5ff72d05f8d138bb70ec9e2f69381076c3fe93ea52","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2015-03-16T18:32:00Z","title_canon_sha256":"64d7e8b471f8cdd3f5c8377d4bb5162b9ded592232f51d9f305bf6668c002f26"},"schema_version":"1.0","source":{"id":"1503.04760","kind":"arxiv","version":1}},"canonical_sha256":"b378c300b695e4ee77277597f6c1eb482c2bd2fa930eb93a270d9653549e0329","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b378c300b695e4ee77277597f6c1eb482c2bd2fa930eb93a270d9653549e0329","first_computed_at":"2026-05-18T02:23:24.093164Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:23:24.093164Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ourgE25iDkCCB9MQ4+lCGOH2QlusbTJZmoUdG1JsAs6sI+EdiDPfMfmbK56+L0ESuDBXKCJBY+8uihZnymMOCg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:23:24.093809Z","signed_message":"canonical_sha256_bytes"},"source_id":"1503.04760","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:184d5e39f8f83ce1da6a1d8d06b8ff376c55035342a2230d533f3607b2dc4386","sha256:12ec8af162d6717ea339a9f1a4cebabe84a8edf8246e939282ba026b2b206256"],"state_sha256":"07b58238da8b3a54703288954ce9091e498f769adf6d2c14bbc18c7cd5e057fb"}