{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2021:742XVVHCKTPWYYDXCY2RSJTYIQ","short_pith_number":"pith:742XVVHC","canonical_record":{"source":{"id":"2112.14064","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NA","submitted_at":"2021-12-28T09:24:01Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"6872534b041e0a5644ed91d141b9db6446324cdbf614722cf94df056d27fc022","abstract_canon_sha256":"a10ac035e5e7a716e98e46a264b1ea700f223a40770466e038a951a8311f0202"},"schema_version":"1.0"},"canonical_sha256":"ff357ad4e254df6c607716351926784422a0b4be690d6511e3537f067995ec85","source":{"kind":"arxiv","id":"2112.14064","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2112.14064","created_at":"2026-07-05T04:43:38Z"},{"alias_kind":"arxiv_version","alias_value":"2112.14064v1","created_at":"2026-07-05T04:43:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2112.14064","created_at":"2026-07-05T04:43:38Z"},{"alias_kind":"pith_short_12","alias_value":"742XVVHCKTPW","created_at":"2026-07-05T04:43:38Z"},{"alias_kind":"pith_short_16","alias_value":"742XVVHCKTPWYYDX","created_at":"2026-07-05T04:43:38Z"},{"alias_kind":"pith_short_8","alias_value":"742XVVHC","created_at":"2026-07-05T04:43:38Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2021:742XVVHCKTPWYYDXCY2RSJTYIQ","target":"record","payload":{"canonical_record":{"source":{"id":"2112.14064","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NA","submitted_at":"2021-12-28T09:24:01Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"6872534b041e0a5644ed91d141b9db6446324cdbf614722cf94df056d27fc022","abstract_canon_sha256":"a10ac035e5e7a716e98e46a264b1ea700f223a40770466e038a951a8311f0202"},"schema_version":"1.0"},"canonical_sha256":"ff357ad4e254df6c607716351926784422a0b4be690d6511e3537f067995ec85","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T04:43:38.253837Z","signature_b64":"WtIIfMMmhiHHV+JvUDYX1u6HpKQ0XHhP6U/SW2FQBjUV8//LkdwyOI0vM9sEzEZdK9wudyIN62ZUTgIos6HtBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ff357ad4e254df6c607716351926784422a0b4be690d6511e3537f067995ec85","last_reissued_at":"2026-07-05T04:43:38.253486Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T04:43:38.253486Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2112.14064","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":"2026-07-05T04:43:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"AHwmrkEH+l2amAAXC5lhcTKc6paN75DPj4V7VvDdML6v1QUpY0RrKbKMmo4SQy6a7dsqCGXRd5jp7FGgIHnZAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-09T04:32:17.375960Z"},"content_sha256":"3f14b49d1df8eb15770d4b5d61ef3f8922c81762254b5b391f6f29c1e949fb5e","schema_version":"1.0","event_id":"sha256:3f14b49d1df8eb15770d4b5d61ef3f8922c81762254b5b391f6f29c1e949fb5e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2021:742XVVHCKTPWYYDXCY2RSJTYIQ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Performance of Refined Isogeometric Analysis in Solving Quadratic Eigenvalue Problems","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"Ali Hashemian, Daniel Garcia, David Pardo, Victor M. Calo","submitted_at":"2021-12-28T09:24:01Z","abstract_excerpt":"Certain applications that analyze damping effects require the solution of quadratic eigenvalue problems (QEPs). We use refined isogeometric analysis (rIGA) to solve quadratic eigenproblems. rIGA discretization, while conserving desirable properties of maximum-continuity isogeometric analysis (IGA), reduces the interconnection between degrees of freedom by adding low-continuity basis functions. This connectivity reduction in rIGA's algebraic system results in faster matrix LU factorizations when using multifrontal direct solvers. We compare computational costs of rIGA versus those of IGA when e"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2112.14064","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/2112.14064/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":"2026-07-05T04:43:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"slrwXcWyMcDuPlYrtr0iU5TEzc+lRCuW9vM05DT41Ttn5kFbQlyYt7K+IUj9REo7t5B5Te9JOmPevMSmGRdJAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-09T04:32:17.376349Z"},"content_sha256":"768792a16387910aca9f2361876c45e29efaf3e115469079eddeac74f7e77d46","schema_version":"1.0","event_id":"sha256:768792a16387910aca9f2361876c45e29efaf3e115469079eddeac74f7e77d46"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/742XVVHCKTPWYYDXCY2RSJTYIQ/bundle.json","state_url":"https://pith.science/pith/742XVVHCKTPWYYDXCY2RSJTYIQ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/742XVVHCKTPWYYDXCY2RSJTYIQ/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":"2026-07-09T04:32:17Z","links":{"resolver":"https://pith.science/pith/742XVVHCKTPWYYDXCY2RSJTYIQ","bundle":"https://pith.science/pith/742XVVHCKTPWYYDXCY2RSJTYIQ/bundle.json","state":"https://pith.science/pith/742XVVHCKTPWYYDXCY2RSJTYIQ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/742XVVHCKTPWYYDXCY2RSJTYIQ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:742XVVHCKTPWYYDXCY2RSJTYIQ","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":"a10ac035e5e7a716e98e46a264b1ea700f223a40770466e038a951a8311f0202","cross_cats_sorted":["cs.NA"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NA","submitted_at":"2021-12-28T09:24:01Z","title_canon_sha256":"6872534b041e0a5644ed91d141b9db6446324cdbf614722cf94df056d27fc022"},"schema_version":"1.0","source":{"id":"2112.14064","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2112.14064","created_at":"2026-07-05T04:43:38Z"},{"alias_kind":"arxiv_version","alias_value":"2112.14064v1","created_at":"2026-07-05T04:43:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2112.14064","created_at":"2026-07-05T04:43:38Z"},{"alias_kind":"pith_short_12","alias_value":"742XVVHCKTPW","created_at":"2026-07-05T04:43:38Z"},{"alias_kind":"pith_short_16","alias_value":"742XVVHCKTPWYYDX","created_at":"2026-07-05T04:43:38Z"},{"alias_kind":"pith_short_8","alias_value":"742XVVHC","created_at":"2026-07-05T04:43:38Z"}],"graph_snapshots":[{"event_id":"sha256:768792a16387910aca9f2361876c45e29efaf3e115469079eddeac74f7e77d46","target":"graph","created_at":"2026-07-05T04:43:38Z","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/2112.14064/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Certain applications that analyze damping effects require the solution of quadratic eigenvalue problems (QEPs). We use refined isogeometric analysis (rIGA) to solve quadratic eigenproblems. rIGA discretization, while conserving desirable properties of maximum-continuity isogeometric analysis (IGA), reduces the interconnection between degrees of freedom by adding low-continuity basis functions. This connectivity reduction in rIGA's algebraic system results in faster matrix LU factorizations when using multifrontal direct solvers. We compare computational costs of rIGA versus those of IGA when e","authors_text":"Ali Hashemian, Daniel Garcia, David Pardo, Victor M. Calo","cross_cats":["cs.NA"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NA","submitted_at":"2021-12-28T09:24:01Z","title":"Performance of Refined Isogeometric Analysis in Solving Quadratic Eigenvalue Problems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2112.14064","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":"sha256:3f14b49d1df8eb15770d4b5d61ef3f8922c81762254b5b391f6f29c1e949fb5e","target":"record","created_at":"2026-07-05T04:43:38Z","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":"a10ac035e5e7a716e98e46a264b1ea700f223a40770466e038a951a8311f0202","cross_cats_sorted":["cs.NA"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NA","submitted_at":"2021-12-28T09:24:01Z","title_canon_sha256":"6872534b041e0a5644ed91d141b9db6446324cdbf614722cf94df056d27fc022"},"schema_version":"1.0","source":{"id":"2112.14064","kind":"arxiv","version":1}},"canonical_sha256":"ff357ad4e254df6c607716351926784422a0b4be690d6511e3537f067995ec85","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ff357ad4e254df6c607716351926784422a0b4be690d6511e3537f067995ec85","first_computed_at":"2026-07-05T04:43:38.253486Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T04:43:38.253486Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"WtIIfMMmhiHHV+JvUDYX1u6HpKQ0XHhP6U/SW2FQBjUV8//LkdwyOI0vM9sEzEZdK9wudyIN62ZUTgIos6HtBg==","signature_status":"signed_v1","signed_at":"2026-07-05T04:43:38.253837Z","signed_message":"canonical_sha256_bytes"},"source_id":"2112.14064","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3f14b49d1df8eb15770d4b5d61ef3f8922c81762254b5b391f6f29c1e949fb5e","sha256:768792a16387910aca9f2361876c45e29efaf3e115469079eddeac74f7e77d46"],"state_sha256":"12e607c7be2f2a6601a25fc6981ac837b74bfa010ebd6ee784c8a2743badaef6"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gTfRGPxetZScUbbSikr3zvppvXBbVhLoS1i3SsZUCLCoiZkSjYP+CHcx5kO5ZxUns20vGw3g/cIS0T0BzVD2Bw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-09T04:32:17.378591Z","bundle_sha256":"31ec9e78752ab15301f012de76760134c0189df6eb0e02644a34315f0bcb4439"}}