{"id":"https://openalex.org/W7212809376","doi":"https://doi.org/10.48550/arxiv.2609.12493","title":"Recoverability Is a Subspace Property: A Benchmark for Certified State Estimation from Partial PDE Observations","display_name":"Recoverability Is a Subspace Property: A Benchmark for Certified State Estimation from Partial PDE Observations","publication_year":2026,"publication_date":"2026-09-11","ids":{"openalex":"https://openalex.org/W7212809376","doi":"https://doi.org/10.48550/arxiv.2609.12493"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.12493","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.12493","pdf_url":"https://arxiv.org/pdf/2609.12493","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2609.12493","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5018809359","display_name":"Qingwei Dong","orcid":"https://orcid.org/0000-0002-6783-8647","observed_orcids":["https://orcid.org/0000-0002-6783-8647"]},"institutions":[{"id":"https://openalex.org/I142078773","display_name":"Shenyang Institute of Automation","ror":"https://ror.org/00ft6nj33","country_code":"CN","type":"facility","lineage":["https://openalex.org/I142078773","https://openalex.org/I19820366"]},{"id":"https://openalex.org/I19820366","display_name":"Chinese Academy of Sciences","ror":"https://ror.org/034t30j35","country_code":"CN","type":"government","lineage":["https://openalex.org/I19820366"]},{"id":"https://openalex.org/I4391768281","display_name":"State Key Laboratory of Robotics","ror":"https://ror.org/03pcw1780","country_code":"CN","type":"facility","lineage":["https://openalex.org/I142078773","https://openalex.org/I19820366","https://openalex.org/I4391768281"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Dong, Qingwei","raw_affiliation_strings":["Key Laboratory of Networked Control Systems , Chinese Academy of Sciences , Shenyang 110016 , China","State Key Laboratory of Robotics , Shenyang Institute of Automation ,"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Key Laboratory of Networked Control Systems , Chinese Academy of Sciences , Shenyang 110016 , China","institution_ids":["https://openalex.org/I19820366"]},{"raw_affiliation_string":"State Key Laboratory of Robotics , Shenyang Institute of Automation ,","institution_ids":["https://openalex.org/I142078773","https://openalex.org/I4391768281"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5005866333","display_name":"Peng Zeng","orcid":"https://orcid.org/0000-0001-7863-3260","observed_orcids":["https://orcid.org/0000-0001-7863-3260","https://orcid.org/0000-0003-4673-3632"]},"institutions":[{"id":"https://openalex.org/I142078773","display_name":"Shenyang Institute of Automation","ror":"https://ror.org/00ft6nj33","country_code":"CN","type":"facility","lineage":["https://openalex.org/I142078773","https://openalex.org/I19820366"]},{"id":"https://openalex.org/I19820366","display_name":"Chinese Academy of Sciences","ror":"https://ror.org/034t30j35","country_code":"CN","type":"government","lineage":["https://openalex.org/I19820366"]},{"id":"https://openalex.org/I4391768281","display_name":"State Key Laboratory of Robotics","ror":"https://ror.org/03pcw1780","country_code":"CN","type":"facility","lineage":["https://openalex.org/I142078773","https://openalex.org/I19820366","https://openalex.org/I4391768281"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Zeng, Peng","raw_affiliation_strings":["Key Laboratory of Networked Control Systems , Chinese Academy of Sciences , Shenyang 110016 , China","State Key Laboratory of Robotics , Shenyang Institute of Automation ,"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Key Laboratory of Networked Control Systems , Chinese Academy of Sciences , Shenyang 110016 , China","institution_ids":["https://openalex.org/I19820366"]},{"raw_affiliation_string":"State Key Laboratory of Robotics , Shenyang Institute of Automation ,","institution_ids":["https://openalex.org/I142078773","https://openalex.org/I4391768281"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5079519256","display_name":"Guangxi Wan","orcid":"https://orcid.org/0000-0003-4456-6236","observed_orcids":["https://orcid.org/0000-0003-4456-6236"]},"institutions":[{"id":"https://openalex.org/I142078773","display_name":"Shenyang Institute of Automation","ror":"https://ror.org/00ft6nj33","country_code":"CN","type":"facility","lineage":["https://openalex.org/I142078773","https://openalex.org/I19820366"]},{"id":"https://openalex.org/I19820366","display_name":"Chinese Academy of Sciences","ror":"https://ror.org/034t30j35","country_code":"CN","type":"government","lineage":["https://openalex.org/I19820366"]},{"id":"https://openalex.org/I4391768281","display_name":"State Key Laboratory of Robotics","ror":"https://ror.org/03pcw1780","country_code":"CN","type":"facility","lineage":["https://openalex.org/I142078773","https://openalex.org/I19820366","https://openalex.org/I4391768281"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Wan, Guangxi","raw_affiliation_strings":["Key Laboratory of Networked Control Systems , Chinese Academy of Sciences , Shenyang 110016 , China","State Key Laboratory of Robotics , Shenyang Institute of Automation ,"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Key Laboratory of Networked Control Systems , Chinese Academy of Sciences , Shenyang 110016 , China","institution_ids":["https://openalex.org/I19820366"]},{"raw_affiliation_string":"State Key Laboratory of Robotics , Shenyang Institute of Automation ,","institution_ids":["https://openalex.org/I142078773","https://openalex.org/I4391768281"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5151696814","display_name":"Jiyuan Zhang","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Zhang, Jiyuan","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5151613159","display_name":"Ruikai Liu","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Liu, Ruikai","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5150903162","display_name":"Yuqi Liu","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I142078773","display_name":"Shenyang Institute of Automation","ror":"https://ror.org/00ft6nj33","country_code":"CN","type":"facility","lineage":["https://openalex.org/I142078773","https://openalex.org/I19820366"]},{"id":"https://openalex.org/I19820366","display_name":"Chinese Academy of Sciences","ror":"https://ror.org/034t30j35","country_code":"CN","type":"government","lineage":["https://openalex.org/I19820366"]},{"id":"https://openalex.org/I4391768281","display_name":"State Key Laboratory of Robotics","ror":"https://ror.org/03pcw1780","country_code":"CN","type":"facility","lineage":["https://openalex.org/I142078773","https://openalex.org/I19820366","https://openalex.org/I4391768281"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Liu, Yuqi","raw_affiliation_strings":["Key Laboratory of Networked Control Systems , Chinese Academy of Sciences , Shenyang 110016 , China","State Key Laboratory of Robotics , Shenyang Institute of Automation ,"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Key Laboratory of Networked Control Systems , Chinese Academy of Sciences , Shenyang 110016 , China","institution_ids":["https://openalex.org/I19820366"]},{"raw_affiliation_string":"State Key Laboratory of Robotics , Shenyang Institute of Automation ,","institution_ids":["https://openalex.org/I142078773","https://openalex.org/I4391768281"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11206","display_name":"Model Reduction and Neural Networks","score":0.9009000062942505,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11206","display_name":"Model Reduction and Neural Networks","score":0.9009000062942505,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11236","display_name":"Control Systems and Identification","score":0.04529999941587448,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11110","display_name":"Stability and Controllability of Differential Equations","score":0.040699999779462814,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/partial-differential-equations","display_name":"partial differential equations","score":0.8460000157356262},{"id":"https://openalex.org/keywords/partial-observability","display_name":"partial observability","score":0.7749999761581421},{"id":"https://openalex.org/keywords/observation-geometry","display_name":"observation geometry","score":0.5120000243186951},{"id":"https://openalex.org/keywords/sensitivity-analysis","display_name":"sensitivity analysis","score":0.5740000009536743},{"id":"https://openalex.org/keywords/right-singular-vectors","display_name":"right singular vectors","score":0.6019999980926514},{"id":"https://openalex.org/keywords/confidence-based-selection","display_name":"confidence-based selection","score":0.7540000081062317},{"id":"https://openalex.org/keywords/abstention","display_name":"abstention","score":0.7009999752044678},{"id":"https://openalex.org/keywords/benchmark-protocol","display_name":"benchmark protocol","score":0.3610000014305115}],"concepts":[{"id":"https://openalex.org/C185429906","wikidata":"https://www.wikidata.org/wiki/Q1130160","display_name":"Estimator","level":2,"score":0.6187000274658203},{"id":"https://openalex.org/C21200559","wikidata":"https://www.wikidata.org/wiki/Q7451068","display_name":"Sensitivity (control systems)","level":2,"score":0.5956000089645386},{"id":"https://openalex.org/C32834561","wikidata":"https://www.wikidata.org/wiki/Q660730","display_name":"Subspace topology","level":2,"score":0.5936999917030334},{"id":"https://openalex.org/C185798385","wikidata":"https://www.wikidata.org/wiki/Q1161707","display_name":"Benchmark (surveying)","level":2,"score":0.5393000245094299},{"id":"https://openalex.org/C2780385302","wikidata":"https://www.wikidata.org/wiki/Q367158","display_name":"Protocol (science)","level":3,"score":0.5309000015258789},{"id":"https://openalex.org/C200331156","wikidata":"https://www.wikidata.org/wiki/Q506041","display_name":"Jacobian matrix and determinant","level":2,"score":0.5188000202178955},{"id":"https://openalex.org/C81917197","wikidata":"https://www.wikidata.org/wiki/Q628760","display_name":"Selection (genetic algorithm)","level":2,"score":0.5045999884605408},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.5033000111579895},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4968000054359436},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.482699990272522},{"id":"https://openalex.org/C12426560","wikidata":"https://www.wikidata.org/wiki/Q189569","display_name":"Basis (linear algebra)","level":2,"score":0.48159998655319214},{"id":"https://openalex.org/C48103436","wikidata":"https://www.wikidata.org/wiki/Q599031","display_name":"State (computer science)","level":2,"score":0.4706000089645386},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.4578999876976013},{"id":"https://openalex.org/C99498987","wikidata":"https://www.wikidata.org/wiki/Q2210247","display_name":"Noise (video)","level":3,"score":0.4562000036239624},{"id":"https://openalex.org/C4679612","wikidata":"https://www.wikidata.org/wiki/Q866298","display_name":"Aggregate (composite)","level":2,"score":0.45590001344680786},{"id":"https://openalex.org/C178650346","wikidata":"https://www.wikidata.org/wiki/Q201984","display_name":"Covariance","level":2,"score":0.4512999951839447},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.43209999799728394},{"id":"https://openalex.org/C189430467","wikidata":"https://www.wikidata.org/wiki/Q7293293","display_name":"Ranking (information retrieval)","level":2,"score":0.42989999055862427},{"id":"https://openalex.org/C2780695315","wikidata":"https://www.wikidata.org/wiki/Q3799040","display_name":"Unobservable","level":2,"score":0.41040000319480896},{"id":"https://openalex.org/C184898388","wikidata":"https://www.wikidata.org/wiki/Q1435712","display_name":"Pairwise comparison","level":2,"score":0.3837999999523163},{"id":"https://openalex.org/C185142706","wikidata":"https://www.wikidata.org/wiki/Q1134404","display_name":"Covariance matrix","level":2,"score":0.36739999055862427},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.36079999804496765},{"id":"https://openalex.org/C49937458","wikidata":"https://www.wikidata.org/wiki/Q2599292","display_name":"Probabilistic logic","level":2,"score":0.34380000829696655},{"id":"https://openalex.org/C93226319","wikidata":"https://www.wikidata.org/wiki/Q193137","display_name":"Differential (mechanical device)","level":2,"score":0.3278000056743622},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.3075999915599823},{"id":"https://openalex.org/C143724316","wikidata":"https://www.wikidata.org/wiki/Q312468","display_name":"Series (stratigraphy)","level":2,"score":0.3061999976634979},{"id":"https://openalex.org/C124101348","wikidata":"https://www.wikidata.org/wiki/Q172491","display_name":"Data mining","level":1,"score":0.2976999878883362},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.2782000005245209},{"id":"https://openalex.org/C2776436953","wikidata":"https://www.wikidata.org/wiki/Q5163215","display_name":"Consistency (knowledge bases)","level":2,"score":0.2732999920845032},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.2702000141143799},{"id":"https://openalex.org/C129537906","wikidata":"https://www.wikidata.org/wiki/Q7603913","display_name":"State variable","level":2,"score":0.26589998602867126},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.2590999901294708},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.25859999656677246},{"id":"https://openalex.org/C110121322","wikidata":"https://www.wikidata.org/wiki/Q865811","display_name":"Distribution (mathematics)","level":2,"score":0.25699999928474426},{"id":"https://openalex.org/C182365436","wikidata":"https://www.wikidata.org/wiki/Q50701","display_name":"Variable (mathematics)","level":2,"score":0.2563000023365021},{"id":"https://openalex.org/C32230216","wikidata":"https://www.wikidata.org/wiki/Q7882499","display_name":"Uncertainty quantification","level":2,"score":0.25429999828338623},{"id":"https://openalex.org/C63002673","wikidata":"https://www.wikidata.org/wiki/Q2260590","display_name":"Scoring rule","level":2,"score":0.25270000100135803}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.12493","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.12493","pdf_url":"https://arxiv.org/pdf/2609.12493","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.2609.12493","doi":"https://doi.org/10.48550/arxiv.2609.12493","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.12493","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2609.12493","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.12493","pdf_url":"https://arxiv.org/pdf/2609.12493","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"study_designs":[],"awards":[{"id":"https://openalex.org/G1068830511","display_name":null,"funder_award_id":"2024-MSBA-83","funder_id":"https://openalex.org/F4320323086","funder_display_name":"Natural Science Foundation of Liaoning Province"},{"id":"https://openalex.org/G170409383","display_name":null,"funder_award_id":"92367301","funder_id":"https://openalex.org/F4320326907","funder_display_name":"State Key Laboratory of Robotics"},{"id":"https://openalex.org/G1706880264","display_name":null,"funder_award_id":"92067205","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G3067006959","display_name":null,"funder_award_id":"92267301","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G4431596456","display_name":null,"funder_award_id":"92267301","funder_id":"https://openalex.org/F4320326907","funder_display_name":"State Key Laboratory of Robotics"},{"id":"https://openalex.org/G74403156","display_name":null,"funder_award_id":"92267205","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G7588867604","display_name":null,"funder_award_id":"92367301","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320323086","display_name":"Natural Science Foundation of Liaoning Province","ror":null},{"id":"https://openalex.org/F4320326907","display_name":"State Key Laboratory of Robotics","ror":"https://ror.org/03pcw1780"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7212809376.pdf","grobid_xml":"https://content.openalex.org/works/W7212809376.grobid-xml"},"referenced_works_count":5,"referenced_works":["https://openalex.org/W2053469438","https://openalex.org/W2157825442","https://openalex.org/W7117243124","https://openalex.org/W7162764273","https://openalex.org/W7196955754"],"related_works":["https://openalex.org/W7214926531","https://openalex.org/W7168340270","https://openalex.org/W6990034368","https://openalex.org/W4404565534","https://openalex.org/W6922704924","https://openalex.org/W1025543685","https://openalex.org/W2044386089","https://openalex.org/W3100790143","https://openalex.org/W203831624","https://openalex.org/W2275566567"],"abstract_inverted_index":{"When":[0],"reconstructing":[1],"the":[2,31,65,70,75,94,111,116,122,138,173],"hidden":[3],"state":[4,83,189],"of":[5,64,93,186],"a":[6,21,40,53,82,97],"partial":[7,13],"differential":[8],"equation":[9],"(PDE)":[10],"system":[11],"from":[12,170],"observations,":[14],"aggregate":[15,192],"prediction":[16,56,119,176],"error":[17],"measures":[18],"performance":[19,177],"on":[20,158],"given":[22],"data":[23],"distribution":[24],"but":[25],"does":[26],"not":[27],"reveal":[28],"how":[29],"strongly":[30],"observations":[32],"constrain":[33],"each":[34],"predicted":[35],"direction.":[36],"We":[37],"introduce":[38],"UniPDE-Bench,":[39],"direction-wise":[41],"evaluation":[42,185],"protocol":[43,68,112,174],"that":[44,61],"incorporates":[45],"local":[46,179],"observation":[47,72,142,180],"geometry":[48],"into":[49,102],"state-estimation":[50],"assessment,":[51],"providing":[52],"reference":[54],"for":[55],"recovery":[57,114,126,169],"and":[58,78,104,115,121,127,141,182],"confidence-based":[59,131],"selection":[60,132],"is":[62],"independent":[63],"estimator.":[66],"The":[67],"whitens":[69],"joint":[71,91],"Jacobian":[73],"by":[74,81],"noise":[76],"covariance":[77],"normalizes":[79],"it":[80],"metric.":[84],"Its":[85],"complete":[86],"right":[87],"singular":[88],"basis":[89],"represents":[90],"variations":[92],"state,":[95],"which":[96],"relative":[98],"sensitivity":[99,181],"threshold":[100],"partitions":[101],"retained":[103],"below-threshold":[105,159],"directions.":[106],"In":[107,137],"this":[108],"common":[109],"basis,":[110],"evaluates":[113],"agreement":[117],"between":[118],"claims":[120],"geometric":[123],"partition,":[124],"while":[125],"abstention":[128,157],"curves":[129],"describe":[130],"at":[133,161],"different":[134],"claim":[135,164],"coverages.":[136,165],"simulated":[139],"tasks":[140],"configurations":[143],"studied":[144],"here,":[145],"confidence":[146],"rules":[147],"whose":[148],"overall":[149],"ranking":[150],"exceeds":[151],"chance":[152],"can":[153],"still":[154],"exhibit":[155],"below-random":[156],"directions":[160],"some":[162],"high":[163],"By":[166],"separating":[167],"empirical":[168],"direction-selection":[171],"quality,":[172],"relates":[175],"to":[178],"provides":[183],"an":[184],"partially":[187],"observed":[188],"estimators":[190],"beyond":[191],"error.":[193]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-09-15T00:00:00"}
