{"id":"https://openalex.org/W7161735351","doi":"https://doi.org/10.48550/arxiv.2605.17390","title":"NOETHER: A Constructive Framework for Metamorphic Pattern Discovery from Operator Algebras","display_name":"NOETHER: A Constructive Framework for Metamorphic Pattern Discovery from Operator Algebras","publication_year":2026,"publication_date":"2026-05-17","ids":{"openalex":"https://openalex.org/W7161735351","doi":"https://doi.org/10.48550/arxiv.2605.17390"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2605.17390","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2605.17390","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article"},"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.48550/arxiv.2605.17390","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5135604461","display_name":"Li M","orcid":null},"institutions":[{"id":"https://openalex.org/I91935597","display_name":"University of South China","ror":"https://ror.org/03mqfn238","country_code":"CN","type":"education","lineage":["https://openalex.org/I91935597"]},{"id":"https://openalex.org/I96478251","display_name":"Hunan Institute of Technology","ror":"https://ror.org/04n3k2k71","country_code":"CN","type":"education","lineage":["https://openalex.org/I96478251"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Li, Meng","raw_affiliation_strings":["School of Computing, University of South China, Hengyang, 421001, China","Hunan Engineering Research Center of Software Evaluation and Testing for Intellectual Equipment, Hengyang, 421001, China","CNNC Key Laboratory on High Trusted Computing, Hengyang, 421001, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Computing, University of South China, Hengyang, 421001, China","institution_ids":["https://openalex.org/I91935597"]},{"raw_affiliation_string":"Hunan Engineering Research Center of Software Evaluation and Testing for Intellectual Equipment, Hengyang, 421001, China","institution_ids":["https://openalex.org/I96478251"]},{"raw_affiliation_string":"CNNC Key Laboratory on High Trusted Computing, Hengyang, 421001, China","institution_ids":["https://openalex.org/I91935597"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5136493765","display_name":"Xiaohua Yang","orcid":null},"institutions":[{"id":"https://openalex.org/I91935597","display_name":"University of South China","ror":"https://ror.org/03mqfn238","country_code":"CN","type":"education","lineage":["https://openalex.org/I91935597"]},{"id":"https://openalex.org/I96478251","display_name":"Hunan Institute of Technology","ror":"https://ror.org/04n3k2k71","country_code":"CN","type":"education","lineage":["https://openalex.org/I96478251"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yang, Xiaohua","raw_affiliation_strings":["School of Computing, University of South China, Hengyang, 421001, China","Hunan Engineering Research Center of Software Evaluation and Testing for Intellectual Equipment, Hengyang, 421001, China","CNNC Key Laboratory on High Trusted Computing, Hengyang, 421001, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Computing, University of South China, Hengyang, 421001, China","institution_ids":["https://openalex.org/I91935597"]},{"raw_affiliation_string":"Hunan Engineering Research Center of Software Evaluation and Testing for Intellectual Equipment, Hengyang, 421001, China","institution_ids":["https://openalex.org/I96478251"]},{"raw_affiliation_string":"CNNC Key Laboratory on High Trusted Computing, Hengyang, 421001, China","institution_ids":["https://openalex.org/I91935597"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5027294310","display_name":"J T Liu","orcid":null},"institutions":[{"id":"https://openalex.org/I91935597","display_name":"University of South China","ror":"https://ror.org/03mqfn238","country_code":"CN","type":"education","lineage":["https://openalex.org/I91935597"]},{"id":"https://openalex.org/I96478251","display_name":"Hunan Institute of Technology","ror":"https://ror.org/04n3k2k71","country_code":"CN","type":"education","lineage":["https://openalex.org/I96478251"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Liu, Jie","raw_affiliation_strings":["School of Computing, University of South China, Hengyang, 421001, China","Hunan Engineering Research Center of Software Evaluation and Testing for Intellectual Equipment, Hengyang, 421001, China","CNNC Key Laboratory on High Trusted Computing, Hengyang, 421001, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Computing, University of South China, Hengyang, 421001, China","institution_ids":["https://openalex.org/I91935597"]},{"raw_affiliation_string":"Hunan Engineering Research Center of Software Evaluation and Testing for Intellectual Equipment, Hengyang, 421001, China","institution_ids":["https://openalex.org/I96478251"]},{"raw_affiliation_string":"CNNC Key Laboratory on High Trusted Computing, Hengyang, 421001, China","institution_ids":["https://openalex.org/I91935597"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5136460725","display_name":"Shiyu Yan","orcid":null},"institutions":[{"id":"https://openalex.org/I91935597","display_name":"University of South China","ror":"https://ror.org/03mqfn238","country_code":"CN","type":"education","lineage":["https://openalex.org/I91935597"]},{"id":"https://openalex.org/I96478251","display_name":"Hunan Institute of Technology","ror":"https://ror.org/04n3k2k71","country_code":"CN","type":"education","lineage":["https://openalex.org/I96478251"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yan, Shiyu","raw_affiliation_strings":["School of Computing, University of South China, Hengyang, 421001, China","Hunan Engineering Research Center of Software Evaluation and Testing for Intellectual Equipment, Hengyang, 421001, China","CNNC Key Laboratory on High Trusted Computing, Hengyang, 421001, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Computing, University of South China, Hengyang, 421001, China","institution_ids":["https://openalex.org/I91935597"]},{"raw_affiliation_string":"Hunan Engineering Research Center of Software Evaluation and Testing for Intellectual Equipment, Hengyang, 421001, China","institution_ids":["https://openalex.org/I96478251"]},{"raw_affiliation_string":"CNNC Key Laboratory on High Trusted Computing, Hengyang, 421001, China","institution_ids":["https://openalex.org/I91935597"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"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/T10142","display_name":"Formal Methods in Verification","score":0.3077999949455261,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10142","display_name":"Formal Methods in Verification","score":0.3077999949455261,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10743","display_name":"Software Testing and Debugging Techniques","score":0.1655000001192093,"subfield":{"id":"https://openalex.org/subfields/1712","display_name":"Software"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11689","display_name":"Adversarial Robustness in Machine Learning","score":0.0471000000834465,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.504800021648407},{"id":"https://openalex.org/keywords/tuple","display_name":"Tuple","score":0.4577000141143799},{"id":"https://openalex.org/keywords/noethers-theorem","display_name":"Noether's theorem","score":0.4496000111103058},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.4316999912261963},{"id":"https://openalex.org/keywords/decidability","display_name":"Decidability","score":0.42419999837875366},{"id":"https://openalex.org/keywords/executable","display_name":"Executable","score":0.41940000653266907},{"id":"https://openalex.org/keywords/falsifiability","display_name":"Falsifiability","score":0.4124000072479248},{"id":"https://openalex.org/keywords/soundness","display_name":"Soundness","score":0.4113999903202057},{"id":"https://openalex.org/keywords/unary-operation","display_name":"Unary operation","score":0.40209999680519104},{"id":"https://openalex.org/keywords/operator","display_name":"Operator (biology)","score":0.39320001006126404}],"concepts":[{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.504800021648407},{"id":"https://openalex.org/C118930307","wikidata":"https://www.wikidata.org/wiki/Q600590","display_name":"Tuple","level":2,"score":0.4577000141143799},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4499000012874603},{"id":"https://openalex.org/C80892491","wikidata":"https://www.wikidata.org/wiki/Q578555","display_name":"Noether's theorem","level":3,"score":0.4496000111103058},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.4316999912261963},{"id":"https://openalex.org/C153269930","wikidata":"https://www.wikidata.org/wiki/Q430001","display_name":"Decidability","level":2,"score":0.42419999837875366},{"id":"https://openalex.org/C160145156","wikidata":"https://www.wikidata.org/wiki/Q778586","display_name":"Executable","level":2,"score":0.41940000653266907},{"id":"https://openalex.org/C116222747","wikidata":"https://www.wikidata.org/wiki/Q220888","display_name":"Falsifiability","level":2,"score":0.4124000072479248},{"id":"https://openalex.org/C39920170","wikidata":"https://www.wikidata.org/wiki/Q693083","display_name":"Soundness","level":2,"score":0.4113999903202057},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.4059999883174896},{"id":"https://openalex.org/C78023250","wikidata":"https://www.wikidata.org/wiki/Q657596","display_name":"Unary operation","level":2,"score":0.40209999680519104},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.39320001006126404},{"id":"https://openalex.org/C127705205","wikidata":"https://www.wikidata.org/wiki/Q5748245","display_name":"Heuristics","level":2,"score":0.38350000977516174},{"id":"https://openalex.org/C2778220771","wikidata":"https://www.wikidata.org/wiki/Q1522579","display_name":"Substitution (logic)","level":2,"score":0.37229999899864197},{"id":"https://openalex.org/C25343380","wikidata":"https://www.wikidata.org/wiki/Q277521","display_name":"Relation (database)","level":2,"score":0.3628999888896942},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3571000099182129},{"id":"https://openalex.org/C2778012447","wikidata":"https://www.wikidata.org/wiki/Q1034415","display_name":"Scope (computer science)","level":2,"score":0.35190001130104065},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.3458999991416931},{"id":"https://openalex.org/C95916125","wikidata":"https://www.wikidata.org/wiki/Q840540","display_name":"Relational algebra","level":3,"score":0.33809998631477356},{"id":"https://openalex.org/C2776545253","wikidata":"https://www.wikidata.org/wiki/Q5464292","display_name":"Folding (DSP implementation)","level":2,"score":0.33379998803138733},{"id":"https://openalex.org/C2164484","wikidata":"https://www.wikidata.org/wiki/Q5170150","display_name":"Core (optical fiber)","level":2,"score":0.33239999413490295},{"id":"https://openalex.org/C165464430","wikidata":"https://www.wikidata.org/wiki/Q1570441","display_name":"Parameterized complexity","level":2,"score":0.31769999861717224},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.31709998846054077},{"id":"https://openalex.org/C191413488","wikidata":"https://www.wikidata.org/wiki/Q1892554","display_name":"Operator algebra","level":2,"score":0.3070000112056732},{"id":"https://openalex.org/C159423971","wikidata":"https://www.wikidata.org/wiki/Q177251","display_name":"Associative property","level":2,"score":0.3052999973297119},{"id":"https://openalex.org/C9136319","wikidata":"https://www.wikidata.org/wiki/Q362640","display_name":"Covariant transformation","level":2,"score":0.3037000000476837},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.2928999960422516},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.28369998931884766},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.2824000120162964},{"id":"https://openalex.org/C2778701210","wikidata":"https://www.wikidata.org/wiki/Q28130034","display_name":"Constructive","level":3,"score":0.27810001373291016},{"id":"https://openalex.org/C155281189","wikidata":"https://www.wikidata.org/wiki/Q3518150","display_name":"Tensor (intrinsic definition)","level":2,"score":0.2727999985218048},{"id":"https://openalex.org/C162838799","wikidata":"https://www.wikidata.org/wiki/Q596077","display_name":"Counterexample","level":2,"score":0.2709999978542328},{"id":"https://openalex.org/C158154518","wikidata":"https://www.wikidata.org/wiki/Q7310970","display_name":"Relevance (law)","level":2,"score":0.26820001006126404},{"id":"https://openalex.org/C183778304","wikidata":"https://www.wikidata.org/wiki/Q165474","display_name":"Commutative property","level":2,"score":0.266400009393692},{"id":"https://openalex.org/C173801870","wikidata":"https://www.wikidata.org/wiki/Q201413","display_name":"Heuristic","level":2,"score":0.25450000166893005}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2605.17390","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2605.17390","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"doi:10.48550/arxiv.2605.17390","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2605.17390","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"Context.":[0],"Metamorphic":[1],"Testing":[2],"is":[3,18,66,77,88,95,191,208,222],"recognised":[4],"in":[5],"IEEE/ISO":[6],"software-testing":[7],"standards":[8],"and":[9,30,49,68,124,161,224],"increasingly":[10],"recommended":[11],"for":[12,156],"AI":[13],"systems,":[14],"but":[15],"its":[16],"progress":[17],"bottlenecked":[19],"by":[20],"metamorphic":[21],"relation":[22],"(MR)":[23],"identification:":[24],"existing":[25],"approaches":[26],"(structured":[27],"frameworks,":[28],"mining":[29],"evolutionary":[31],"pipelines,":[32],"LLM-assisted":[33],"methods,":[34],"MetaPattern":[35,64,118],"catalogues)":[36],"share":[37],"an":[38,96],"inductive":[39,147],"grounding":[40],"that":[41,201],"leaves":[42],"three":[43,135],"foundational":[44],"questions":[45],"open:":[46],"origin,":[47],"closure,":[48],"transferability.":[50],"Objective.":[51],"We":[52,130],"propose":[53],"a":[54,78,89,117,145,215],"framework":[55,133],"whose":[56],"downstream":[57,113,220],"step":[58,221],"from":[59,210],"program-induced":[60],"operator":[61],"algebra":[62,76],"to":[63,214],"set":[65,119],"mechanical":[67],"provable,":[69],"while":[70],"the":[71,75,132,170,183,219],"upstream":[72,93],"curation":[73],"of":[74],"stated":[79],"empirical":[80],"hypothesis":[81],"with":[82,120],"explicit":[83],"scope":[84],"precondition.":[85],"Method.":[86],"NOETHER":[87,143],"two-layer":[90],"framework.":[91],"The":[92,112,173,186],"layer":[94],"eight-block":[97],"decomposition":[98],"over":[99],"recurrent":[100],"mathematical":[101],"structures":[102],"(symmetry,":[103],"order,":[104],"self-adjoint,":[105],"time-reversal,":[106],"limit,":[107],"qualitative-dynamics,":[108],"method-comparison,":[109],"relational":[110,165],"equivalence).":[111],"CONSTRUCT-MP":[114],"algorithm":[115],"produces":[116],"algebraic-closure":[121],"(Theorem":[122,127,189],"1)":[123],"polynomial-time":[125],"decidability":[126],"2)":[128],"guarantees.":[129],"test":[131],"on":[134,149,164,178,182,193],"operator-algebraic":[136],"domains.":[137],"Results.":[138],"On":[139],"Boltzmann":[140],"reactor":[141],"physics":[142],"systematises":[144],"prior":[146],"catalogue;":[148],"equivariant":[150],"ML":[151],"it":[152,168],"derives":[153],"executable":[154],"MRs":[155],"rotation":[157],"invariance,":[158],"adjoint":[159],"duality,":[160],"training-trajectory":[162],"reversibility;":[163],"query":[166],"optimisers":[167],"exercises":[169],"relational-equivalence":[171],"block.":[172],"central":[174],"falsifiable":[175],"prediction":[176],"(L*-blindness":[177],"homogeneity-preserving":[179],"mutators)":[180],"holds":[181],"in-scope":[184],"substrate.":[185],"absolute-completeness":[187],"conjecture":[188],"1')":[190],"falsified":[192],"PWR":[194],"core":[195],"diffusion":[196],"via":[197],"two":[198],"pairwise-independent":[199],"counterexamples":[200],"identify":[202],"five":[203],"Translate-extension":[204],"dimensions.":[205],"Conclusion.":[206],"Induction":[207],"relocated":[209],"per-program":[211],"MR":[212],"sampling":[213],"per-domain":[216],"algebraic":[217],"layer;":[218],"deductive":[223],"mechanical.":[225]},"counts_by_year":[],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2026-05-20T00:00:00"}