{"id":"https://openalex.org/W7221126124","doi":"https://doi.org/10.48550/arxiv.2610.11002","title":"Classification of bipartite observables I: stable and uniformly stable observables","display_name":"Classification of bipartite observables I: stable and uniformly stable observables","publication_year":2026,"publication_date":"2026-10-07","ids":{"openalex":"https://openalex.org/W7221126124","doi":"https://doi.org/10.48550/arxiv.2610.11002"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2610.11002","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.11002","pdf_url":"https://arxiv.org/pdf/2610.11002","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/2610.11002","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5037080454","display_name":"Eduardo Du\u00e9\u00f1ez","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I45438204","display_name":"The University of Texas at San Antonio","ror":"https://ror.org/01kd65564","country_code":"US","type":"education","lineage":["https://openalex.org/I45438204"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Due\u00f1ez, Eduardo","raw_affiliation_strings":["Department of Mathematics , The University of Texas at San Antonio , One UTSA Circle , San Antonio , TX 78249 , USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics , The University of Texas at San Antonio , One UTSA Circle , San Antonio , TX 78249 , USA","institution_ids":["https://openalex.org/I45438204"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5056456551","display_name":"Jos\u00e9 Iovino","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I45438204","display_name":"The University of Texas at San Antonio","ror":"https://ror.org/01kd65564","country_code":"US","type":"education","lineage":["https://openalex.org/I45438204"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Iovino, Jos\u00e9","raw_affiliation_strings":["Department of Mathematics , The University of Texas at San Antonio , One UTSA Circle , San Antonio , TX 78249 , USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics , The University of Texas at San Antonio , One UTSA Circle , San Antonio , TX 78249 , USA","institution_ids":["https://openalex.org/I45438204"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I45438204"],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":2,"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/T10622","display_name":"Quantum Mechanics and Applications","score":0.5121999979019165,"subfield":{"id":"https://openalex.org/subfields/3107","display_name":"Atomic and Molecular Physics, and Optics"},"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/T10622","display_name":"Quantum Mechanics and Applications","score":0.5121999979019165,"subfield":{"id":"https://openalex.org/subfields/3107","display_name":"Atomic and Molecular Physics, and Optics"},"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/T10020","display_name":"Quantum Information and Cryptography","score":0.2930000126361847,"subfield":{"id":"https://openalex.org/subfields/3107","display_name":"Atomic and Molecular Physics, and Optics"},"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/T10682","display_name":"Quantum Computing Algorithms and Architecture","score":0.121799997985363,"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/classification-theory","display_name":"classification theory","score":0.5979999899864197},{"id":"https://openalex.org/keywords/uniform-stability","display_name":"uniform stability","score":0.7870000004768372},{"id":"https://openalex.org/keywords/weak-compactness","display_name":"weak compactness","score":0.906000018119812},{"id":"https://openalex.org/keywords/reflexive-banach-spaces","display_name":"reflexive Banach spaces","score":0.9940000176429749},{"id":"https://openalex.org/keywords/mixture-models","display_name":"mixture models","score":0.7609999775886536},{"id":"https://openalex.org/keywords/online-prediction","display_name":"online prediction","score":0.9229999780654907},{"id":"https://openalex.org/keywords/swap-test","display_name":"swap test","score":0.7770000100135803},{"id":"https://openalex.org/keywords/hong-ou-mandel-interference","display_name":"Hong-Ou-Mandel interference","score":0.8330000042915344},{"id":"https://openalex.org/keywords/product-states","display_name":"product states","score":0.722000002861023}],"concepts":[{"id":"https://openalex.org/C32848918","wikidata":"https://www.wikidata.org/wiki/Q845789","display_name":"Observable","level":2,"score":0.8758000135421753},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.7271000146865845},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7267000079154968},{"id":"https://openalex.org/C197657726","wikidata":"https://www.wikidata.org/wiki/Q174733","display_name":"Bipartite graph","level":3,"score":0.6243000030517578},{"id":"https://openalex.org/C108710211","wikidata":"https://www.wikidata.org/wiki/Q11538","display_name":"Mathematical proof","level":2,"score":0.4724000096321106},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.46129998564720154},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.4478999972343445},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.41670000553131104},{"id":"https://openalex.org/C90673727","wikidata":"https://www.wikidata.org/wiki/Q901718","display_name":"Product (mathematics)","level":2,"score":0.38370001316070557},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3799000084400177},{"id":"https://openalex.org/C14103023","wikidata":"https://www.wikidata.org/wiki/Q11681459","display_name":"Pairing","level":3,"score":0.36340001225471497},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3626999855041504},{"id":"https://openalex.org/C122203268","wikidata":"https://www.wikidata.org/wiki/Q5862903","display_name":"Probability theory","level":2,"score":0.35109999775886536},{"id":"https://openalex.org/C99821215","wikidata":"https://www.wikidata.org/wiki/Q1136583","display_name":"Swap (finance)","level":2,"score":0.3488999903202057},{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.3416000008583069},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.34139999747276306},{"id":"https://openalex.org/C90377204","wikidata":"https://www.wikidata.org/wiki/Q1052594","display_name":"Uniform boundedness","level":3,"score":0.3327000141143799},{"id":"https://openalex.org/C2777151079","wikidata":"https://www.wikidata.org/wiki/Q141160","display_name":"Parity (physics)","level":2,"score":0.33000001311302185},{"id":"https://openalex.org/C2777759810","wikidata":"https://www.wikidata.org/wiki/Q149316","display_name":"Lemma (botany)","level":3,"score":0.3237999975681305},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.30230000615119934},{"id":"https://openalex.org/C2778926657","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum system","level":3,"score":0.3018999993801117},{"id":"https://openalex.org/C2779193601","wikidata":"https://www.wikidata.org/wiki/Q20026918","display_name":"Mathematical theory","level":2,"score":0.30090001225471497},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.30059999227523804},{"id":"https://openalex.org/C116672817","wikidata":"https://www.wikidata.org/wiki/Q1454986","display_name":"Physical system","level":2,"score":0.2992999851703644},{"id":"https://openalex.org/C55689738","wikidata":"https://www.wikidata.org/wiki/Q15963867","display_name":"Discrete time and continuous time","level":2,"score":0.29030001163482666},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.2793999910354614},{"id":"https://openalex.org/C2778112365","wikidata":"https://www.wikidata.org/wiki/Q3511065","display_name":"Sequence (biology)","level":2,"score":0.27810001373291016},{"id":"https://openalex.org/C169654258","wikidata":"https://www.wikidata.org/wiki/Q12479","display_name":"Number theory","level":2,"score":0.2766000032424927},{"id":"https://openalex.org/C21031990","wikidata":"https://www.wikidata.org/wiki/Q355020","display_name":"Probability measure","level":2,"score":0.273499995470047},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.2720000147819519},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.26739999651908875},{"id":"https://openalex.org/C136979486","wikidata":"https://www.wikidata.org/wiki/Q773483","display_name":"Existential quantification","level":2,"score":0.257999986410141},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.2574999928474426},{"id":"https://openalex.org/C149441793","wikidata":"https://www.wikidata.org/wiki/Q200726","display_name":"Probability distribution","level":2,"score":0.2563999891281128}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2610.11002","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.11002","pdf_url":"https://arxiv.org/pdf/2610.11002","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.2610.11002","doi":"https://doi.org/10.48550/arxiv.2610.11002","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2610.11002","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2610.11002","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.11002","pdf_url":"https://arxiv.org/pdf/2610.11002","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":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7221126124.pdf","grobid_xml":"https://content.openalex.org/works/W7221126124.grobid-xml"},"referenced_works_count":5,"referenced_works":["https://openalex.org/W1540659618","https://openalex.org/W4390575983","https://openalex.org/W4403592872","https://openalex.org/W7118340270","https://openalex.org/W7171382818"],"related_works":["https://openalex.org/W7221531926","https://openalex.org/W7222605118","https://openalex.org/W4396769326","https://openalex.org/W7097811626","https://openalex.org/W7080151807","https://openalex.org/W2339529584","https://openalex.org/W7170999846","https://openalex.org/W2593958474","https://openalex.org/W2502398430","https://openalex.org/W3151530607"],"abstract_inverted_index":{"This":[0],"is":[1,55],"the":[2,9,33,36,39,43,46,69,91,100,107],"first":[3],"of":[4,12,18,35,45,72,78,84,94,103,120],"three":[5],"papers":[6],"that":[7,53],"read":[8],"dividing":[10],"lines":[11],"Shelah's":[13],"classification":[14],"theory":[15],"as":[16],"properties":[17],"bipartite":[19],"quantum":[20],"observables,":[21],"through":[22,62],"their":[23],"expectation":[24,37],"functions":[25],"on":[26],"product":[27],"states.":[28],"Here":[29],"we":[30],"study":[31],"stability:":[32],"independence":[34],"from":[38],"order":[40],"in":[41],"which":[42,86],"preparations":[44,74],"two":[47],"systems":[48],"are":[49],"idealized.":[50],"We":[51],"show":[52],"stability":[54],"characterized":[56],"by":[57,60,68,75],"weak":[58],"compactness,":[59],"factorization":[61],"a":[63],"reflexive":[64],"Banach":[65],"space,":[66],"and":[67,99,112],"uniform":[70,82],"simulation":[71],"idealized":[73],"finite":[76,92],"mixtures":[77],"actual":[79],"ones.":[80],"A":[81],"version":[83],"stability,":[85],"bounds":[87,118],"at":[88],"every":[89],"margin":[90],"staircases":[93],"responses,":[95],"governs":[96],"adaptive":[97],"discrimination":[98],"online":[101],"prediction":[102],"thresholded":[104],"expectations;":[105],"for":[106],"swap":[108],"test,":[109],"Hong--Ou--Mandel":[110],"coincidences":[111],"discrete":[113],"equality":[114],"tests,":[115],"it":[116],"yields":[117],"independent":[119],"dimension.":[121]},"counts_by_year":[{"year":2026,"cited_by_count":2}],"updated_date":"2026-11-08T12:12:28.789561","created_date":"2026-10-10T00:00:00"}