{"id":"https://openalex.org/W4417190875","doi":"https://doi.org/10.1177/22113568241309768","title":"A jump operator on the Weihrauch degrees","display_name":"A jump operator on the Weihrauch degrees","publication_year":2025,"publication_date":"2025-05-01","ids":{"openalex":"https://openalex.org/W4417190875","doi":"https://doi.org/10.1177/22113568241309768"},"language":"en","primary_location":{"id":"doi:10.1177/22113568241309768","is_oa":false,"landing_page_url":"https://doi.org/10.1177/22113568241309768","pdf_url":null,"source":{"id":"https://openalex.org/S4210231662","display_name":"Computability","issn_l":"2211-3568","issn":["2211-3568","2211-3576"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310318577","host_organization_name":"IOS Press","host_organization_lineage":["https://openalex.org/P4310318577"],"host_organization_lineage_names":["IOS Press"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computability","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5022967955","display_name":"Uri Andrews","orcid":"https://orcid.org/0000-0002-4653-7458"},"institutions":[{"id":"https://openalex.org/I135310074","display_name":"University of Wisconsin\u2013Madison","ror":"https://ror.org/01y2jtd41","country_code":"US","type":"education","lineage":["https://openalex.org/I135310074"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Uri Andrews","raw_affiliation_strings":["Department of Mathematics, University of Wisconsin, Madison, WI, USA"],"raw_orcid":"https://orcid.org/0000-0002-4653-7458","affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Wisconsin, Madison, WI, USA","institution_ids":["https://openalex.org/I135310074"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5032435178","display_name":"Steffen Lempp","orcid":"https://orcid.org/0000-0002-2958-4017"},"institutions":[{"id":"https://openalex.org/I135310074","display_name":"University of Wisconsin\u2013Madison","ror":"https://ror.org/01y2jtd41","country_code":"US","type":"education","lineage":["https://openalex.org/I135310074"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Steffen Lempp","raw_affiliation_strings":["Department of Mathematics, University of Wisconsin, Madison, WI, USA"],"raw_orcid":"https://orcid.org/0000-0002-2958-4017","affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Wisconsin, Madison, WI, USA","institution_ids":["https://openalex.org/I135310074"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5047796693","display_name":"Alberto Marcone","orcid":"https://orcid.org/0000-0001-8356-0086"},"institutions":[{"id":"https://openalex.org/I129043915","display_name":"University of Udine","ror":"https://ror.org/05ht0mh31","country_code":"IT","type":"education","lineage":["https://openalex.org/I129043915"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Alberto Marcone","raw_affiliation_strings":["Dipartimento di Scienze Matematiche, Informatiche e Fisiche, University of Udine, Italy"],"raw_orcid":"https://orcid.org/0000-0001-8356-0086","affiliations":[{"raw_affiliation_string":"Dipartimento di Scienze Matematiche, Informatiche e Fisiche, University of Udine, Italy","institution_ids":["https://openalex.org/I129043915"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5064815634","display_name":"Joseph S. Miller","orcid":"https://orcid.org/0000-0002-6411-5670"},"institutions":[{"id":"https://openalex.org/I135310074","display_name":"University of Wisconsin\u2013Madison","ror":"https://ror.org/01y2jtd41","country_code":"US","type":"education","lineage":["https://openalex.org/I135310074"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Joseph S Miller","raw_affiliation_strings":["Department of Mathematics, University of Wisconsin, Madison, WI, USA"],"raw_orcid":"https://orcid.org/0000-0002-6411-5670","affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Wisconsin, Madison, WI, USA","institution_ids":["https://openalex.org/I135310074"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5087902603","display_name":"Manlio Valenti","orcid":"https://orcid.org/0000-0003-0351-3058"},"institutions":[{"id":"https://openalex.org/I135310074","display_name":"University of Wisconsin\u2013Madison","ror":"https://ror.org/01y2jtd41","country_code":"US","type":"education","lineage":["https://openalex.org/I135310074"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Manlio Valenti","raw_affiliation_strings":["Department of Mathematics, University of Wisconsin, Madison, WI, USA"],"raw_orcid":"https://orcid.org/0000-0003-0351-3058","affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Wisconsin, Madison, WI, USA","institution_ids":["https://openalex.org/I135310074"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5087902603"],"corresponding_institution_ids":["https://openalex.org/I135310074"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.48848485,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"14","issue":"2","first_page":"73","last_page":"94"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10884","display_name":"Holomorphic and Operator Theory","score":0.427700012922287,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10884","display_name":"Holomorphic and Operator Theory","score":0.427700012922287,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10899","display_name":"Advanced Operator Algebra Research","score":0.12409999966621399,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11545","display_name":"Advanced Banach Space Theory","score":0.0835999995470047,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/jump","display_name":"Jump","score":0.6992999911308289},{"id":"https://openalex.org/keywords/operator","display_name":"Operator (biology)","score":0.597100019454956},{"id":"https://openalex.org/keywords/injective-function","display_name":"Injective function","score":0.5228999853134155},{"id":"https://openalex.org/keywords/endomorphism","display_name":"Endomorphism","score":0.45590001344680786},{"id":"https://openalex.org/keywords/lattice","display_name":"Lattice (music)","score":0.41449999809265137},{"id":"https://openalex.org/keywords/shift-operator","display_name":"Shift operator","score":0.37860000133514404}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8812999725341797},{"id":"https://openalex.org/C2780695682","wikidata":"https://www.wikidata.org/wiki/Q4005959","display_name":"Jump","level":2,"score":0.6992999911308289},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.597100019454956},{"id":"https://openalex.org/C128107574","wikidata":"https://www.wikidata.org/wiki/Q182003","display_name":"Injective function","level":2,"score":0.5228999853134155},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.49889999628067017},{"id":"https://openalex.org/C116858840","wikidata":"https://www.wikidata.org/wiki/Q1340800","display_name":"Endomorphism","level":2,"score":0.45590001344680786},{"id":"https://openalex.org/C2781204021","wikidata":"https://www.wikidata.org/wiki/Q6497091","display_name":"Lattice (music)","level":2,"score":0.41449999809265137},{"id":"https://openalex.org/C65630602","wikidata":"https://www.wikidata.org/wiki/Q2278680","display_name":"Shift operator","level":4,"score":0.37860000133514404},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.3758000135421753},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3594000041484833},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.32260000705718994},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.3156999945640564},{"id":"https://openalex.org/C24250787","wikidata":"https://www.wikidata.org/wiki/Q7269510","display_name":"Quasinormal operator","level":4,"score":0.26330000162124634},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.26019999384880066},{"id":"https://openalex.org/C191413488","wikidata":"https://www.wikidata.org/wiki/Q1892554","display_name":"Operator algebra","level":2,"score":0.2502000033855438}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1177/22113568241309768","is_oa":false,"landing_page_url":"https://doi.org/10.1177/22113568241309768","pdf_url":null,"source":{"id":"https://openalex.org/S4210231662","display_name":"Computability","issn_l":"2211-3568","issn":["2211-3568","2211-3576"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310318577","host_organization_name":"IOS Press","host_organization_lineage":["https://openalex.org/P4310318577"],"host_organization_lineage_names":["IOS Press"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computability","raw_type":"journal-article"},{"id":"pmh:oai:air.uniud.it:11390/1326604","is_oa":false,"landing_page_url":"https://hdl.handle.net/11390/1326604","pdf_url":null,"source":{"id":"https://openalex.org/S4306401163","display_name":"Institutional Research Information System (University of Udine)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I129043915","host_organization_name":"University of Udine","host_organization_lineage":["https://openalex.org/I129043915"],"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":"info:eu-repo/semantics/article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G4922788685","display_name":null,"funder_award_id":"DMS-2053848","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G7892346488","display_name":null,"funder_award_id":"626304","funder_id":"https://openalex.org/F4320306164","funder_display_name":"Simons Foundation"},{"id":"https://openalex.org/G8454458828","display_name":null,"funder_award_id":"2022TECZJA","funder_id":"https://openalex.org/F4320331528","funder_display_name":"Ministero dell'Universit\u00e0 e della Ricerca"},{"id":"https://openalex.org/G8769963373","display_name":null,"funder_award_id":"2017NWTM8R","funder_id":"https://openalex.org/F4320331528","funder_display_name":"Ministero dell'Universit\u00e0 e della Ricerca"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320306164","display_name":"Simons Foundation","ror":"https://ror.org/01cmst727"},{"id":"https://openalex.org/F4320331528","display_name":"Ministero dell'Universit\u00e0 e della Ricerca","ror":null}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":15,"referenced_works":["https://openalex.org/W1559786600","https://openalex.org/W2018837422","https://openalex.org/W2044009111","https://openalex.org/W2070956093","https://openalex.org/W2082980239","https://openalex.org/W2114190286","https://openalex.org/W2204710697","https://openalex.org/W2407347945","https://openalex.org/W2736063278","https://openalex.org/W2982356607","https://openalex.org/W3041438237","https://openalex.org/W3105030062","https://openalex.org/W3195227553","https://openalex.org/W4205550270","https://openalex.org/W4401952113"],"related_works":[],"abstract_inverted_index":{"A":[0],"partial":[1,121],"order":[2],"<mml:math":[3,24,66,74],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[4,25,67,75],"display=\"inline\"":[5,26,68,76],"overflow=\"scroll\">":[6,27,69,77],"<mml:mo":[7,12,31],"stretchy=\"false\">(</mml:mo>":[8],"<mml:mi>P</mml:mi>":[9,30,33],"<mml:mo>,</mml:mo>":[10],"<mml:mo>\u2a7d</mml:mo>":[11],"stretchy=\"false\">)</mml:mo>":[13],"</mml:math>":[14,34,71,92],"admits":[15],"a":[16,22,100,132,152],"jump":[17,46,101,133,141,160,177],"operator":[18,102,119,154],"if":[19],"there":[20,63,99],"is":[21,36,59],"map":[23],"<mml:mi>j</mml:mi>":[28],"<mml:mo>:</mml:mo>":[29],"stretchy=\"false\">\u2192</mml:mo>":[32],"that":[35,73],"strictly":[37],"increasing":[38],"and":[39,62,112,178],"weakly":[40],"monotone.":[41],"Despite":[42],"its":[43,180],"name,":[44],"the":[45,48,96,104,128,139,149,166,175,187],"in":[47,103,146,186],"Weihrauch":[49,105,129,167,188],"lattice":[50],"fails":[51],"to":[52,127],"satisfy":[53],"both":[54],"of":[55,148,165,174],"these":[56],"properties:":[57],"it":[58],"not":[60],"degree-theoretic,":[61],"are":[64],"functions":[65,123],"<mml:mi>f</mml:mi>":[70,78,89],"such":[72],"<mml:msub>":[79],"<mml:mo>\u2261</mml:mo>":[80],"<mml:mrow>":[81,82],"<mml:mi":[83],"mathvariant=\"normal\">W</mml:mi>":[84],"</mml:mrow>":[85,86],"</mml:msub>":[87],"<mml:msup>":[88],"<mml:mo>\u2032</mml:mo>":[90],"</mml:msup>":[91],".":[93],"This":[94,135],"raises":[95],"question:":[97],"Is":[98],"lattice?":[106],"We":[107,169],"answer":[108],"this":[109],"question":[110],"positively":[111],"provide":[113],"an":[114,118,162],"explicit":[115],"definition":[116],"for":[117],"on":[120,155,182],"multi-valued":[122],"that,":[124],"when":[125],"lifted":[126],"degrees,":[130],"induces":[131,161],"operator.":[134],"new":[136],"operator,":[137],"called":[138],"totalizing":[140,159,176],",":[142],"can":[143],"be":[144],"characterized":[145],"terms":[147],"total":[150],"continuation,":[151],"well-known":[153],"computational":[156],"problems.":[157],"The":[158],"injective":[163],"endomorphism":[164],"degrees.":[168],"study":[170],"some":[171,183],"algebraic":[172],"properties":[173],"characterize":[179],"behavior":[181],"pivotal":[184],"problems":[185],"lattice.":[189]},"counts_by_year":[],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-12-10T00:00:00"}
