{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,30]],"date-time":"2026-04-30T02:53:05Z","timestamp":1777517585917,"version":"3.51.4"},"reference-count":18,"publisher":"SAGE Publications","issue":"2","license":[{"start":{"date-parts":[[2025,5,1]],"date-time":"2025-05-01T00:00:00Z","timestamp":1746057600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/journals.sagepub.com\/page\/policies\/text-and-data-mining-license"}],"funder":[{"DOI":"10.13039\/100000893","name":"Simons Foundation","doi-asserted-by":"publisher","award":["626304"],"award-info":[{"award-number":["626304"]}],"id":[{"id":"10.13039\/100000893","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100021856","name":"Ministero dell'Universit\u00e0 e della Ricerca","doi-asserted-by":"publisher","award":["2017NWTM8R"],"award-info":[{"award-number":["2017NWTM8R"]}],"id":[{"id":"10.13039\/501100021856","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100021856","name":"Ministero dell'Universit\u00e0 e della Ricerca","doi-asserted-by":"publisher","award":["2022TECZJA"],"award-info":[{"award-number":["2022TECZJA"]}],"id":[{"id":"10.13039\/501100021856","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","award":["DMS-2053848"],"award-info":[{"award-number":["DMS-2053848"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["journals.sagepub.com"],"crossmark-restriction":true},"short-container-title":["Computability"],"published-print":{"date-parts":[[2025,5]]},"abstract":"<jats:p>\n                    A partial order\n                    <jats:inline-formula>\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"inline\" overflow=\"scroll\">\n                        <mml:mo stretchy=\"false\">(<\/mml:mo>\n                        <mml:mi>P<\/mml:mi>\n                        <mml:mo>,<\/mml:mo>\n                        <mml:mo>\u2a7d<\/mml:mo>\n                        <mml:mo stretchy=\"false\">)<\/mml:mo>\n                      <\/mml:math>\n                    <\/jats:inline-formula>\n                    admits a jump operator if there is a map\n                    <jats:inline-formula>\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"inline\" overflow=\"scroll\">\n                        <mml:mi>j<\/mml:mi>\n                        <mml:mo>:<\/mml:mo>\n                        <mml:mi>P<\/mml:mi>\n                        <mml:mo stretchy=\"false\">\u2192<\/mml:mo>\n                        <mml:mi>P<\/mml:mi>\n                      <\/mml:math>\n                    <\/jats:inline-formula>\n                    that is strictly increasing and weakly monotone. Despite its name, the jump in the Weihrauch lattice fails to satisfy both of these properties: it is not degree-theoretic, and there are functions\n                    <jats:inline-formula>\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"inline\" overflow=\"scroll\">\n                        <mml:mi>f<\/mml:mi>\n                      <\/mml:math>\n                    <\/jats:inline-formula>\n                    such that\n                    <jats:inline-formula>\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"inline\" overflow=\"scroll\">\n                        <mml:mi>f<\/mml:mi>\n                        <mml:msub>\n                          <mml:mo>\u2261<\/mml:mo>\n                          <mml:mrow>\n                            <mml:mrow>\n                              <mml:mi mathvariant=\"normal\">W<\/mml:mi>\n                            <\/mml:mrow>\n                          <\/mml:mrow>\n                        <\/mml:msub>\n                        <mml:msup>\n                          <mml:mi>f<\/mml:mi>\n                          <mml:mo>\u2032<\/mml:mo>\n                        <\/mml:msup>\n                      <\/mml:math>\n                    <\/jats:inline-formula>\n                    . This raises the question: Is there a jump operator in the Weihrauch lattice? We answer this question positively and provide an explicit definition for an operator on partial multi-valued functions that, when lifted to the Weihrauch degrees, induces a jump operator. This new operator, called the\n                    <jats:italic toggle=\"yes\">totalizing jump<\/jats:italic>\n                    , can be characterized in terms of the total continuation, a well-known operator on computational problems. The totalizing jump induces an injective endomorphism of the Weihrauch degrees. We study some algebraic properties of the totalizing jump and characterize its behavior on some pivotal problems in the Weihrauch lattice.\n                  <\/jats:p>","DOI":"10.1177\/22113568241309768","type":"journal-article","created":{"date-parts":[[2025,12,10]],"date-time":"2025-12-10T10:47:59Z","timestamp":1765363679000},"page":"73-94","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":1,"title":["A jump operator on the Weihrauch degrees"],"prefix":"10.1177","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-4653-7458","authenticated-orcid":false,"given":"Uri","family":"Andrews","sequence":"first","affiliation":[{"name":"Department of Mathematics, University of Wisconsin, Madison, WI, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2958-4017","authenticated-orcid":false,"given":"Steffen","family":"Lempp","sequence":"additional","affiliation":[{"name":"Department of Mathematics, University of Wisconsin, Madison, WI, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8356-0086","authenticated-orcid":false,"given":"Alberto","family":"Marcone","sequence":"additional","affiliation":[{"name":"Dipartimento di Scienze Matematiche, Informatiche e Fisiche, University of Udine, Italy"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6411-5670","authenticated-orcid":false,"given":"Joseph S","family":"Miller","sequence":"additional","affiliation":[{"name":"Department of Mathematics, University of Wisconsin, Madison, WI, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0351-3058","authenticated-orcid":false,"given":"Manlio","family":"Valenti","sequence":"additional","affiliation":[{"name":"Department of Mathematics, University of Wisconsin, Madison, WI, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"179","published-online":{"date-parts":[[2025,12,10]]},"reference":[{"key":"e_1_3_4_2_2","doi-asserted-by":"crossref","unstructured":"Brattka V Gherardi G Pauly A. Weihrauch complexity in computable analysis. In: Brattka V and Hertling P (eds) Handbook of computability and complexity in analysis. Cham: Springer International Publishing 2021 pp.367\u2013417.","DOI":"10.1007\/978-3-030-59234-9_11"},{"key":"e_1_3_4_3_2","doi-asserted-by":"publisher","DOI":"10.2307\/2274700"},{"key":"e_1_3_4_4_2","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511750779"},{"key":"e_1_3_4_5_2","doi-asserted-by":"publisher","DOI":"10.2178\/jsl\/1058448451"},{"key":"e_1_3_4_6_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.apal.2011.10.006"},{"key":"e_1_3_4_7_2","first-page":"1","article-title":"On the algebraic structure of Weihrauch degrees","volume":"14","author":"Brattka V","year":"2018","unstructured":"Brattka V, Pauly A. On the algebraic structure of Weihrauch degrees. 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