{"id":"https://openalex.org/W7225707580","doi":"https://doi.org/10.66977/xsci.2611.001e","title":"The Shamanskii Frontier: Sharp Order Barriers and Dimensional Saturation","display_name":"The Shamanskii Frontier: Sharp Order Barriers and Dimensional Saturation","publication_year":2026,"publication_date":"2026-11-11","ids":{"openalex":"https://openalex.org/W7225707580","doi":"https://doi.org/10.66977/xsci.2611.001e"},"language":"en","primary_location":{"id":"doi:10.66977/xsci.2611.001e","doi":"https://doi.org/10.66977/xsci.2611.001e","is_oa":false,"landing_page_url":"https://doi.org/10.66977/xsci.2611.001e","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"posted-content"},"volume":null,"type":"preprint","is_traditional":true,"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/A5161369180","display_name":"Rodrigo Alberto Castro Mar\u00edn","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Rodrigo Alberto Castro Mar\u00edn","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5161369180"],"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/T12661","display_name":"Iterative Methods for Nonlinear Equations","score":0.9980000257492065,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"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/T12661","display_name":"Iterative Methods for Nonlinear Equations","score":0.9980000257492065,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"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/T10792","display_name":"Matrix Theory and Algorithms","score":0.0008999999845400453,"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/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.0006000000284984708,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[],"concepts":[{"id":"https://openalex.org/C200106649","wikidata":"https://www.wikidata.org/wiki/Q223683","display_name":"Transpose","level":3,"score":0.6898999810218811},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6840999722480774},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.5705000162124634},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.5281000137329102},{"id":"https://openalex.org/C185798385","wikidata":"https://www.wikidata.org/wiki/Q1161707","display_name":"Benchmark (surveying)","level":2,"score":0.5056999921798706},{"id":"https://openalex.org/C97137487","wikidata":"https://www.wikidata.org/wiki/Q729138","display_name":"Integer (computer science)","level":2,"score":0.48660001158714294},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4611999988555908},{"id":"https://openalex.org/C207467116","wikidata":"https://www.wikidata.org/wiki/Q4385666","display_name":"Inverse","level":2,"score":0.44620001316070557},{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.4242999851703644},{"id":"https://openalex.org/C165064840","wikidata":"https://www.wikidata.org/wiki/Q1321061","display_name":"Matching (statistics)","level":2,"score":0.3930000066757202},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.38019999861717224},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.3750999867916107},{"id":"https://openalex.org/C57691317","wikidata":"https://www.wikidata.org/wiki/Q1289248","display_name":"Scalar (mathematics)","level":2,"score":0.3456999957561493},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3456000089645386},{"id":"https://openalex.org/C57869625","wikidata":"https://www.wikidata.org/wiki/Q1783502","display_name":"Rate of convergence","level":3,"score":0.3431999981403351},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.322299987077713},{"id":"https://openalex.org/C164226766","wikidata":"https://www.wikidata.org/wiki/Q7293202","display_name":"Rank (graph theory)","level":2,"score":0.3156000077724457},{"id":"https://openalex.org/C72169020","wikidata":"https://www.wikidata.org/wiki/Q194404","display_name":"Monotonic function","level":2,"score":0.3133000135421753},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.3125},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.29679998755455017},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.2802000045776367},{"id":"https://openalex.org/C80469333","wikidata":"https://www.wikidata.org/wiki/Q189088","display_name":"Von Neumann architecture","level":2,"score":0.2655999958515167},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.26159998774528503},{"id":"https://openalex.org/C56086750","wikidata":"https://www.wikidata.org/wiki/Q6042592","display_name":"Integer programming","level":2,"score":0.2599000036716461},{"id":"https://openalex.org/C183115368","wikidata":"https://www.wikidata.org/wiki/Q856577","display_name":"Weighting","level":2,"score":0.25589999556541443},{"id":"https://openalex.org/C159694833","wikidata":"https://www.wikidata.org/wiki/Q2321565","display_name":"Iterative method","level":2,"score":0.25360000133514404}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.66977/xsci.2611.001e","doi":"https://doi.org/10.66977/xsci.2611.001e","is_oa":false,"landing_page_url":"https://doi.org/10.66977/xsci.2611.001e","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"posted-content"}],"best_oa_location":null,"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"Shamanskii\u2019s":[0],"frozen-Jacobian":[1],"method":[2,12],"is":[3,135,190],"a":[4,69,93,138,146,187,259,263],"natural":[5],"benchmark":[6,31],"for":[7,13,125,192,266],"assessing":[8],"whether":[9],"an":[10,50],"iterative":[11],"nonlinear":[14],"systems":[15],"gains":[16],"enough":[17],"local":[18],"convergence":[19],"order":[20,252],"to":[21,194],"justify":[22],"its":[23],"computational":[24],"cost.":[25],"We":[26,157,235],"call":[27],"the":[28,32,104,115,150,160,169,173,184,202,209,213,224,250,255,270,277],"corresponding":[29],"order\u2013cost":[30],"Shamanskii":[33,214,251,281],"frontier":[34],"and":[35,78,84,114,145,175,180,216,243],"ask":[36],"which":[37,63],"algorithmic":[38],"constructions":[39],"can":[40],"improve":[41],"on":[42],"it.":[43],"To":[44],"address":[45],"this":[46],"question,":[47],"we":[48,102,207],"study":[49],"explicitly":[51],"typed":[52],"operational":[53],"class":[54],"of":[55,87,95,162,171,227,239,280],"deterministic,":[56],"causal":[57],"methods":[58],"without":[59],"intercycle":[60],"memory":[61],"in":[62,212,269],"new":[64,99],"directions":[65],"are":[66,90],"obtained":[67],"from":[68,168],"single":[70],"frozen":[71],"inverse.":[72],"Arbitrary":[73],"adaptive":[74],"scalar":[75],"rules,":[76],"functional":[77],"differential":[79],"evaluations":[80],"along":[81],"accessible":[82],"directions,":[83],"exact":[85,154],"reuse":[86],"inverse":[88,100],"responses":[89],"permitted.":[91],"For":[92,201],"budget":[94],"s":[96,111],"<":[97],"n":[98],"queries,":[101],"prove":[103],"sharp":[105,188],"universal":[106,278],"local-order":[107],"bound":[108,134,253],"p":[109,129],"\u2264":[110],"+":[112],"1":[113],"dimensional":[116],"law":[117],"Smin(p,":[118],"n)":[119],"=":[120],"min{p":[121],"\u2212":[122],"1,":[123],"n}":[124],"every":[126],"integer":[127,210],"target":[128],"\u2265":[130],"2.":[131],"The":[132],"lower":[133],"established":[136,191],"by":[137],"fixed":[139,220],"quadratic":[140],"vector":[141,178],"field,":[142],"accessible-subspace":[143],"filtrations,":[144],"bounded":[147],"separating":[148],"functional;":[149],"matching":[151],"construction":[152],"uses":[153],"response":[155],"reconstruction.":[156],"also":[158],"determine":[159],"role":[161],"compatible":[163],"initial":[164],"information,":[165],"distinguish":[166],"rank":[167],"cost":[170,205,260],"preparing":[172],"data,":[174],"examine":[176],"external":[177],"resources":[179],"transpose":[181,199],"solves.":[182,200],"In":[183],"latter":[185],"setting,":[186],"result":[189],"up":[193],"three":[195],"total":[196],"direct":[197],"or":[198],"conventional":[203],"dense":[204],"normalization,":[206],"characterize":[208],"optimum":[211],"family":[215],"show":[217],"that,":[218],"with":[219,254],"normalized":[221],"elementary":[222],"costs,":[223],"optimal":[225],"number":[226],"corrections":[228,246],"satisfies":[229],"m\u2217(n)":[230],"\u223c":[231],"n/(3":[232],"log":[233],"n).":[234],"then":[236],"identify":[237],"classes":[238],"extrapolation,":[240],"derivative-assisted,":[241],"defect-polynomial,":[242],"learned":[244],"low-rank":[245],"that":[247],"cannot":[248],"exceed":[249],"same":[256],"inverse-query":[257],"budget;":[258],"comparison":[261],"gives":[262],"further":[264],"criterion":[265,275],"excluding":[267],"improvements":[268],"modeled":[271],"efficiency":[272],"index.":[273],"Neither":[274],"asserts":[276],"optimality":[279],"under":[282],"unrestricted":[283],"matrix":[284],"processing.":[285]},"counts_by_year":[],"updated_date":"2026-11-11T12:16:26.678958","created_date":"2026-11-11T00:00:00"}
